https:///escher/api.php?action=feedcontributions&user=Huling&feedformat=atomEscherMath - User contributions [en]2021-02-25T14:30:49ZUser contributionsMediaWiki 1.34.1EscherMath:Resources2017-03-07T15:34:59Z<p>Huling: </p>
<hr />
<div>===Use This Book===<br />
Math & the Art of M.C. Escher is intended as a freely available online textbook for anyone to use (see the [[EscherMath:Copyrights|Copyrights]] page for details).<br />
<br />
Hello?<br />
<br />
===Get An Account===<br />
If you are an instructor teaching a course entirely or partly from this book, you should request an account on the wiki.<br />
<br />
Write to [[User:Bryan|Bryan]] or [[User:Barta|Anneke]] and please request a specific username.<br />
<br />
Getting an account will allow you to view instructor-only pages, and allow you to edit the wiki!<br />
<br />
<br />
===Teaching Math & Escher===<br />
* [[General Philosophy behind the course]]<br />
* [[Elementary Education (K-8)]] NCTM standards and some resources.<br />
* [[Secondary Education (9-12)]] NCTM standards and some resources.<br />
<br />
* In the Summer of 2008, Anneke and Bryan hosted an MAA online workshop [http://math.slu.edu/prep08 Geometry and Art]. The workshop has extensive discussions of how we teach this material. Additionally, there is [http://math.slu.edu/prep08/index.php/Participant_Contributions new curricular material] developed during the workshop, some of which may eventually move into this book, but all of which is good fodder for teaching ideas.<br />
<br />
===Instructors Notes===<br />
* Most instructors notes are on the 'Discussion' page associated to each page of content.<br />
* [[:Category:Solutions|Solutions to Exercises]] As well as solutions to a selected number of explorations.<br />
* [[Symmetric Art Project Grading Rubric]]<br />
* [[Tessellation Art Project Grading Rubric]], [[Tessellation Art Project Lite Grading Rubric]]<br />
* [[Art and Mathematics Project Grading Rubric]]<br />
<br />
===References===<br />
Many pages cite particular references, which will appear at the foot of the page. Also, there is a page of [[References]].<br />
<br />
===Other Math and Art Courses===<br />
* [http://mathserver.neu.edu/~eigen/MTH1220.html Man and Art], Stanley Eigen, Northeastern University. Also on this site [[Course:NU_MATH_1220:_Math_and_Art_-_Spring_2017_-_Stanley_Eigen|NU_MATH_1220:_Math_and_Art_-_Spring_2017_-_Stanley_Eigen]]<br />
* [http://mathofart.blogspot.com The Mathematics of Art] blog from Simpson College<br />
* [http://mathserver.neu.edu/~eigen/MTH1220.html Math and Art] Course at Northeastern University<br />
<br />
===Past SLU course pages===<br />
* [[Course:SLU MATH 1240: Math and Escher - Fall 2015 - Dr. Anneke Bart|SLU MATH 1240: Math and Escher - Fall 2015 - Dr. Anneke Bart]]<br />
* [[Course:SLU MATH 1240: Math and Escher - Fall 2015 - Dr. Bryan Clair|SLU MATH 1240: Math and Escher - Fall 2015 - Dr. Bryan Clair]]<br />
* [[Course:SLU MATH 124: Math and Escher - Fall 2014 - Dr. Bryan Clair|SLU MATH 124: Math and Escher - Fall 2014 - Dr. Bryan Clair]]<br />
* [[Course:SLU MATH 124: Math and Escher - Fall 2013 - Dr. Kim Druschel|SLU MATH 124: Math and Escher - Fall 2013 - Dr. Kim Druschel]]<br />
* [[Course:SLU MATH 124: Math and Escher - Fall 2013 - Dr. Bryan Clair|SLU MATH 124: Math and Escher - Fall 2013 - Dr. Bryan Clair]]<br />
* [[Course:SLU MATH 124: Math and Escher - Fall 2012 - Dr. Anneke Bart|SLU MATH 124: Math and Escher - Fall 2012 - Dr. Anneke Bart]]<br />
* [[Course:SLU MATH 124: Math and Escher - Fall 2012 - Dr. Kim Druschel|SLU MATH 124: Math and Escher - Fall 2012 - Dr. Kim Druschel]]<br />
* [[Course:SLU MATH 124: Math and Escher - Spring 2012 - Dr. Bryan Clair|SLU MATH 124: Math and Escher - Spring 2012 - Dr. Bryan Clair]]<br />
* [[Course:Minicourse MAA 2012|MAA Minicourse 2012]]<br />
* [[Course:SLU MATH 124: Math and Escher - Fall 2011 - Dr. Bryan Clair|SLU MATH 124: Math and Escher - Fall 2011 - Dr. Bryan Clair]]<br />
* [[Course:SLU MATH 124: Math and Escher - Spring 2011 - Dr. Anneke Bart|SLU MATH 124: Math and Escher - Spring 2011 - Dr. Anneke Bart]]<br />
* [[Course:SLU MATH 124: Math and Escher - Fall 2010 - Dr. Bryan Clair|SLU MATH 124: Math and Escher - Fall 2010 - Dr. Bryan Clair]]<br />
* [[Course:SLU MATH 124: Math and Escher - Fall 2009 - Dr. Anneke Bart|SLU MATH 124: Math and Escher - Fall 2009 - Dr. Anneke Bart]]<br />
* [[Course:SLU_MATH_124:_Math_and_Escher_-_Fall_2009_-_Philip_Huling|SLU MATH 124: Math and Escher - Fall_2009 - Dr. Philip Huling]]<br />
* [[Course:SLU MATH 124: Math and Escher - Spring 2009 - Dr. Bryan Clair| SLU MATH 124: Math and Escher - Spring 2009 - Dr. Bryan Clair]]<br />
* [[Course:SLU MATH 124: Math and Escher - Fall 2008 - Dr. Anneke Bart|SLU MATH 124: Math and Escher - Fall 2008 - Dr. Anneke Bart]]<br />
* [[Course:SLU MATH 124: Math and Escher - Fall 2008 - Dr. Steve Harris|SLU MATH 124: Math and Escher - Fall 2008 - Dr. Steve Harris]]<br />
* [[Course:SLU MATH 124: Math and Escher - Spring 2008 - Dr. Bryan Clair|SLU MATH 124: Math and Escher - Spring 2008 - Dr. Bryan Clair]]<br />
* [[Course:SLU MATH 124: Math and Escher - Fall 2007 - Dr. Anneke Bart|SLU MATH 124: Math and Escher - Fall 2007 - Dr. Anneke Bart]]<br />
* [[Course: SLU MATH 124: Math and Escher - Fall 2007 - Dr. Steve Harris| SLU MATH 124: Math and Escher - Fall 2007 - Dr. Steve Harris]]</div>HulingTalk:Wallpaper Exploration2011-06-20T20:02:54Z<p>Huling: Created page with "Link 2 appears to be broken"</p>
<hr />
<div>Link 2 appears to be broken</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-12-03T15:01:32Z<p>Huling: /* Week 15: Fourth Dimension and Topology */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
* Wednesday: [[Hyperbolic Escher Exploration]]<br />
<br />
* Friday: [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: Fourth Dimension and Topology===<br />
November 29 - December 3<br />
<br />
* Monday: [[Flatland Exploration]] and discussion<br />
<br />
* Wednesday: [[Dimensions Exploration]] and Hypercube Discussion<br />
<br />
* Friday: [[Fractals]] Discussion and Review<br />
<br />
''Extra Credit:'' Read ([http://web.archive.org/web/20080115153446/http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html And he built a crooked house… ], Short story by Robert A. Heinlein) and write a two page "book report" on it. Submit it Monday.<br />
<br />
===Week 16: Exam 2===<br />
* Monday: '''Exam 2''' See [[Exam 2 Outline]] for information</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-12-03T15:00:34Z<p>Huling: /* Week 15: Fourth Dimension and Topology */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
* Wednesday: [[Hyperbolic Escher Exploration]]<br />
<br />
* Friday: [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: Fourth Dimension and Topology===<br />
November 29 - December 3<br />
<br />
* Monday: [[Flatland Exploration]] and discussion<br />
<br />
* Wednesday: [[Dimensions Exploration]] and Hypercube Discussion<br />
<br />
* Friday: Fractal Discussion and Review<br />
<br />
''Extra Credit:'' Read ([http://web.archive.org/web/20080115153446/http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html And he built a crooked house… ], Short story by Robert A. Heinlein) and write a two page "book report" on it. Submit it Monday.<br />
<br />
===Week 16: Exam 2===<br />
* Monday: '''Exam 2''' See [[Exam 2 Outline]] for information</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-12-01T15:45:19Z<p>Huling: /* Week 15: Fourth Dimension and Topology */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
* Wednesday: [[Hyperbolic Escher Exploration]]<br />
<br />
* Friday: [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: Fourth Dimension and Topology===<br />
November 29 - December 3<br />
<br />
* Monday: [[Flatland Exploration]] and discussion<br />
<br />
* Wednesday: [[Dimensions Exploration]] and Hypercube Discussion<br />
<br />
''Extra Credit:'' Read ([http://web.archive.org/web/20080115153446/http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html And he built a crooked house… ], Short story by Robert A. Heinlein) and write a two page "book report" on it. Submit it Monday.<br />
<br />
===Week 16: Exam 2===<br />
