Course:SLU MATH 124: Math and Escher - Fall 2013 - Dr. Bryan Clair

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This class is over.


  1. Due Wednesday, September 4
    Read M.C. Escher and Introduction to Symmetry.
    Do Rosette Exercises # 3,4,6,8,9,10,11,13,14,15,18,19
  2. Due Friday, September 13
    Read Visions of Symmetry pg. 15-31.
    Read Frieze Patterns.
    Do Frieze Exercises # 1,2,3,6-11
  3. Due Friday, September 20
    Read Escher's essay, "The Regular Division of the Plane..." (paper handout).
    Read The Alhambra and The Alcazar (Spain) Read Wallpaper Patterns.
    Do Wallpaper Exercises # 1,2,3,5,6,7,8,9,11,12,13
  4. Due Friday, September 27
    Read Escher's Combinatorial Patterns
    Do Symmetric Art Project
  5. Due Friday, October 11
    Read Fundamental Concepts (if needed), Introduction to Tessellations, begin Tessellations by Polygons
    Do Polygonal Tessellation Exercises # 2,3,4,6,12,13,14
  6. Due Wednesday, October 23
    Read Tessellations by Recognizable Figures
    Do Tessellation Art Project Lite
  7. Due Friday, October 25
    Finish reading Tessellations by Polygons
    Do Polygonal Tessellation Exercises # 7, 8, 9, 10, 11, 15
  8. Due Friday, November 1
    Begin reading Spherical Geometry.
    Do Spherical Geometry Exercises #1-5, 8-12, 16, 17, 19, 43ab
  9. Due Friday, Nov. 15
    Finish reading Spherical Geometry.
    Do Spherical Geometry Exercises #22-30, 13, 20, 32, 33, 35, 39, 42, 44
  10. Due Monday, Nov. 25
    Read Hyperbolic Geometry and The Three Geometries.
    Do Hyperbolic Geometry Exercises #1-9, 11*, 12*, 13*, 16a, 18, 21-25. For the * exercises, skip the part about area.
  11. Due Monday, Dec. 9
    Read Depth and Perspective
    Do Depth and Perspective Exercises # 1, 2, 4, 5, 6, 10, 11, 12

Course Information


  • Class Meets: MWF 12:00-12:50 in RH 316
  • Instructor:
    • Bryan Clair (
    • Office: Ritter Hall 110
    • Office Hours: M 2-3, Tu 11:00-12:00, F 10-11 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 most weeks. 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.
  • Art Projects. There will be four art projects over the course of the semester, which will be drawn or painted. You will need some decent quality paper for these, better than printer paper or posterboard. You may also want drawing materials, such as ink pens, colored pencils, or pastels.
  • Exams. I give makeup exams only for severe and documented reasons.
    • Exam 1: Monday, 9/30
    • Exam 2: Monday, 11/4
    • Final exam: Wednesday, December 11, 12-1:50pm
  • Grading is on a straight scale, with 90%,80%,70%,60% guaranteeing A-, B-, C-, D respectively. Grading is weighted as follows:
    • Homework: 15%
    • Attendance and in-class work: 20%
    • Art Projects: 25%
    • Exams: 40%


The main text for this course is the Math and the Art of MC Escher online book, at

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, so you'll need to find a used copy. This is a beautiful coffee table book with prints of Escher's artwork, something you will probably want to keep after taking this course. When in print, it was about a $40 book, and I don't suggest you pay much more than that for a copy today. Here is a link with details about the book, but feel free to search for it elsewhere.

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 Academic 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.


In recognition that people learn in a variety of ways and that learning is influenced by multiple factors (e.g., prior experience, study skills, learning disability), resources to support student success are available on campus. Students who think they might benefit from these resources can find out more about:

Course-level support (e.g., faculty member, departmental resources, etc.) by asking your course instructor. University-level support (e.g., tutoring/writing services, Disability Services) by visiting the Student Success Center (BSC 331) or by going to Students who believe that, due to a disability, they could benefit from academic accommodations are encouraged to contact Disability Services at 314-977-8885 or visit the Student Success Center. Confidentiality will be observed in all inquiries.

Course instructors support student accommodation requests when an approved letter from Disability Services has been received and when students discuss these accommodations with the instructor after receipt of the approved letter.


Week 1 (8/26-8/30)

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

Week 2 (9/2-9/6)

Monday: Labor Day, no class.

Frieze symmetry. Frieze Marking Exploration.

Week 3 (9/9-9/13)

Frieze Group Exploration. Frieze Names Exploration. Wallpaper symmetry. Wallpaper Exploration.

Week 4 (9/16-9/20)

Wallpaper Symmetry Exploration. Escher's Wallpaper Groups Exploration. Islamic Patterns Exploration.

Week 5 (9/23-9/27)

Square Block Pattern Exploration. Potato Stamping Exploration. Tessellations.

Symmetric Art Project due Friday 9/27.

Week 6 (9/30-10/4)

Monday: Exam 1.

Metamorphosis Exploration. Tessellations.

Friday: Field trip to the Pulitzer Foundation for the Arts.

Week 7 (10/7-10/11)

Quadrilateral Tessellation Exploration. Pentagon Tessellation Exploration. Tessellations by Recognizable Figures.

Week 8 (10/14-10/18)

Angles of Polygons and Regular Tessellations Exploration. Pattern Block Exploration.

Week 9 (10/21-10/25)

Monday: Fall Break, no class.

Tessellation Art Project Lite due Wednesday 10/23.

Spherical geometry. Spherical Geometry Exploration. Using Spherical Easel.

Week 10 (10/28-11/1)

Spherical Triangles Exploration. Spherical tessellations.

Week 11 (11/4-11/8)

Monday: Exam 2.

Regular Spherical Tessellations Exploration. Platonic solids. Platonic Solids Exploration.

Week 12 (11/11-11/15)

Euler characteristic and duality. Duality Exploration. Hyperbolic geometry. Hyperbolic Paper Exploration.

Week 13 (11/18-11/22)

Hyperbolic geometry. Hyperbolic Geometry Exploration. Circle Limit Exploration. Hyperbolic Tessellations Exploration

Week 14 (11/25-11/29)

Finish Circle Limit Exploration. Wednesday, Friday: Thanksgiving break, no class.

Week 15 (12/2-12/6)

Non-Euclidean Art Project is due Wednesday, 12/4. Only the partial written component is required.

Depth Exploration. Perspective Exploration. Impossible Exploration.

Last day of class is Monday, 12/9. Evaluations. Review for third exam.

Final Exam Period (Wednesday, Dec 11, 12-1:50)

Final Exam