Course:SLU MATH 124: Math and Escher - Fall 2014 - Dr. Bryan Clair

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This course is over.


  1. Due Friday, September 5
    Read M.C. Escher and Introduction to Symmetry.
    Do Rosette Exercises # 2-4, 6, 8-14, 16-19
  2. Due Monday, September 15
    Read Frieze Patterns.
    Do Frieze Exercises # 1,2,3,6-11 Answer these Course:SLUMA Questions that require you to visit "The Dream" at SLUMA (see above).
  3. Due Wednesday, September 24
    Read The Alhambra and The Alcazar (Spain), Wallpaper Patterns, and skim Escher's Combinatorial Patterns
    Do Wallpaper Exercises # 1,2,3,5-9
  4. Due Friday, October 10
    Read Fundamental Concepts (if needed), Introduction to Tessellations, Tessellations by Polygons,
    Do Polygonal Tessellation Exercises # 2,3,4,6-15
  5. Due Friday, October 17
    Read Tessellations by Recognizable Figures, Escher's essay, "The Regular Division of the Plane..." (paper handout)
    Do Recognizable Tessellation Exercises #1,2,3,7,8
  6. Due Friday, October 31
    Read Aperiodic_Tessellations#Penrose_Tilings. Begin reading Spherical Geometry.
    Do Aperiodic Tessellation Exercises #6, 7 ,8.
    Do Spherical Geometry Exercises #1-5, 8-12, 14ab, 22, 23, 25.
  7. Due Friday, Nov. 14
    Finish reading Spherical Geometry.
    Do Spherical Geometry Exercises #26, 27, 31, 32-36, 38, 40-44, 50, 52, 53
  8. Due Monday, Nov. 24
    Read Hyperbolic Geometry and The Three Geometries.
    Do Hyperbolic Geometry Exercises #1-9, 11, 12abce, 13abce, 16a, 18, 21-25.
  9. Due Monday, Dec. 8
    Read Depth and Perspective
    Do Depth and Perspective Exercises # 1, 2, 4, 5, 6, 10, 11, 14

Course Information


  • Class Meets: MWF 12:00-12:50 in RH 316
  • Instructor:
  • 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, September 29
    • Exam 2: Monday, November 3
    • Final exam: Wednesday, December 10, 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.


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 (8/25-8/29)

Rosette symmetry. Rotations, reflections. Symmetry groups. Symmetric Figures Exploration. Symmetry of Stars and Polygons Exploration. Symmetry and Celtic Knots Exploration.

Week 2 (9/1-9/5)

Monday: Labor Day, no class.

The classification of rosette symmetries. Composition Exploration. Frieze symmetry. Frieze Marking Exploration.

Week 3 (9/8-9/12)

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

Week 4 (9/15-9/19)

Islamic Patterns Exploration. Wallpaper Symmetry Exploration. Potato Stamping Exploration.

Week 5 (9/22-9/26)

Escher's Wallpaper Groups Exploration. Metamorphosis Exploration.


Friday: Symmetric Art Project due.

Week 6 (9/29-10/3)

Monday: Exam 1.

Quadrilateral Tessellation Exploration. Pentagon Tessellation Exploration.

Week 7 (10/6-10/10)

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

Week 8 (10/13-10/17)

Tessellations by Recognizable Figures. Penrose Tiling Exploration.

Week 9 (10/20-10/24)

Monday: Fall Break, no class.

Wednesday: Tessellation Art Project Lite due.

Spherical geometry. Spherical Geometry Exploration. Spherical Easel Exploration.

Week 10 (10/27-10/31)

Spherical Triangles Exploration. Spherical tessellations.

Week 11 (11/3-11/7)

Monday: Exam 2.

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

Week 12 (11/10-11/14)

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

Week 13 (11/17-11/21)

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

Week 14 (11/24-11/28)

Wednesday, Friday: Thanksgiving break, no class.

Week 15 (12/1-12/5)

Depth Exploration. Perspective Exploration. Impossible Exploration.

Last day of class is Monday, 12/8. Evaluations. Review for third exam.

Final Exam Period (Wednesday, Dec 10, 12-1:50)

Final Exam