* Monday: '''Exam 2''' See [[Exam 2 Outline]] for information</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-12-01T15:41:24Z<p>Huling: /* =Week 16: Exam 2 */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
* Wednesday: [[Hyperbolic Escher Exploration]]<br />
<br />
* Friday: [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: Fourth Dimension and Topology===<br />
November 29 - December 3<br />
<br />
* Monday: [[Flatland Exploration]] and discussion<br />
<br />
* Wednesday: [[Dimensions Exploration]] and Hypercube Discussion<br />
<br />
''Extra Credit:'' Read ([http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html And he built a crooked house… ], Short story by Robert A. Heinlein) and write a two page "book report" on it. Submit it Monday.<br />
<br />
===Week 16: Exam 2===<br />
* Monday: '''Exam 2''' See [[Exam 2 Outline]] for information</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-12-01T15:41:13Z<p>Huling: /* Week 16: Exam 2 */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
* Wednesday: [[Hyperbolic Escher Exploration]]<br />
<br />
* Friday: [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: Fourth Dimension and Topology===<br />
November 29 - December 3<br />
<br />
* Monday: [[Flatland Exploration]] and discussion<br />
<br />
* Wednesday: [[Dimensions Exploration]] and Hypercube Discussion<br />
<br />
''Extra Credit:'' Read ([http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html And he built a crooked house… ], Short story by Robert A. Heinlein) and write a two page "book report" on it. Submit it Monday.<br />
<br />
===Week 16: Exam 2==<br />
* Monday: '''Exam 2''' See [[Exam 2 Outline]] for information</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2009 - Dr. Anneke Bart2010-12-01T15:40:47Z<p>Huling: /* Week 16: Review for Final */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 in RH 316<br />
*'''Instructor:'''<br />
** Anneke Bart (http://math.slu.edu/~bart)<br />
** Office: Ritter Hall 115<br />
** Office Hours: MW 1-2 and Tue 9-10 or by appointment.<br />
** Email: barta@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance''' is required. You will have in-class work to be done in groups.<br />
One unexcused absence is allowed. Six absences will cause you to lose two letter grades.<br />
I only excuse absences when presented with official documentation. Being late twice or leaving early counts as an absence.<br />
</li><br />
<li><br />
'''Homework''' will be due weekly. Your work should be <br />
neat, legible, and stapled. Cooperation is good, but write up results separately. <br />
Late homework is always accepted, but I will not write comments and will <br />
automatically give a score of 5 (out of 10) if the work is of reasonable quality. <br />
</li><br />
<li>'''Exams'''. I give makeup exams only for severe and documented reasons.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>'''Final: Monday December 14. Time: 8:00 - 9:50. Place: RH 316''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Exams: two @15% each</li><br />
<li>Homework and in-class work: 20%</li><br />
<li>Tessellation Project: 10% </li><br />
<li>Cathedral Poster Assignment: 10% </li><br />
<li>Final: 30% (the final is comprehensive)</li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Homework Assignments==<br />
'''On Friday August 28, Homework #1 is due:'''<br />
Read {{VOS}} pg. 1-15.<br><br />
Read [[M.C. Escher]] and [[Introduction_to_Symmetry]].<br><br />
Do [[Rosette Exercises]] # 1-5, 8-12, 14<br />
(Extension given)<br />
<br />
<br />
'''Due Wednesday, September 9: Homework #2''' <br><br />
Read Visions of Symmetry pg. 15-31. <br><br />
Read [[Frieze Patterns]].<br><br />
Do [[Frieze Exercises]] # 1-9<br />
<br />
'''Homework #3: Due Wednesday September 23, 2009''' <br><br />
[[Image:Homework3-wallpaper.pdf | Homework handout]] Available for download.<br />
<br />
'''Homework #4: Due Monday September 28'''<br><br />
* Create 2 interesting tessellations using the techniques described on the page. Use two different techniques, and do not just copy what is used as an example on the page. The tessellation should show recognizable figures: plants, animals, objects, etc.<br />
* Give a short 1 paragraph description of how you made each of the tessellations.<br />
* Identify the Symmetry Group.<br />
<br />
'''Cathedral Basilica Project: Due Friday October 23.''' <br><br />
for details see: [[Cathedral Basilica Field Trip and Poster Assignment]]<br />
<br />
'''Tessellation Project: Due Monday November 3.''' <br><br />
for details see: [[Tessellation Project Fall 2009 - Bart]]<br />
<br />
'''Spherical Geometry: Homework Part I'''<br><br />
Due Wednesday November 4. Download pdf here: [[Image:SphericalHW-P1.pdf]]<br><br />
Note that the handout gives the due date as being Monday. This was extended to Wednesday.<br />
<br />
'''Spherical Geometry: Homework Part II'''<br><br />
Due Monday November 9. Download pdf here: [[Image:Spherical Geometry Homework2.pdf]]<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 24 - 28<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]]<br />
<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 31 - September 4<br />
<br />
* Monday: Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]] and [[Frieze Names Exploration]]<br />
* Wednesday: Quiz and start on new homework.<br />
* Friday: Do [[Identifying Frieze Patterns Exploration]]<br />
<br />
<br />
(Fri September 4 Last day to drop without a "W")<br />
<br />
===Week 3: Wallpaper Patterns===<br />
September 7 - 11<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
* Wednesday: An introduction to wallpaper patterns [[Tessellations, a first look Exploration]]<br />
* Friday: Went over border patterns and discussed some problems from homework 2.<br />
<br />
Some points to remember: <br><br />
* Start homework early, so you have time to ask questions.<br />
* Anything on homework or explorations can show up on an exam.<br />
* Always explain your answer. You will need to explain yourself on any exam to get full credit, but apart from that it is a good idea to explain how you arrived at your conclusions. It will be easier to assign partial credit if more information is given, and it will also be easier for the instructor to give feedback in case there is some confusion.<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 14 - 18<br />
<br />
* Monday: Lecture on Wallpaper Patterns.<br />
* Wednesday: A short [[Tiling Worksheet]] to think about how to draw different tessellations. And we will start on [[Wallpaper Symmetry Exploration]]<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 21 - 25<br />
<br />
* Monday: Short lecture about some terminology we need. Do [[Tessellation Exploration: The Basics]]<br />
* Wednesday: Do [[Angles of Polygons and Regular Tessellations Exploration]]<br />
* Friday: Short introduction to Tessellations by Recognizable figures, and do [[Escher-Like Tessellations Explorations]]<br />
<br />
===Week 6: Escher-like Tessellations and Geometer Sketchpad===<br />
September 28 - October 2<br />
<br />
<br />
* Your assignment for this week is to do the following three Geometer Sketchpad Explorations at your own pace. The first part of the Introductions to GSP Exploration is heavily based on and inspired by materials developed by Mike Riedy. <br />
* [[GSP Introduction Exploration]]<br />
* [[GSP Quadrilateral Tessellation Exploration]] <br />
<br />
* Friday we start on [[Sketches for the Art Project Exploration]]. The precise assignment will be given later. This exploration will help you create a collection of sketches to choose your final art project from.<br />
<br />
<br />
* '''Exam 1 is scheduled for Monday October 5'''<br />
** [[Course:Study Guide - Exam 1 - Bart-Fall09|Study Guide - Exam 1 - Bart-Fall09]]<br />
<br />
===Week 7: Exam I, Field Trip and Intro to Spherical Geometry===<br />
October 5 - 9<br />
<br />
* Monday: Exam I<br />
* Wednesday: Discuss the field trip to the Basilica. Create teams of two or three people. Introduction to Spherical Geometry<br />
* Friday: [[Cathedral Basilica Field Trip and Poster Assignment]]<br />
<br />
===Week 8: Art Project Assignment and intro to Spherical Geometry===<br />
October 12 - 16<br />
<br />
''(October 12-17 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
