Course:SLU MATH 124: Math and Escher - Fall 2009 - Dr. Anneke Bart
Contents
- 1 Course Information
- 2 Homework Assignments
- 3 Schedule
- 3.1 Week 1: Introduction, Symmetry
- 3.2 Week 2: Symmetry, Isometries, and Frieze Patterns
- 3.3 Week 3: Wallpaper Patterns
- 3.4 Week 4: Wallpaper Patterns
- 3.5 Week 5: Tessellations and Isometries
- 3.6 Week 6: Escher-like Tessellations and Geometer Sketchpad
- 3.7 Week 7: Exam I, Field Trip and Intro to Spherical Geometry
- 3.8 Week 8: Art Project Assignment and intro to Spherical Geometry
- 3.9 Week 9: Spherical Geometry
- 3.10 Week 10: Spherical Geometry
- 3.11 Week 11: Spherical Geometry
- 3.12 Week 12: Hyperbolic Geometry
- 3.13 Week 13: Hyperbolic Geometry
- 3.14 Week 14: Hyperbolic Geometry
- 3.15 Week 15: Depth, Perspective and Impossible Figures
- 3.16 Week 16: Review for Final
Course Information
General
- Class Meets: MWF 9:00-9:50 in RH 316
- Instructor:
- Anneke Bart (http://math.slu.edu/~bart)
- Office: Ritter Hall 115
- Office Hours: MW 1-2 and Tue 9-10 or by appointment.
- Email: barta@slu.edu
- Prerequisite: 3 years of high school mathematics or Math 120 (College Algebra).
Grading
- Attendance is required. You will have in-class work to be done in groups. One unexcused absence is allowed. Six absences will cause you to lose two letter grades. I only excuse absences when presented with official documentation. Being late twice or leaving early counts as an absence.
- Homework will be due weekly. Your work should be neat, legible, and stapled. Cooperation is good, but write up results separately. Late homework is always accepted, but I will not write comments and will automatically give a score of 5 (out of 10) if the work is of reasonable quality.
- Exams. I give makeup exams only for severe and documented reasons.
- Exam 1: TBA
- Exam 2: TBA
- Final: Monday December 14. Time: 8:00 - 9:50. Place: RH 316
- Grading is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D.
Grading is weighted as follows:
- Exams: two @15% each
- Homework and in-class work: 20%
- Tessellation Project: 10%
- Cathedral Poster Assignment: 10%
- Final: 30% (the final is comprehensive)
Textbooks
The main text for this course is the Math and the Art of MC Escher online book, at http://math.slu.edu/escher
One traditional textbook is required for the course:
- D. Schattschneider, Visions of Symmetry. H. Abrams 2004. (The paperback 1990 edition is also acceptable).
Honesty
Students are expected to be honest in their academic work, as per the Honesty Policy of the College of Arts & Sciences. Plagiarism, cheating and dishonesty will be reported to the dean and may result in probation, expulsion, or worse.
Homework Assignments
On Friday August 28, Homework #1 is due:
Read Visions of Symmetry pg. 1-15.
Read M.C. Escher and Introduction_to_Symmetry.
Do Rosette Exercises # 1-5, 8-12, 14
(Extension given)
Due Wednesday, September 9: Homework #2
Read Visions of Symmetry pg. 15-31.
Read Frieze Patterns.
Do Frieze Exercises # 1-9
Homework #3: Due Wednesday September 23, 2009
File:Homework3-wallpaper.pdf Available for download.
Homework #4: Due Monday September 28
- 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.
- Give a short 1 paragraph description of how you made each of the tessellations.
- Identify the Symmetry Group.
Cathedral Basilica Project: Due Friday October 23.
for details see: Cathedral Basilica Field Trip and Poster Assignment
Tessellation Project: Due Monday November 3.
for details see: Tessellation Project Fall 2009 - Bart
Spherical Geometry: Homework Part I
Due Wednesday November 4. Download pdf here: File:SphericalHW-P1.pdf
Note that the handout gives the due date as being Monday. This was extended to Wednesday.
Spherical Geometry: Homework Part II
Due Monday November 9. Download pdf here: File:Spherical Geometry Homework2.pdf
Schedule
This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.
