Course:SLU MATH 124: Math and Escher - Spring 2008 - Dr. Bryan Clair
- 1 News
- 2 Homework and Reading Assignments
- 3 Course Information
- 4 Schedule
- 4.1 Week 1 (1/21-1/25)
- 4.2 Week 2 (1/28-2/1)
- 4.3 Week 3 (2/4-2/8)
- 4.4 Week 4 (2/11-2/15)
- 4.5 Week 5 (2/18-2/22)
- 4.6 Week 6 (2/25-2/29)
- 4.7 Week 7 (3/3-3/7)
- 4.8 Week 8 (3/10-3/14)
- 4.9 Week 9 (3/24-3/28)
- 4.10 Week 10 (3/31-4/4)
- 4.11 Week 11 (4/7-4/11)
- 4.12 Week 12 (4/14-4/18)
- 4.13 Week 13 (4/21-4/25)
- 4.14 Week 14 (4/28-5/2)
- 4.15 Week 15 (5/5-5/9)
Exam 3 is Friday, May 9 from 12-1:50pm.
The Art and Mathematics Project is due at the start of Exam 3.
Extra Credit: The Math/CS club is showing the movie Flatland on Wednesday 4/23 at 4pm in the Ritter Hall lobby.
Homework and Reading Assignments
- Due Friday, February 1:
Read Visions of Symmetry pg. 1-15.
Read M.C. Escher and Introduction_to_Symmetry.
Do Rosette Exercises # 1-5, 8-12, 14
- Due Monday, February 11:
Read Visions of Symmetry pg. 15-31.
Read Frieze Patterns.
Do Frieze Exercises # 1-9
- Due Monday, February 18
Read Visions of Symmetry pg. 31-44, 77-78
Read Wallpaper Patterns.
Do Wallpaper Exercises # 1-7
- Due Wednesday, February 27
Read Visions of Symmetry pg 106-117, 254-260
Read Introduction to Tessellations, Tessellations by Polygons.
Do Polygonal Tessellation Exercises # 1-7, 9,10,12,14
- Due Friday, March 7
Read Visions of Symmetry page 236-240, 266-274.
Read Tessellations by Recognizable Figures.
Preliminary sketches for Tessellation Art Project should be presented in class.
- Due Friday, March 28
Read Visions of Symmetry pg 91, 248-254
Read Similarity Transformations.
Do Self-Similarity Exercises # 1-14
- Due Friday, April 4
Read Visions of Symmetry pg 243-247
Begin reading Spherical Geometry.
Do Spherical Geometry Exercises #1-8, 12-15
- Due Friday, April 11
Finish reading Spherical Geometry.
Read Calter's Geometry in Art And Architecture Unit 6: Platonic Solids.
Do Spherical Geometry Exercises #18-27,29-32,34
- Due Friday, April 25
Read Hyperbolic Geometry.
Read The Three Geometries.
Do Hyperbolic Geometry Exercises #1-13, 16,19
- Due Friday, May 2
Read Depth and Perspective.
Read Calter's Geometry in Art And Architecture Unit 11: Brunelleschi's Peepshow & The Origins of Perspective.
Do Depth and Perspective Exercises #1-11
- Class Meets: MWF 12:00-12:50 in RH 316
- Bryan Clair (http://math.slu.edu/~clair)
- Office: Ritter Hall 110
- Office Hours: W 10-11, Th 10-11, F 1:10-2.
- Email: email@example.com
- Prerequisite: 3 years of high school mathematics or MT A 120 (College Algebra).
- Attendance is required. You will have in-class work to be done in groups. You can lose up to two letter grades by missing class.
- 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: Friday, February 29
- Exam 2: Friday, April 11
- Exam 3: Friday May 9, 12:00–1:50 pm
- Grading is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D.