* Monday: [[Spherical Easel Exploration]]<br />
* Wednesday: Bring your photographs so you can upload them to the website. [[PBWorks Assignment]]<br />
<br />
===Week 9: Spherical Geometry===<br />
October 19 - 23<br />
* '''Monday: Fall Break'''<br />
* Wednesday: [[The Axioms of Spherical Geometry Exploration]]<br />
* Friday: discuss the A = .5 (base)(height) formula on the sphere. Allow for finishing the Axiom of Spherical geometry Exploration. Do [[Spherical Geometry Exploration]] problems 1-8 and 10.<br />
<br />
===Week 10: Spherical Geometry===<br />
October 26 - 30<br />
<br />
* Monday: [[Spherical Geometry Exploration]]<br />
* [[Spherical Geometry: Polygons]]<br />
* Spherical Homework Part 1; Due Wednesday Nov 4, 2009<br />
* Spherical Homework Part 2; Due Monday Nov 9, 2009<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 2 - 6<br />
<br />
* [[Spherical Triangles Exploration]]<br />
* We went over [[Spherical versus Euclidean Polygons Exploration]] and looked at the different definitions from Euclidean geometry and compared them to the definitions we (could) use in spherical geometry.<br />
* We looked at Kaleidotile in class. We found regular and semi-regular tessellations on the sphere. There are 5 regular tessellations on the sphere (as opposed to 3 in the plane), and we found at least 10 semi-regular tessellations (as opposed to only 8 in the plane).<br />
* We did the [[Platonic Solids Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 9 - 13<br />
<br />
* Introduction to Hyperbolic Geometry<br />
* Monday: Do [[Escher's Circle Limit Exploration]]<br />
* Wednesday: [[Hyperbolic Geometry Exploration]] and the Jos Leys Hyperbolic Geometry Exploration<br />
* Friday: Started on Spherical Geometry Homework part 3, due Monday.<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 16 - 20<br />
<br />
During this week we worked on a variety of explorations:<br />
* [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
* [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
And we worked on the homework.<br />
<br />
===Week 14: Hyperbolic Geometry===<br />
November 23 - 27<br />
<br />
* Monday:<br />
* '''Wednesday: Thanksgiving: Official University Holiday'''<br />
* '''Friday: Thanksgiving: Official University Holiday'''<br />
<br />
===Week 15: Depth, Perspective and Impossible Figures===<br />
November 30 - December 4<br />
* Monday: Discussed the exam on Friday. Talked about the concepts of [[Depth and Perspective]]. We did the [[Depth Exploration]]<br />
* Wednesday: Time for some questions about the exam. Followed by the [[Impossible Figures and Escher Exploration]]<br />
* Friday: Exam II See [[Exam 2 Outline]] for more detail.<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-12-01T15:38:34Z<p>Huling: /* Week 16: Exam 2 */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
* Wednesday: [[Hyperbolic Escher Exploration]]<br />
<br />
* Friday: [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: Fourth Dimension and Topology===<br />
November 29 - December 3<br />
<br />
* Monday: [[Flatland Exploration]] and discussion<br />
<br />
* Wednesday: [[Dimensions Exploration]] and Hypercube Discussion<br />
<br />
''Extra Credit:'' Read ([http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html And he built a crooked house… ], Short story by Robert A. Heinlein) and write a two page "book report" on it. Submit it Monday.<br />
<br />
===Week 16: Exam 2===<br />
* Monday December 7: '''Exam 2''' See [[Exam 2 Outline]] for information</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2009 - Dr. Anneke Bart2010-12-01T15:37:50Z<p>Huling: /* Week 16: Exam 2 */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 in RH 316<br />
*'''Instructor:'''<br />
** Anneke Bart (http://math.slu.edu/~bart)<br />
** Office: Ritter Hall 115<br />
** Office Hours: MW 1-2 and Tue 9-10 or by appointment.<br />
** Email: barta@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance''' is required. You will have in-class work to be done in groups.<br />
One unexcused absence is allowed. Six absences will cause you to lose two letter grades.<br />
I only excuse absences when presented with official documentation. Being late twice or leaving early counts as an absence.<br />
</li><br />
<li><br />
'''Homework''' will be due weekly. Your work should be <br />
neat, legible, and stapled. Cooperation is good, but write up results separately. <br />
Late homework is always accepted, but I will not write comments and will <br />
automatically give a score of 5 (out of 10) if the work is of reasonable quality. <br />
</li><br />
<li>'''Exams'''. I give makeup exams only for severe and documented reasons.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>'''Final: Monday December 14. Time: 8:00 - 9:50. Place: RH 316''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Exams: two @15% each</li><br />
<li>Homework and in-class work: 20%</li><br />
<li>Tessellation Project: 10% </li><br />
<li>Cathedral Poster Assignment: 10% </li><br />
<li>Final: 30% (the final is comprehensive)</li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Homework Assignments==<br />
'''On Friday August 28, Homework #1 is due:'''<br />
Read {{VOS}} pg. 1-15.<br><br />
Read [[M.C. Escher]] and [[Introduction_to_Symmetry]].<br><br />
Do [[Rosette Exercises]] # 1-5, 8-12, 14<br />
(Extension given)<br />
<br />
<br />
'''Due Wednesday, September 9: Homework #2''' <br><br />
Read Visions of Symmetry pg. 15-31. <br><br />
Read [[Frieze Patterns]].<br><br />
Do [[Frieze Exercises]] # 1-9<br />
<br />
'''Homework #3: Due Wednesday September 23, 2009''' <br><br />
[[Image:Homework3-wallpaper.pdf | Homework handout]] Available for download.<br />
<br />
'''Homework #4: Due Monday September 28'''<br><br />
* Create 2 interesting tessellations using the techniques described on the page. Use two different techniques, and do not just copy what is used as an example on the page. The tessellation should show recognizable figures: plants, animals, objects, etc.<br />
* Give a short 1 paragraph description of how you made each of the tessellations.<br />
* Identify the Symmetry Group.<br />
<br />
'''Cathedral Basilica Project: Due Friday October 23.''' <br><br />
for details see: [[Cathedral Basilica Field Trip and Poster Assignment]]<br />
<br />
'''Tessellation Project: Due Monday November 3.''' <br><br />
for details see: [[Tessellation Project Fall 2009 - Bart]]<br />
<br />
'''Spherical Geometry: Homework Part I'''<br><br />
Due Wednesday November 4. Download pdf here: [[Image:SphericalHW-P1.pdf]]<br><br />
Note that the handout gives the due date as being Monday. This was extended to Wednesday.<br />
<br />
'''Spherical Geometry: Homework Part II'''<br><br />
Due Monday November 9. Download pdf here: [[Image:Spherical Geometry Homework2.pdf]]<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 24 - 28<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]]<br />
<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 31 - September 4<br />
<br />
* Monday: Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]] and [[Frieze Names Exploration]]<br />
* Wednesday: Quiz and start on new homework.<br />
* Friday: Do [[Identifying Frieze Patterns Exploration]]<br />
<br />
<br />
(Fri September 4 Last day to drop without a "W")<br />
<br />
===Week 3: Wallpaper Patterns===<br />
September 7 - 11<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
* Wednesday: An introduction to wallpaper patterns [[Tessellations, a first look Exploration]]<br />
* Friday: Went over border patterns and discussed some problems from homework 2.<br />
<br />
Some points to remember: <br><br />
* Start homework early, so you have time to ask questions.<br />
* Anything on homework or explorations can show up on an exam.<br />
* Always explain your answer. You will need to explain yourself on any exam to get full credit, but apart from that it is a good idea to explain how you arrived at your conclusions. It will be easier to assign partial credit if more information is given, and it will also be easier for the instructor to give feedback in case there is some confusion.<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 14 - 18<br />
<br />
* Monday: Lecture on Wallpaper Patterns.<br />