Week 1: Introduction, Symmetry
August 24 - 28
- Monday: Introduction to the course; First topic is "Symmetry"
- Wednesday: Do the Symmetry of Stars and Polygons Exploration and Rozette Symmetry Groups with Kali Exploration.
- Friday: Rotational and Reflectional Symmetry in Escher’s Sketches and Symmetry, Escher and Architecture Exploration
Week 2: Symmetry, Isometries, and Frieze Patterns
August 31 - September 4
- Monday: Introduction to Frieze patterns. Do exploration Frieze Marking Exploration and Frieze Names Exploration
- Wednesday: Quiz and start on new homework.
- Friday: Do Identifying Frieze Patterns Exploration
(Fri September 4 Last day to drop without a "W")
Week 3: Wallpaper Patterns
September 7 - 11
- Monday: Labor Day: Official University Holiday
- Wednesday: An introduction to wallpaper patterns Tessellations, a first look Exploration
- Friday: Went over border patterns and discussed some problems from homework 2.
Some points to remember:
- Start homework early, so you have time to ask questions.
- Anything on homework or explorations can show up on an exam.
- 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.
Week 4: Wallpaper Patterns
September 14 - 18
- Monday: Lecture on Wallpaper Patterns.
- Wednesday: A short Tiling Worksheet to think about how to draw different tessellations. And we will start on Wallpaper Symmetry Exploration
- Friday: Escher's Wallpaper Groups Exploration
Week 5: Tessellations and Isometries
September 21 - 25
- Monday: Short lecture about some terminology we need. Do Tessellation Exploration: The Basics
- Wednesday: Do Angles of Polygons and Regular Tessellations Exploration
- Friday: Short introduction to Tessellations by Recognizable figures, and do Escher-Like Tessellations Explorations
Week 6: Escher-like Tessellations and Geometer Sketchpad
September 28 - October 2
- 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.
- GSP Introduction Exploration
- GSP Quadrilateral Tessellation Exploration
- 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.
- Exam 1 is scheduled for Monday October 5
Week 7: Exam I, Field Trip and Intro to Spherical Geometry
October 5 - 9
- Monday: Exam I
- Wednesday: Discuss the field trip to the Basilica. Create teams of two or three people. Introduction to Spherical Geometry
- Friday: Cathedral Basilica Field Trip and Poster Assignment
Week 8: Art Project Assignment and intro to Spherical Geometry
October 12 - 16
(October 12-17 Midterm Exams - Note: we do not necessarily have an exam this week)
- Monday: Spherical Easel Exploration
- Wednesday: Bring your photographs so you can upload them to the website. PBWorks Assignment
Week 9: Spherical Geometry
October 19 - 23
- Monday: Fall Break
- Wednesday: The Axioms of Spherical Geometry Exploration
- 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.
Week 10: Spherical Geometry
October 26 - 30
- Monday: Spherical Geometry Exploration
- Spherical Geometry: Polygons
- Spherical Homework Part 1; Due Wednesday Nov 4, 2009
- Spherical Homework Part 2; Due Monday Nov 9, 2009
(Fri October 30 Last Day to Withdraw)
Week 11: Spherical Geometry
November 2 - 6
- Spherical Triangles Exploration
- 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.
- 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).
- We did the Platonic Solids Exploration
Week 12: Hyperbolic Geometry
November 9 - 13
- Introduction to Hyperbolic Geometry
- Monday: Do Escher's Circle Limit Exploration
- Wednesday: Hyperbolic Geometry Exploration and the Jos Leys Hyperbolic Geometry Exploration
- Friday: Started on Spherical Geometry Homework part 3, due Monday.
Week 13: Hyperbolic Geometry
November 16 - 20
During this week we worked on a variety of explorations:
And we worked on the homework.
Week 14: Hyperbolic Geometry
November 23 - 27
- Monday:
- Wednesday: Thanksgiving: Official University Holiday
- Friday: Thanksgiving: Official University Holiday
Week 15: Depth, Perspective and Impossible Figures
November 30 - December 4
- Monday: Discussed the exam on Friday. Talked about the concepts of Depth and Perspective. We did the Depth Exploration
- Wednesday: Time for some questions about the exam. Followed by the Impossible Figures and Escher Exploration
- Friday: Exam II See Exam 2 Outline for more detail.
Week 16: Review for Final
- Monday December 7: Last Day of Class and Review