Course:SLU MATH 124: Math and Escher - Fall 2010 - Dr. Bryan Clair

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The Art and Mathematics Project is due Friday, December 10. A plan for your project and some preliminary work is due Friday, December 3.

The third exam is Friday, December 10 at 12:00.

Remaining office hours are Monday, 12/6 from 12-1, Thursday 12/9 from 11-12, or by appointment.

Homework and Reading Assignments

  1. Due Wednesday, Sep. 1
    Read Visions of Symmetry pg. 1-15.
    Read M.C. Escher and Introduction_to_Symmetry.
    Do Rosette Exercises # 2-6,8-11, 13, 14, 18, 19.
  2. Due Wednesday, Sep. 8
    Read Visions of Symmetry pg. 15-31.
    Read Frieze Patterns.
    Do Frieze Exercises #1-9.
  3. Due Wednesday, Sep. 15
    Read Visions of Symmetry pg. 31-44,77-78.
    Read Wallpaper Patterns.
    Do Wallpaper Exercises #1-7,9,10.
  4. Due Wednesday, Sep. 22
    Read The_Alhambra_and_The_Alcazar_(Spain).
    Read Fundamental Concepts (except the optional section).
    Do City Museum 2010 posters.
    Do Polygon Exercises #1,7, 13, 14
  5. Due Wednesday, Sep. 29
    Read Visions of Symmetry pg 106-117, 254-260
    Read Introduction to Tessellations, Tessellations by Polygons.
    Do Polygonal Tessellation Exercises # 2, 3, 6-15
  6. Due Friday, Oct. 22
    Read Visions of Symmetry pg 91, 248-254
    Read Similarity Transformations.
    Do Self-Similarity Exercises #1-14
  7. Due Friday, Oct. 29
    Read Visions of Symmetry pg 243-247
    Begin reading Spherical Geometry.
    Do Spherical Geometry Exercises #1-5, 8-12, 16, 17, 19, 33
  8. Due Friday, Nov. 5
    Finish reading Spherical Geometry.
    Do Spherical Geometry Exercises #13, 22-30, 32, 34, 35, 38, 42
  9. Due Monday, Nov. 22
    Read Hyperbolic Geometry, The Three Geometries.
    Do Hyperbolic Geometry Exercises # 1-13, 16, 21-25
  10. Not Due
    Read Depth and Perspective.
    Do Depth and Perspective Exercises # 1, 2, 4-14

Course Information


  • Class Meets: MWF 1:10-2:00 in RH 316
  • Instructor:
    • Bryan Clair (
    • Office: Ritter Hall 110
    • Office Hours: M 12-1, Tu 11-12, Th 11-12 or by appointment.
    • Email:
  • Prerequisite: 3 years of high school mathematics or Math 120 (College Algebra).


  • 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.
  • 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, Oct. 1
    • Exam 2: Friday, Nov. 12
    • Exam 3 (Final exam period): Friday Dec. 10, 12-1:50pm
  • 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

Also required for the course is D. Schattschneider, Visions of Symmetry. H. Abrams 2004, available at the university bookstore. The paperback 1990 edition is also acceptable.

Finally, it is highly recommended that you purchase a copy of J. Locher, Magic of M.C. Escher. H. Abrams 2000. Unfortunately, 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. You shouldn't need to spend more than $50 for this beautiful book. Here are some links to try:

If you can't get Magic of M.C. Escher, the cheap paperback M.C. Escher: The Graphic Work is a pathetic but acceptable substitute.


This course is goverened by 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.


Week 1 (8/23-8/27)

Rosette symmetry. Rotations, reflections. Symmetry groups. Symmetric Figures Exploration. Symmetry of Stars and Polygons Exploration. Composition Exploration and the classification of rosette symmetries.

Week 2 (8/30-9/3)

Frieze symmetry. Frieze Marking Exploration, Frieze Group Exploration.

Week 3 (9/6-9/10)

Monday: Labor Day, no class. Wallpaper symmetry. Wallpaper Exploration. Wallpaper Symmetry Exploration.

Week 4 (9/13-9/17)

Begin tessellations. Metamorphosis Exploration. Friday: Field trip to City Museum, 6:30-9:30pm.: City Museum 2010

Week 5 (9/20-9/24)

Tessellations. Quadrilateral Tessellation Exploration. Angles of Polygons and Regular Tessellations Exploration.

Week 6 (9/27-10/1)

Tessellations. Pattern Block Exploration. Friday: Exam 1.

Week 7 (10/4-10/8)

Tessellations by Recognizable Figures. In-class sketching.

Week 8 (10/11-10/15)

Dilation Exploration. Iteration Exploration. Self-Similarity Exploration. Tessellation Art Project due Friday.

Week 9 (10/18-10/22)

Monday: No class, Fall break. Spherical geometry. Spherical Geometry Exploration. Using Spherical Easel.

Week 10 (10/25-10/29)

Spherical Triangles Exploration. Spherical tessellations. Regular Spherical Tessellations Exploration. Platonic solids.

Week 11 (11/1-11/5)

Euler characteristic and duality. Platonic Solids Exploration. Duality Exploration.

Week 12 (11/8-11/12)

Hyperbolic geometry. Hyperbolic Paper Exploration. Friday: Exam 2.

Week 13 (11/15-11/19)

Hyperbolic geometry. Hyperbolic Geometry Exploration. Escher's Circle Limit Exploration. Hyperbolic Tessellations Exploration.

Week 14 (11/22-11/26)

Wednesday, Friday: Thanksgiving. No Class

Week 15 (11/29-12/3)

Depth and perspective. Depth Exploration. Perspective Exploration. Impossible Exploration. Flatness Exploration.

Review for third exam, discuss art projects, class evaluations.

Friday, 12/3: Preliminary work due for Art and Mathematics Project

Last day of class is Monday, 12/6.

Final Exam (Friday, December 10, 12-1:50)

Third exam. Art and Mathematics Project due.