* Wednesday: A short [[Tiling Worksheet]] to think about how to draw different tessellations. And we will start on [[Wallpaper Symmetry Exploration]]<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 21 - 25<br />
<br />
* Monday: Short lecture about some terminology we need. Do [[Tessellation Exploration: The Basics]]<br />
* Wednesday: Do [[Angles of Polygons and Regular Tessellations Exploration]]<br />
* Friday: Short introduction to Tessellations by Recognizable figures, and do [[Escher-Like Tessellations Explorations]]<br />
<br />
===Week 6: Escher-like Tessellations and Geometer Sketchpad===<br />
September 28 - October 2<br />
<br />
<br />
* Your assignment for this week is to do the following three Geometer Sketchpad Explorations at your own pace. The first part of the Introductions to GSP Exploration is heavily based on and inspired by materials developed by Mike Riedy. <br />
* [[GSP Introduction Exploration]]<br />
* [[GSP Quadrilateral Tessellation Exploration]] <br />
<br />
* Friday we start on [[Sketches for the Art Project Exploration]]. The precise assignment will be given later. This exploration will help you create a collection of sketches to choose your final art project from.<br />
<br />
<br />
* '''Exam 1 is scheduled for Monday October 5'''<br />
** [[Course:Study Guide - Exam 1 - Bart-Fall09|Study Guide - Exam 1 - Bart-Fall09]]<br />
<br />
===Week 7: Exam I, Field Trip and Intro to Spherical Geometry===<br />
October 5 - 9<br />
<br />
* Monday: Exam I<br />
* Wednesday: Discuss the field trip to the Basilica. Create teams of two or three people. Introduction to Spherical Geometry<br />
* Friday: [[Cathedral Basilica Field Trip and Poster Assignment]]<br />
<br />
===Week 8: Art Project Assignment and intro to Spherical Geometry===<br />
October 12 - 16<br />
<br />
''(October 12-17 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
* Monday: [[Spherical Easel Exploration]]<br />
* Wednesday: Bring your photographs so you can upload them to the website. [[PBWorks Assignment]]<br />
<br />
===Week 9: Spherical Geometry===<br />
October 19 - 23<br />
* '''Monday: Fall Break'''<br />
* Wednesday: [[The Axioms of Spherical Geometry Exploration]]<br />
* Friday: discuss the A = .5 (base)(height) formula on the sphere. Allow for finishing the Axiom of Spherical geometry Exploration. Do [[Spherical Geometry Exploration]] problems 1-8 and 10.<br />
<br />
===Week 10: Spherical Geometry===<br />
October 26 - 30<br />
<br />
* Monday: [[Spherical Geometry Exploration]]<br />
* [[Spherical Geometry: Polygons]]<br />
* Spherical Homework Part 1; Due Wednesday Nov 4, 2009<br />
* Spherical Homework Part 2; Due Monday Nov 9, 2009<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 2 - 6<br />
<br />
* [[Spherical Triangles Exploration]]<br />
* We went over [[Spherical versus Euclidean Polygons Exploration]] and looked at the different definitions from Euclidean geometry and compared them to the definitions we (could) use in spherical geometry.<br />
* We looked at Kaleidotile in class. We found regular and semi-regular tessellations on the sphere. There are 5 regular tessellations on the sphere (as opposed to 3 in the plane), and we found at least 10 semi-regular tessellations (as opposed to only 8 in the plane).<br />
* We did the [[Platonic Solids Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 9 - 13<br />
<br />
* Introduction to Hyperbolic Geometry<br />
* Monday: Do [[Escher's Circle Limit Exploration]]<br />
* Wednesday: [[Hyperbolic Geometry Exploration]] and the Jos Leys Hyperbolic Geometry Exploration<br />
* Friday: Started on Spherical Geometry Homework part 3, due Monday.<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 16 - 20<br />
<br />
During this week we worked on a variety of explorations:<br />
* [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
* [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
And we worked on the homework.<br />
<br />
===Week 14: Hyperbolic Geometry===<br />
November 23 - 27<br />
<br />
* Monday:<br />
* '''Wednesday: Thanksgiving: Official University Holiday'''<br />
* '''Friday: Thanksgiving: Official University Holiday'''<br />
<br />
===Week 15: Depth, Perspective and Impossible Figures===<br />
November 30 - December 4<br />
* Monday: Discussed the exam on Friday. Talked about the concepts of [[Depth and Perspective]]. We did the [[Depth Exploration]]<br />
* Wednesday: Time for some questions about the exam. Followed by the [[Impossible Figures and Escher Exploration]]<br />
* Friday: Exam II See [[Exam 2 Outline]] for more detail.<br />
<br />
===Week 16: Exam 2===<br />
* Monday December 7: '''Exam 2''' See [[Exam 2 Outline]] for information</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2009 - Dr. Anneke Bart2010-12-01T15:37:33Z<p>Huling: /* Week 16: Exam 2 */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 in RH 316<br />
*'''Instructor:'''<br />
** Anneke Bart (http://math.slu.edu/~bart)<br />
** Office: Ritter Hall 115<br />
** Office Hours: MW 1-2 and Tue 9-10 or by appointment.<br />
** Email: barta@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance''' is required. You will have in-class work to be done in groups.<br />
One unexcused absence is allowed. Six absences will cause you to lose two letter grades.<br />
I only excuse absences when presented with official documentation. Being late twice or leaving early counts as an absence.<br />
</li><br />
<li><br />
'''Homework''' will be due weekly. Your work should be <br />
neat, legible, and stapled. Cooperation is good, but write up results separately. <br />
Late homework is always accepted, but I will not write comments and will <br />
automatically give a score of 5 (out of 10) if the work is of reasonable quality. <br />
</li><br />
<li>'''Exams'''. I give makeup exams only for severe and documented reasons.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>'''Final: Monday December 14. Time: 8:00 - 9:50. Place: RH 316''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Exams: two @15% each</li><br />
<li>Homework and in-class work: 20%</li><br />
<li>Tessellation Project: 10% </li><br />
<li>Cathedral Poster Assignment: 10% </li><br />
<li>Final: 30% (the final is comprehensive)</li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Homework Assignments==<br />
'''On Friday August 28, Homework #1 is due:'''<br />
Read {{VOS}} pg. 1-15.<br><br />
Read [[M.C. Escher]] and [[Introduction_to_Symmetry]].<br><br />
Do [[Rosette Exercises]] # 1-5, 8-12, 14<br />
(Extension given)<br />
<br />
<br />
'''Due Wednesday, September 9: Homework #2''' <br><br />
Read Visions of Symmetry pg. 15-31. <br><br />
Read [[Frieze Patterns]].<br><br />
Do [[Frieze Exercises]] # 1-9<br />
<br />
'''Homework #3: Due Wednesday September 23, 2009''' <br><br />
[[Image:Homework3-wallpaper.pdf | Homework handout]] Available for download.<br />
<br />
'''Homework #4: Due Monday September 28'''<br><br />
* Create 2 interesting tessellations using the techniques described on the page. Use two different techniques, and do not just copy what is used as an example on the page. The tessellation should show recognizable figures: plants, animals, objects, etc.<br />
* Give a short 1 paragraph description of how you made each of the tessellations.<br />
* Identify the Symmetry Group.<br />
<br />
'''Cathedral Basilica Project: Due Friday October 23.''' <br><br />
for details see: [[Cathedral Basilica Field Trip and Poster Assignment]]<br />
<br />
'''Tessellation Project: Due Monday November 3.''' <br><br />
for details see: [[Tessellation Project Fall 2009 - Bart]]<br />
<br />
'''Spherical Geometry: Homework Part I'''<br><br />
Due Wednesday November 4. Download pdf here: [[Image:SphericalHW-P1.pdf]]<br><br />
Note that the handout gives the due date as being Monday. This was extended to Wednesday.<br />
<br />
'''Spherical Geometry: Homework Part II'''<br><br />
Due Monday November 9. Download pdf here: [[Image:Spherical Geometry Homework2.pdf]]<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 24 - 28<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]]<br />
<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 31 - September 4<br />
<br />
* Monday: Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]] and [[Frieze Names Exploration]]<br />