Grading is weighted as follows:
- Homework: 20%
- Attendance and in-class work: 20%
- Projects: two @15% each
- Exams: three @10% each
The main text for this course is the Math and the Art of MC Escher online book, at http://math.slu.edu/escher
Two traditional textbooks are required for the course:
- D. Schattschneider, Visions of Symmetry. H. Abrams 2004. (The paperback 1990 edition is also acceptable).
- J. Locher, Magic of M.C. Escher. H. Abrams 2000. This book is out of print in the U.S. You can sometimes still find a copy for sale in the U.S., or order the UK version, still in print. It's available at amazon.uk ( http://www.amazon.co.uk/Magic-M-C-Escher/dp/0500512892/ref=sr_1_4?ie=UTF8&s=books&qid=1200083862&sr=8-4 ) or direct from the publisher ( http://www.thamesandhudson.com/books/The_Magic_of_M_C_Escher/9780500512890.mxs/1/1/ )
Students are expected to be honest in their academic work. Plagiarism, cheating and dishonesty will be reported to the dean and may result in probation, expulsion, or worse.
Week 1 (1/21-1/25)
Monday, 1/21: MLK - NO CLASS
Rosette symmetry. Rotations, reflections. Symmetry groups. Did a loose variant of Symmetric Figures Exploration on Monday Symmetry of Stars and Polygons Exploration on Wednesday.
Week 2 (1/28-2/1)
Composition Exploration and the classification of rosette symmetries on Monday. Wednesday, began frieze symmetry with Frieze Marking Exploration. Translation. Glide reflection. Friday: snow day, no class.
Week 3 (2/4-2/8)
Frieze symmetry groups. Frieze Group Exploration. Begin wallpaper groups with Wallpaper Exploration.
Week 4 (2/11-2/15)
Continue wallpaper symmetry. Wallpaper Symmetry Exploration. Begin tessellations, Metamorphosis Exploration
Week 5 (2/18-2/22)
Monday, Feb 18: Field trip to Cathedral from 4:10-5pm, instead of usual class meeting. Triangle tessellations. Quadrilateral tessellations. Quadrilateral Tessellation Exploration.
Week 6 (2/25-2/29)
Angles of Polygons and Regular Tessellations Exploration, classification of convex polygon tessellations. Regular polygons and regular tessellations. Friday, 2/29: EXAM 1
Week 7 (3/3-3/7)
Creating shapes that tessellate. Techniques from Tessellations by Recognizable Figures.
Week 8 (3/10-3/14)
Dilations, Dilation Exploration. Iterations, Iteration Exploration. Fractals, Print Gallery, and the Droste effect, Self-Similarity Exploration.
Friday, 3/14: Tessellation art project due.
SPRING BREAK (3/19-3/21)
Week 9 (3/24-3/28)
Monday, 3/24: NO CLASS.
Spherical geometry. Geodesics. Triangles. Spherical Geometry Exploration.
Week 10 (3/31-4/4)
Spherical triangles: Angle sum, defect, area fraction. Spherical Triangles Exploration. Regular Spherical Tessellations Exploration. Introduce Platonic Solids.
Week 11 (4/7-4/11)
Polyhedra, duality, Euler characteristic. Platonic Solids Exploration. Review. Friday, 4/11: EXAM 2
Week 12 (4/14-4/18)
Hyperbolic Paper Exploration. Hyperbolic Geometry Exploration. The Poincaré Disk. Geodesics. Hyperbolic triangles. Escher's Circle Limit Exploration.
Week 13 (4/21-4/25)
Hyperbolic Tessellations Exploration. The classification of regular tessellations in the three geometries. Depth Exploration.
Week 14 (4/28-5/2)
Perspective Exploration. Impossible figures, Impossible Exploration. 2D vs. 3D, Flatness Exploration.
Week 15 (5/5-5/9)
Monday 5/5: Last day of class. Review.
Friday 5/9: The final exam period is 12:00–1:50 pm. The final art project is due at this time. There will be a one hour (not comprehensive) exam.