Course:SLU MATH 124: Math and Escher - Spring 2009 - Dr. Bryan Clair

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Extra Credit oppportunity

There's an exhibit of work by Marcel Duchamp at the SLU Museum of Art (on Lindell, across from Pius library). Visit the show for some extra credit. There's one catch - the show doesn't open until May 6, so you have to go May 6, 7, or 8 (when our class ends!) to take advantage. For more information, visit .

Final Project

The Art and Mathematics Project is due Friday, May 8 during our final exam period. Your preliminary work and written plan are due Wednesday, April 29.

Third Exam

The third exam is during our final exam period, Friday, May 8, from 12-1:50.

Office Hours

Finals week office hours Tuesday 10-12, Thursday 10-11, or by appointment.

Homework and Reading Assignments

  1. Due Wednesday, January 21
    Read Visions of Symmetry pg. 1-15.
    Read M.C. Escher and Introduction_to_Symmetry.
    Do Rosette Exercises # 2-6,8,10,11,12,14,16,19
  2. Due Friday, January 30:
    Read Visions of Symmetry pg. 15-31.
    Read Frieze Patterns.
    Do Frieze Exercises # 1-9
  3. Due Friday, February 6:
    Read Visions of Symmetry pg. 31-44, 77-78.
    Read Wallpaper Patterns.
    Do Wallpaper Exercises # 1-7, 9, 10
  4. Due Monday, February 16:
    Cathedral Poster (for your group).
  5. Due Friday, February 20:
    Read Visions of Symmetry pg 106-117, 254-260
    Read Introduction to Tessellations. Read Tessellations by Polygons.
    Do Polygonal Tessellation Exercises # 2, 3, 4, 5, 12, 13, 14.
  6. Due Friday, February 27:
    Read Visions of Symmetry pg 236-240, 266-274
    Read Tessellations by Recognizable Figures.
    Do Polygonal Tessellation Exercises # 6 - 11, 15
  7. Due Wednesday, March 18
    Read Visions of Symmetry pg 91, 248-254
    Read Similarity Transformations.
    Do Self-Similarity Exercises # 1-14
  8. Due Wednesday, March 25
    Read Visions of Symmetry pg 241-247
    Begin reading Spherical Geometry.
    Do Spherical Geometry Exercises # 1-8,10,12-15
  9. Due Wednesday, March 31
    Finish Spherical Geometry.
    Read Platonic Solids, by Paul Calter.
    Do Spherical Geometry Exercises # 18-27, 29-32, 34
  10. Due Wednesday, April 22
    Read Hyperbolic Geometry and The Three Geometries.
    Do Hyperbolic Geometry Exercises # 1-13, 16, 18, 19, 21-25
  11. Due Friday, May 1
    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 #1-12

Course Information


  • Class Meets: MWF 12:00-12:50 in RH 316
  • Instructor:
    • Bryan Clair (
    • Office: Ritter Hall 110
    • Office Hours: M10-11, Th10-11, F1-2 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, Feb. 13
    • Exam 2: Friday, Apr. 3
    • Exam 3 (Final exam period): Friday, May 8, 12:00-1:50
  • 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

Two traditional textbooks are required for the course:

  1. D. Schattschneider, Visions of Symmetry. H. Abrams 2004. (The paperback 1990 edition is also acceptable).
  2. 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 ( ) or direct from the publisher ( )


Students are expected to be honest in their academic work, as per 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 (1/12-1/16)

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 (1/19-1/23)

Monday: MLK, no class. Frieze symmetry. Frieze Marking Exploration, Frieze Group Exploration.

Week 3 (1/26-1/30)

Frieze Names Exploration. Wallpaper symmetry. Wallpaper Exploration

Week 4 (2/2-2/6)

Wallpaper Symmetry Exploration. Begin tessellations. Metamorphosis Exploration.

Week 5 (2/9-2/13)

Monday: Field trip to Cathedral Basilica, 4431 Lindell (at Newstead). The trip will be at 4:00pm, and we will not meet at our usual class time.


Friday: Exam 1.

Week 6 (2/16-2/20)

Tessellations. Quadrilateral Tessellation Exploration. Pattern Block Exploration.

Week 7 (2/23-2/27)

Tessellations by Recognizable Figures. In-class sketching.

Week 8 (3/2-3/6)

Similarity transformations. Dilation Exploration, Iteration Exploration, Self-Similarity Exploration.

Tessellation Art Project due Friday.

Spring Break (3/9-3/13)

Week 9 (3/16-3/20)

Spherical geometry. Spherical Geometry Exploration. Using Spherical Easel. Spherical Triangles Exploration.

Week 10 (3/23-3/27)

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

Week 11 (3/30-4/3)

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

Week 12 (4/6-4/10)

Hyperbolic geometry. Hyperbolic Paper Exploration. Hyperbolic Geometry Exploration. Friday: Good Friday, no class.

Week 13 (4/13-4/17)

Monday: Easter break, no class. Hyperbolic geometry. Escher's Circle Limit Exploration.

Week 14 (4/20-4/24)

Hyperbolic Tessellations Exploration. Depth and perspective. Depth Exploration.

Week 15 (4/27-5/1)

Perspective Exploration. Impossible Exploration. Flatness Exploration. Review for third exam, discuss art projects, class evaluations.

Last day of class is Monday, 5/4.

Final Exam Period (Friday, May 8, 12-1:50)

Third exam. Art project due.