* Wednesday: Quiz and start on new homework.<br />
* Friday: Do [[Identifying Frieze Patterns Exploration]]<br />
<br />
<br />
(Fri September 4 Last day to drop without a "W")<br />
<br />
===Week 3: Wallpaper Patterns===<br />
September 7 - 11<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
* Wednesday: An introduction to wallpaper patterns [[Tessellations, a first look Exploration]]<br />
* Friday: Went over border patterns and discussed some problems from homework 2.<br />
<br />
Some points to remember: <br><br />
* Start homework early, so you have time to ask questions.<br />
* Anything on homework or explorations can show up on an exam.<br />
* Always explain your answer. You will need to explain yourself on any exam to get full credit, but apart from that it is a good idea to explain how you arrived at your conclusions. It will be easier to assign partial credit if more information is given, and it will also be easier for the instructor to give feedback in case there is some confusion.<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 14 - 18<br />
<br />
* Monday: Lecture on Wallpaper Patterns.<br />
* Wednesday: A short [[Tiling Worksheet]] to think about how to draw different tessellations. And we will start on [[Wallpaper Symmetry Exploration]]<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 21 - 25<br />
<br />
* Monday: Short lecture about some terminology we need. Do [[Tessellation Exploration: The Basics]]<br />
* Wednesday: Do [[Angles of Polygons and Regular Tessellations Exploration]]<br />
* Friday: Short introduction to Tessellations by Recognizable figures, and do [[Escher-Like Tessellations Explorations]]<br />
<br />
===Week 6: Escher-like Tessellations and Geometer Sketchpad===<br />
September 28 - October 2<br />
<br />
<br />
* Your assignment for this week is to do the following three Geometer Sketchpad Explorations at your own pace. The first part of the Introductions to GSP Exploration is heavily based on and inspired by materials developed by Mike Riedy. <br />
* [[GSP Introduction Exploration]]<br />
* [[GSP Quadrilateral Tessellation Exploration]] <br />
<br />
* Friday we start on [[Sketches for the Art Project Exploration]]. The precise assignment will be given later. This exploration will help you create a collection of sketches to choose your final art project from.<br />
<br />
<br />
* '''Exam 1 is scheduled for Monday October 5'''<br />
** [[Course:Study Guide - Exam 1 - Bart-Fall09|Study Guide - Exam 1 - Bart-Fall09]]<br />
<br />
===Week 7: Exam I, Field Trip and Intro to Spherical Geometry===<br />
October 5 - 9<br />
<br />
* Monday: Exam I<br />
* Wednesday: Discuss the field trip to the Basilica. Create teams of two or three people. Introduction to Spherical Geometry<br />
* Friday: [[Cathedral Basilica Field Trip and Poster Assignment]]<br />
<br />
===Week 8: Art Project Assignment and intro to Spherical Geometry===<br />
October 12 - 16<br />
<br />
''(October 12-17 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
* Monday: [[Spherical Easel Exploration]]<br />
* Wednesday: Bring your photographs so you can upload them to the website. [[PBWorks Assignment]]<br />
<br />
===Week 9: Spherical Geometry===<br />
October 19 - 23<br />
* '''Monday: Fall Break'''<br />
* Wednesday: [[The Axioms of Spherical Geometry Exploration]]<br />
* Friday: discuss the A = .5 (base)(height) formula on the sphere. Allow for finishing the Axiom of Spherical geometry Exploration. Do [[Spherical Geometry Exploration]] problems 1-8 and 10.<br />
<br />
===Week 10: Spherical Geometry===<br />
October 26 - 30<br />
<br />
* Monday: [[Spherical Geometry Exploration]]<br />
* [[Spherical Geometry: Polygons]]<br />
* Spherical Homework Part 1; Due Wednesday Nov 4, 2009<br />
* Spherical Homework Part 2; Due Monday Nov 9, 2009<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 2 - 6<br />
<br />
* [[Spherical Triangles Exploration]]<br />
* We went over [[Spherical versus Euclidean Polygons Exploration]] and looked at the different definitions from Euclidean geometry and compared them to the definitions we (could) use in spherical geometry.<br />
* We looked at Kaleidotile in class. We found regular and semi-regular tessellations on the sphere. There are 5 regular tessellations on the sphere (as opposed to 3 in the plane), and we found at least 10 semi-regular tessellations (as opposed to only 8 in the plane).<br />
* We did the [[Platonic Solids Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 9 - 13<br />
<br />
* Introduction to Hyperbolic Geometry<br />
* Monday: Do [[Escher's Circle Limit Exploration]]<br />
* Wednesday: [[Hyperbolic Geometry Exploration]] and the Jos Leys Hyperbolic Geometry Exploration<br />
* Friday: Started on Spherical Geometry Homework part 3, due Monday.<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 16 - 20<br />
<br />
During this week we worked on a variety of explorations:<br />
* [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
* [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
And we worked on the homework.<br />
<br />
===Week 14: Hyperbolic Geometry===<br />
November 23 - 27<br />
<br />
* Monday:<br />
* '''Wednesday: Thanksgiving: Official University Holiday'''<br />
* '''Friday: Thanksgiving: Official University Holiday'''<br />
<br />
===Week 15: Depth, Perspective and Impossible Figures===<br />
November 30 - December 4<br />
* Monday: Discussed the exam on Friday. Talked about the concepts of [[Depth and Perspective]]. We did the [[Depth Exploration]]<br />
* Wednesday: Time for some questions about the exam. Followed by the [[Impossible Figures and Escher Exploration]]<br />
* Friday: Exam II See [[Exam 2 Outline]] for more detail.<br />
<br />
===Week 16: Exam 2===<br />
* Monday December 7: Exam 2. See [[Exam 2 Outline]] for information</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2009 - Dr. Anneke Bart2010-12-01T15:36:25Z<p>Huling: /* Week 16: Review for Final */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 in RH 316<br />
*'''Instructor:'''<br />
** Anneke Bart (http://math.slu.edu/~bart)<br />
** Office: Ritter Hall 115<br />
** Office Hours: MW 1-2 and Tue 9-10 or by appointment.<br />
** Email: barta@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance''' is required. You will have in-class work to be done in groups.<br />
One unexcused absence is allowed. Six absences will cause you to lose two letter grades.<br />
I only excuse absences when presented with official documentation. Being late twice or leaving early counts as an absence.<br />
</li><br />
<li><br />
'''Homework''' will be due weekly. Your work should be <br />
neat, legible, and stapled. Cooperation is good, but write up results separately. <br />
Late homework is always accepted, but I will not write comments and will <br />
automatically give a score of 5 (out of 10) if the work is of reasonable quality. <br />
</li><br />
<li>'''Exams'''. I give makeup exams only for severe and documented reasons.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>'''Final: Monday December 14. Time: 8:00 - 9:50. Place: RH 316''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Exams: two @15% each</li><br />
<li>Homework and in-class work: 20%</li><br />
<li>Tessellation Project: 10% </li><br />
<li>Cathedral Poster Assignment: 10% </li><br />
<li>Final: 30% (the final is comprehensive)</li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Homework Assignments==<br />
'''On Friday August 28, Homework #1 is due:'''<br />
Read {{VOS}} pg. 1-15.<br><br />
Read [[M.C. Escher]] and [[Introduction_to_Symmetry]].<br><br />
Do [[Rosette Exercises]] # 1-5, 8-12, 14<br />
(Extension given)<br />
<br />
<br />
'''Due Wednesday, September 9: Homework #2''' <br><br />
Read Visions of Symmetry pg. 15-31. <br><br />
Read [[Frieze Patterns]].<br><br />
Do [[Frieze Exercises]] # 1-9<br />
<br />
'''Homework #3: Due Wednesday September 23, 2009''' <br><br />
[[Image:Homework3-wallpaper.pdf | Homework handout]] Available for download.<br />
<br />
'''Homework #4: Due Monday September 28'''<br><br />
* Create 2 interesting tessellations using the techniques described on the page. Use two different techniques, and do not just copy what is used as an example on the page. The tessellation should show recognizable figures: plants, animals, objects, etc.<br />
