Course:SLU MATH 124: Math and Escher - Fall 2011 - Dr. Bryan Clair

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Your depth and perspective homework is graded. You may pick it up from my office door (RH 110).

Office hours for finals week: Monday (12/12) from 12-1, Tuesday 10-3, Friday 10-11. I will probably be around after noon on Wednesday, if you want to make an appointment.

The Art and Mathematics Project is due Friday, December 16 at noon. Hand in your art project, your preliminary work, and your written report.

Exam 3 is Friday, December 16, 12-2pm.


  1. Due Friday, September 9
    Read Visions of Symmetry pg. 1-15.
    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 16
    Read Visions of Symmetry pg. 15-31.
    Read Frieze Patterns.
    Do Frieze Exercises # 1,2,3,5-10
  3. Due Friday, September 23
    Read Visions of Symmetry pg. 31-44, 77-78.
    Read Wallpaper Patterns.
    Do Wallpaper Exercises # 1-7,9,10,12
  4. Due Wednesday, October 5
    Read Fundamental Concepts, Introduction to Tessellations, Tessellations by Polygons
    Do Polygonal Tessellation Exercises # 2-4, 6-15
  5. Due Friday, October 28
    Read Visions of Symmetry pg. 345-346
    Read Aperiodic Tessellations
    Do Aperiodic Tessellation Exercises # 1-8
  6. Due Friday, November 4
    Read Visions of Symmetry pg 243-247
    Begin reading Spherical Geometry.
    Do Spherical Geometry Exercises #1-5, 8-12, 16, 17, 19, 38, 43ab
  7. Due Friday, November 18
    Finish reading Spherical Geometry.
    Do Spherical Geometry Exercises #13, 22-30, 32, 33, 34, 35, 42, 44
  8. Due Friday, December 2
    Read Visions of Symmetry pg. 247-254
    Read Hyperbolic Geometry and The Three Geometries.
    Do Hyperbolic Geometry Exercises #1-13, 21-25
  9. Due Friday, December 9
    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 10:30-11:30, 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 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 October 7
    • Exam 2: Friday November 11
    • Exam 3 (Final exam period): Friday, Dec. 16, 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: 30%
    • Exams: 35%


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 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 (8/29-9/2)

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 (9/5-9/9)

Monday: Labor Day, no class. Frieze symmetry. Frieze Marking Exploration, Frieze Group Exploration.

Week 3 (9/12-9/16)

Frieze Names Exploration. Wallpaper symmetry. Wallpaper Exploration

Week 4 (9/19-9/23)

Wallpaper Symmetry Exploration. Begin tessellations. Metamorphosis Exploration. Friday: Field trip to Cathedral Basilica.

Week 5 (9/26-9/30)

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

Week 6 (10/3-10/7)

Tessellations. Pattern Block Exploration.

Friday: Exam 1.

Week 7 (10/10-10/14)

Tessellations by Recognizable Figures. In-class sketching.

Week 8 (10/17-10/21)

Non-periodic tessellations. Random Tessellation Exploration, Substitution Tessellation Exploration, some of Penrose Tiling Exploration

Tessellation Art Project due Friday.

Week 9 (10/24-10/28)

Monday: Fall Break, no class. Spherical geometry. Spherical Geometry Exploration. Using Spherical Easel.

Week 10 (10/31-11/4)

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

Week 11 (11/7-11/11)

Euler characteristic and duality. Platonic Solids Exploration. Duality Exploration. Friday: Exam 2.

Week 12 (11/14-11/18)

Hyperbolic geometry. Hyperbolic Paper Exploration. Hyperbolic Geometry Exploration.

Week 13 (11/21-11/25)

Wednesday, Friday: Thanksgiving break, no class. Hyperbolic geometry. Escher's Circle Limit Exploration.

Week 14 (11/28-12/2)

Hyperbolic Tessellations Exploration. Depth and perspective. Depth Exploration.

Week 15 (12/5-12/9)

Perspective Exploration. Impossible Exploration. Flatness Exploration. Art project proposal due Wednesday, December 7. Course evaluations.

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

Final Exam Period (Friday, Dec16, 12-1:50)

Third exam. Art and Mathematics Project due at noon.