* Give a short 1 paragraph description of how you made each of the tessellations.<br />
* Identify the Symmetry Group.<br />
<br />
'''Cathedral Basilica Project: Due Friday October 23.''' <br><br />
for details see: [[Cathedral Basilica Field Trip and Poster Assignment]]<br />
<br />
'''Tessellation Project: Due Monday November 3.''' <br><br />
for details see: [[Tessellation Project Fall 2009 - Bart]]<br />
<br />
'''Spherical Geometry: Homework Part I'''<br><br />
Due Wednesday November 4. Download pdf here: [[Image:SphericalHW-P1.pdf]]<br><br />
Note that the handout gives the due date as being Monday. This was extended to Wednesday.<br />
<br />
'''Spherical Geometry: Homework Part II'''<br><br />
Due Monday November 9. Download pdf here: [[Image:Spherical Geometry Homework2.pdf]]<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 24 - 28<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]]<br />
<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 31 - September 4<br />
<br />
* Monday: Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]] and [[Frieze Names Exploration]]<br />
* Wednesday: Quiz and start on new homework.<br />
* Friday: Do [[Identifying Frieze Patterns Exploration]]<br />
<br />
<br />
(Fri September 4 Last day to drop without a "W")<br />
<br />
===Week 3: Wallpaper Patterns===<br />
September 7 - 11<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
* Wednesday: An introduction to wallpaper patterns [[Tessellations, a first look Exploration]]<br />
* Friday: Went over border patterns and discussed some problems from homework 2.<br />
<br />
Some points to remember: <br><br />
* Start homework early, so you have time to ask questions.<br />
* Anything on homework or explorations can show up on an exam.<br />
* Always explain your answer. You will need to explain yourself on any exam to get full credit, but apart from that it is a good idea to explain how you arrived at your conclusions. It will be easier to assign partial credit if more information is given, and it will also be easier for the instructor to give feedback in case there is some confusion.<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 14 - 18<br />
<br />
* Monday: Lecture on Wallpaper Patterns.<br />
* Wednesday: A short [[Tiling Worksheet]] to think about how to draw different tessellations. And we will start on [[Wallpaper Symmetry Exploration]]<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 21 - 25<br />
<br />
* Monday: Short lecture about some terminology we need. Do [[Tessellation Exploration: The Basics]]<br />
* Wednesday: Do [[Angles of Polygons and Regular Tessellations Exploration]]<br />
* Friday: Short introduction to Tessellations by Recognizable figures, and do [[Escher-Like Tessellations Explorations]]<br />
<br />
===Week 6: Escher-like Tessellations and Geometer Sketchpad===<br />
September 28 - October 2<br />
<br />
<br />
* Your assignment for this week is to do the following three Geometer Sketchpad Explorations at your own pace. The first part of the Introductions to GSP Exploration is heavily based on and inspired by materials developed by Mike Riedy. <br />
* [[GSP Introduction Exploration]]<br />
* [[GSP Quadrilateral Tessellation Exploration]] <br />
<br />
* Friday we start on [[Sketches for the Art Project Exploration]]. The precise assignment will be given later. This exploration will help you create a collection of sketches to choose your final art project from.<br />
<br />
<br />
* '''Exam 1 is scheduled for Monday October 5'''<br />
** [[Course:Study Guide - Exam 1 - Bart-Fall09|Study Guide - Exam 1 - Bart-Fall09]]<br />
<br />
===Week 7: Exam I, Field Trip and Intro to Spherical Geometry===<br />
October 5 - 9<br />
<br />
* Monday: Exam I<br />
* Wednesday: Discuss the field trip to the Basilica. Create teams of two or three people. Introduction to Spherical Geometry<br />
* Friday: [[Cathedral Basilica Field Trip and Poster Assignment]]<br />
<br />
===Week 8: Art Project Assignment and intro to Spherical Geometry===<br />
October 12 - 16<br />
<br />
''(October 12-17 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
* Monday: [[Spherical Easel Exploration]]<br />
* Wednesday: Bring your photographs so you can upload them to the website. [[PBWorks Assignment]]<br />
<br />
===Week 9: Spherical Geometry===<br />
October 19 - 23<br />
* '''Monday: Fall Break'''<br />
* Wednesday: [[The Axioms of Spherical Geometry Exploration]]<br />
* Friday: discuss the A = .5 (base)(height) formula on the sphere. Allow for finishing the Axiom of Spherical geometry Exploration. Do [[Spherical Geometry Exploration]] problems 1-8 and 10.<br />
<br />
===Week 10: Spherical Geometry===<br />
October 26 - 30<br />
<br />
* Monday: [[Spherical Geometry Exploration]]<br />
* [[Spherical Geometry: Polygons]]<br />
* Spherical Homework Part 1; Due Wednesday Nov 4, 2009<br />
* Spherical Homework Part 2; Due Monday Nov 9, 2009<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 2 - 6<br />
<br />
* [[Spherical Triangles Exploration]]<br />
* We went over [[Spherical versus Euclidean Polygons Exploration]] and looked at the different definitions from Euclidean geometry and compared them to the definitions we (could) use in spherical geometry.<br />
* We looked at Kaleidotile in class. We found regular and semi-regular tessellations on the sphere. There are 5 regular tessellations on the sphere (as opposed to 3 in the plane), and we found at least 10 semi-regular tessellations (as opposed to only 8 in the plane).<br />
* We did the [[Platonic Solids Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 9 - 13<br />
<br />
* Introduction to Hyperbolic Geometry<br />
* Monday: Do [[Escher's Circle Limit Exploration]]<br />
* Wednesday: [[Hyperbolic Geometry Exploration]] and the Jos Leys Hyperbolic Geometry Exploration<br />
* Friday: Started on Spherical Geometry Homework part 3, due Monday.<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 16 - 20<br />
<br />
During this week we worked on a variety of explorations:<br />
* [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
* [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
And we worked on the homework.<br />
<br />
===Week 14: Hyperbolic Geometry===<br />
November 23 - 27<br />
<br />
* Monday:<br />
* '''Wednesday: Thanksgiving: Official University Holiday'''<br />
* '''Friday: Thanksgiving: Official University Holiday'''<br />
<br />
===Week 15: Depth, Perspective and Impossible Figures===<br />
November 30 - December 4<br />
* Monday: Discussed the exam on Friday. Talked about the concepts of [[Depth and Perspective]]. We did the [[Depth Exploration]]<br />
* Wednesday: Time for some questions about the exam. Followed by the [[Impossible Figures and Escher Exploration]]<br />
* Friday: Exam II See [[Exam 2 Outline]] for more detail.<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Exam 2. See [[Exam II Outline]] for information</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-12-01T15:30:15Z<p>Huling: /* Week 15: Fourth Dimension and Topology */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
* Wednesday: [[Hyperbolic Escher Exploration]]<br />
<br />
* Friday: [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: Fourth Dimension and Topology===<br />
November 29 - December 3<br />
<br />
* Monday: [[Flatland Exploration]] and discussion<br />
<br />
* Wednesday: [[Dimensions Exploration]] and Hypercube Discussion<br />
<br />
''Extra Credit:'' Read ([http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html And he built a crooked house… ], Short story by Robert A. Heinlein) and write a two page "book report" on it. Submit it Monday.<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-12-01T14:56:30Z<p>Huling: /* Week 15: Fourth Dimension and Topology */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
* Wednesday: [[Hyperbolic Escher Exploration]]<br />
<br />
* Friday: [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: Fourth Dimension and Topology===<br />
November 29 - December 3<br />
<br />
* Monday: [[Flatland Exploration]] and discussion<br />
<br />
* Wednesday: [[Dimensions Exploration]] and Hypercube Discussion<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-12-01T14:55:48Z<p>Huling: /* Week 15: Fourth Dimension and Topology */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
* Wednesday: [[Hyperbolic Escher Exploration]]<br />
<br />
* Friday: [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: Fourth Dimension and Topology===<br />
November 29 - December 3<br />
<br />
* Monday: [[Flatland Exploration]] and discussion<br />
<br />
* Wednesday: [[Dimension Exploration]] and Hypercube Discussion<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-11-29T15:01:40Z<p>Huling: /* Week 15: TBD */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
* Wednesday: [[Hyperbolic Escher Exploration]]<br />
<br />
* Friday: [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: Fourth Dimension and Topology===<br />
November 29 - December 3<br />
<br />
* Monday: [[Flatland Exploration]] and discussion<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-11-19T14:57:54Z<p>Huling: /* Week 13: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
* Wednesday: [[Hyperbolic Escher Exploration]]<br />
<br />
* Friday: [[Ideal Hyperbolic Tessellations Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-11-17T14:59:03Z<p>Huling: /* Week 13: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
* Wednesday: [[Hyperbolic Escher Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-11-15T15:01:46Z<p>Huling: /* Week 13: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
* Monday: Catch-up and [[Hyperbolic Tessellations Exploration]]<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-11-12T15:02:18Z<p>Huling: /* Week 12: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
* Friday: [[Hyperbolic Geometry II with NonEuclid Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-11-10T15:01:59Z<p>Huling: /* Week 12: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
'''For Friday''' Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-11-10T15:01:38Z<p>Huling: /* Week 12: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
=For Friday= Read [[Hyperbolic Geometry]] until Hyperbolic Tessellations<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-11-10T14:57:49Z<p>Huling: /* Week 12: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
* Wednesday: Review of [[Hyperbolic Paper Exploration]] and [[Hyperbolic Geometry Exploration]]<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-11-08T12:58:42Z<p>Huling: /* Week 12: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
Spherical Geometry Homework Due Wednesday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-11-08T12:57:34Z<p>Huling: /* Week 11: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-11-08T12:56:10Z<p>Huling: /* Week 12: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
Spherical Geometry Homework Due Friday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
* Monday: Class cancelled. Please complete [[Hyperbolic Paper Exploration]] by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-11-03T14:36:01Z<p>Huling: /* Week 11: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
* Wednesday: Intro to Hyperbolic Geometry and [[Escher's Circle Limit Exploration]]<br />
<br />
Spherical Geometry Homework Due Friday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-29T14:27:14Z<p>Huling: /* Week 11: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
Spherical Geometry Homework Due Friday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-29T14:26:45Z<p>Huling: /* Week 11: Hyperbolic Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
Spherical Geometry Homework Due Friday: [[Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36,37<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-29T14:26:13Z<p>Huling: /* Week 11: Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Hyperbolic Geometry===<br />
November 1 - 5<br />
<br />
Spherical Geometry Homework Due Friday:[[Do Spherical Geometry Exercises]] #1,6,9,13,16,21,28,30,36,37<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-27T14:14:18Z<p>Huling: /* Week 10: Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
* Wednesday: [[Platonic Solids Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingPlatonic Solids Exploration2010-10-27T14:04:19Z<p>Huling: </p>
<hr />
<div>{{Exploration}}<br />
{{time|25}}<br />
{{Objective|Learn to identify the Platonic solids, and discover some of their properties.}}<br />
<ol><br />
<li>Look at Escher’s [[Reptiles]] ({{Magic}} #307). What platonic solid is the focal point of this picture?</li><br />
<li>Look at Escher’s [[Crystal]] ({{Magic}} #170). It is built out of two intersecting platonic solids. Which two are they?</li><br />
<li>Look at Dali’s [[The Last Supper]]. What platonic solid forms the window?</li><br />
<li>Fill out the following table:<br />
{| border="1"<br />
! Shape !! # of vertices !! # of edges !! # of faces<br />
|-<br />
| Tetrahedron || || ||<br />
|-<br />
| Cube || || ||<br />
|-<br />
| Octahedron || || ||<br />
|-<br />
| Dodecahedron || || ||<br />
|-<br />
| Icosahedron || || ||<br />
|}<br />
Using paper models will be helpful. You may also find http://nlvm.usu.edu/en/nav/frames_asid_128_g_1_t_3.html?open=instructions helpful.</li><br />
<li>Find mathematical patterns in the table.</li><br />
</ol><br />
{{handin}}<br />
<br />
[[category:Non-Euclidean Geometry Explorations]]</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-25T14:03:13Z<p>Huling: /* Week 10: Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
* Monday: Duality Discussion and [[Duality Exploration]]<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-20T13:54:46Z<p>Huling: /* Week 9: Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
* Wednesday: [[Spherical versus Euclidean Polygons Exploration]] and last chance to get input on Art Project.<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-13T14:12:17Z<p>Huling: /* Week 8: Art Project Assignment and Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-13T14:12:06Z<p>Huling: /* Week 8: Art Project Assignment and Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
'''For Friday: Read [[Spherical Geometry]] until you get to Spherical Tessellations and...<br />
<br />
* Friday: [[Spherical Triangles Exploration]]<br />
<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-12T22:44:06Z<p>Huling: /* Week 8: Art Project Assignment and Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
* Wednesday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]] (Whichever one you did not do on Monday.)<br />
<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-12T22:43:10Z<p>Huling: /* Week 8: Art Project Assignment and Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-12T22:42:53Z<p>Huling: /* Week 8: Art Project Assignment and Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
%'''For Wednesday: Read [[Spherical Geometry]] up to <br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-12T22:42:21Z<p>Huling: /* Week 8: Art Project Assignment and Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
'''For Wednesday: Read [[Spherical Geometry]] up to <br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-11T14:06:26Z<p>Huling: /* Week 8: Art Project Assignment and Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
* Monday: [[Spherical Easel Exploration]] and [[Spherical Geometry Exploration]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-11T00:31:17Z<p>Huling: /* Week 8: Art Project Assignment and Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''For Monday: Read [[Introduction to Non-Euclidean Geometry]]<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-04T12:51:46Z<p>Huling: /* Week 9: Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
'''Friday: Art project due'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-04T12:51:27Z<p>Huling: /* Week 8: Art Project Assignment and Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
'''Friday: Rough draft of art project due'''<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-04T12:51:00Z<p>Huling: /* Week 7: Introduction to Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
'''Friday: Rough sketches for art project due'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingExam 1 Study Guide2010-10-04T12:49:12Z<p>Huling: Created page with '==Part I: Essay type questions== The exam is 50 minutes long. <br/> You should be thorough in your answer. Less than a half a page is likely not detailed enough of an explanatio…'</p>
<hr />
<div>==Part I: Essay type questions==<br />
<br />
The exam is 50 minutes long. <br/><br />
You should be thorough in your answer. Less than a half a page is likely not detailed enough of an explanation. I will ask some or all of the following questions:<br />
<br />
<br />
* '''Compare and contrast the rozette, the frieze and the wallpaper symmetry groups''' <br/><br />
What are we looking for when we determine these symmetry groups? What types of symmetries do we look for in a rozette? In a frieze pattern? In a wallpaper pattern? I.e which patterns have reflections? Which ones have rotations? Of what degree? Which ones can have translations? In what directions? Anything else worth mentioning? Provide a (simple) example of each to show the difference. (Be thorough!)<br />
<br />
<br />
* '''Show carefully that all parallelograms tessellate. ''' <br/><br />
Be thorough in your explanations! How do you argue you can cover the plane without gaps and overlaps? What role do the angle measures play? <br />
<br />
<br />
* '''Show carefully that all triangles tessellate. ''' <br/><br />
Be thorough in your explanations! What role do the angle measures play? Be detailed in your explanation.<br />
<br />
<br />
* '''Why are there exactly 3 regular tessellations?''' <br/><br />
First explain what a regular tessellation is. Then show carefully that there can only be three. Use the outline of the explorations we used. Give as much detail as possible.<br />
<br />
<br />
==Part II: Problems based on explorations and homework==<br />
* I will take some questions from the homework.<br />
* I will take some questions from the explorations.</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-04T12:48:42Z<p>Huling: /* Week 7: Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Introduction to Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingCourse:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling2010-10-04T12:48:19Z<p>Huling: /* Week 7: Spherical Geometry */</p>
<hr />
<div>==Course Information==<br />
===General===<br />
*'''Class Meets:''' MWF 9:00-9:50 PM in RH 225<br />
*'''Instructor:'''<br />
** Dr. Philip Huling<br />
** Office: RH 23<br />
** Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.<br />
** Email: hulingpc@slu.edu<br />
*'''Prerequisite:''' 3 years of high school mathematics or Math 120 (College Algebra).<br />
<br />
===Grading===<br />
<ul><br />
<li><br />
'''Attendance.''' Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero. <br />
</li><br />
<li><br />
'''Homework/Quizzes'''. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers. <br />
</li><br />
<li>'''Exams'''. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.<br />
<ul><br />
<li>Exam 1: TBA</li><br />
<li>Exam 2: TBA</li><br />
<li>Final: '''Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225''' </li><br />
</ul><br />
</li><br />
<li>'''Grading''' is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. <br />
Grading is weighted as follows:<br />
<ul><br />
<li>Homework/Quizzes: 30% </li><br />
<li>Attendance and participation: 10% </li><br />
<li>Projects: two @15% each </li><br />
<li> Exams: three @10% each </li><br />
</ul><br />
</li><br />
</ul><br />
<br />
===Textbooks===<br />
The main text for this course is the [[Main Page|Math and the Art of MC Escher]] online book, at http://math.slu.edu/escher<br />
<br />
One traditional textbook is required for the course:<br />
* '''D. Schattschneider, {{VOS}}. H. Abrams 2004'''. (The paperback 1990 edition is also acceptable).<br />
<br />
<br />
===Honesty===<br />
Students are expected to be honest in their academic work, as per the Honesty Policy <br />
of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be <br />
reported to the dean and may result in probation, expulsion, or worse.<br />
<br />
==Schedule==<br />
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.<br />
<br />
===Week 1: Introduction, Symmetry===<br />
August 23 - 27<br />
<br />
* Monday: Introduction to the course; First topic is "Symmetry" <br><br />
* Wednesday: Do the [[Symmetry of Stars and Polygons Exploration]] and [[Rozette Symmetry Groups with Kali Exploration]].<br />
'''By Friday: Read [[M.C. Escher]] and [[Introduction_to_Symmetry]]'''<br><br />
* Friday: [[Rotational and Reflectional Symmetry in Escher’s Sketches]] and [[Symmetry, Escher and Architecture Exploration]].<br />
<br />
===Week 2: Symmetry, Isometries, and Frieze Patterns===<br />
August 30 - September 3<br />
<br />
* Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration [[Frieze Marking Exploration]]. This is mainly a review of what we covered today.<br />
* Wednesday: Do [[Frieze Names Exploration]] and [[Identifying Frieze Patterns Exploration]].<br />
* Friday: Quiz #1 then [[Frieze and Rosette Group Scavenger Hunt]].<br />
<br />
'''On Monday Homework #1 is due:'''<br />
Do [[Rosette Exercises]] # 1-5, 7-12, 14, 16 (omit 9a-c)<br />
<br />
'''By Wednesday: Read [[Frieze Patterns]]'''<br><br />
<br />
(Fri September 3 Last day to drop without a "W")<br />
<br />
===Week 3: Frieze Patterns and Intro to Wallpaper Patterns===<br />
September 6 - 10<br />
* '''Monday: Labor Day: Official University Holiday'''<br />
<br />
* Wednesday: Homework #1 review and Wallpaper Introduction<br />
<br />
* Friday: [[Wallpaper Exploration]] and [[Wallpaper Symmetry Exploration]]<br />
<br />
'''On Friday Homework #2 is due:'''<br />
Do Homework #2 distributed via email.<br />
<br />
'''Note: Problem 4 will be discussed in class on Wednesday.'''<br />
<br />
===Week 4: Wallpaper Patterns===<br />
September 13 - 17<br />
* Monday: [[Wallpaper Group Scavenger Hunt]]<br />
<br />
* Wednesday: [[Tessellations, a first look Exploration]]<br />
<br />
* Friday: [[City Museum 2010]] and [[Angles of Polygons and Regular Tessellations Exploration]]<br />
<br />
* '''Friday Night: Class Field Trip to City Museum'''<br />
<br />
===Week 5: Tessellations and Isometries===<br />
September 20 - 24<br />
<br />
'''By Wednesday: Read [[Introduction_to_Tessellations]] and [[Tessellations by Polygons]]'''<br><br />
<br />
* Friday: [[Escher's Wallpaper Groups Exploration]]<br />
<br />
Read [[Wallpaper Patterns]].<br /><br />
Homework #3: Do [[Wallpaper Exercises]] # 1-7, 9, 10, [[Polygonal Tessellation Exercises]] # 3,4,6,10-14<br />
<br />
===Week 6: Escher-like Tessellations and GeoGebra===<br />
September 27 - October 1<br />
<br />
* Monday: [[Triangular Tessellations with GeoGebra]]<br />
<br />
* Wednesday: [[Quadrilateral Tessellations with GeoGebra]] Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.<br />
<br />
* Friday: [[Art Project Discussion]] and [[Creating Tessellation Graph Paper]]<br />
<br />
'''City Museum Poster is due Monday September 27th'''<br />
<br />
===Week 7: Spherical Geometry===<br />
October 4 - 8<br />
<br />
[[Exam 1 Study Guide]]<br />
<br />
* Monday: Review for Exam 1.<br />
<br />
'''Homework #3 is due on Monday October 4th'''<br />
<br />
'''Exam #1 is on Wednesday October 6th'''<br />
<br />
===Week 8: Art Project Assignment and Spherical Geometry===<br />
October 11 - 15<br />
<br />
''(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)''<br />
<br />
===Week 9: Spherical Geometry===<br />
October 18 - 22<br />
* '''Monday: Fall Break: No Class'''<br />
<br />
===Week 10: Spherical Geometry===<br />
October 25 - 29<br />
<br />
''(Fri October 30 Last Day to Withdraw)''<br />
<br />
===Week 11: Spherical Geometry===<br />
November 1 - 5<br />
<br />
===Week 12: Hyperbolic Geometry===<br />
November 8 - 12<br />
<br />
===Week 13: Hyperbolic Geometry===<br />
November 15 - 19<br />
<br />
===Week 14: TBD===<br />
November 22 - 26<br />
* '''Wednesday: Thanksgiving Break: No Class'''<br />
* '''Friday: Thanksgiving Break: No Class'''<br />
<br />
===Week 15: TBD===<br />
November 29 - December 3<br />
<br />
===Week 16: Review for Final===<br />
* Monday December 7: Last Day of Class and Review</div>HulingFile:KitePaper.jpg2010-10-01T14:06:41Z<p>Huling: </p>
<hr />
<div></div>HulingFile:ParallelogramPaper1.jpg2010-10-01T14:06:20Z<p>Huling: </p>
<hr />
<div></div>Huling