Course:SLU MATH 124: Math and Escher - Spring 2008 - Dr. Bryan Clair

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Exam 3 is Friday, May 9 from 12-1:50pm.
The Art and Mathematics Project is due at the start of Exam 3.

Extra Credit: The Math/CS club is showing the movie Flatland on Wednesday 4/23 at 4pm in the Ritter Hall lobby.

Homework and Reading Assignments

  1. Due Friday, February 1:
    Read Visions of Symmetry pg. 1-15.
    Read M.C. Escher and Introduction_to_Symmetry.
    Do Rosette Exercises # 1-5, 8-12, 14
  2. Due Monday, February 11:
    Read Visions of Symmetry pg. 15-31.
    Read Frieze Patterns.
    Do Frieze Exercises # 1-9
  3. Due Monday, February 18
    Read Visions of Symmetry pg. 31-44, 77-78
    Read Wallpaper Patterns.
    Do Wallpaper Exercises # 1-7
  4. Due Wednesday, February 27
    Read Visions of Symmetry pg 106-117, 254-260
    Read Introduction to Tessellations, Tessellations by Polygons.
    Do Polygonal Tessellation Exercises # 1-7, 9,10,12,14
  5. Due Friday, March 7
    Read Visions of Symmetry page 236-240, 266-274.
    Read Tessellations by Recognizable Figures.
    Preliminary sketches for Tessellation Art Project should be presented in class.
  6. Due Friday, March 28
    Read Visions of Symmetry pg 91, 248-254
    Read Similarity Transformations.
    Do Self-Similarity Exercises # 1-14
  7. Due Friday, April 4
    Read Visions of Symmetry pg 243-247
    Begin reading Spherical Geometry.
    Do Spherical Geometry Exercises #1-8, 12-15
  8. Due Friday, April 11
    Finish reading Spherical Geometry.
    Read Calter's Geometry in Art And Architecture Unit 6: Platonic Solids.
    Do Spherical Geometry Exercises #18-27,29-32,34
  9. Due Friday, April 25
    Read Hyperbolic Geometry.
    Read The Three Geometries.
    Do Hyperbolic Geometry Exercises #1-13, 16,19
  10. Due Friday, May 2
    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 #1-11

Course Information


  • Class Meets: MWF 12:00-12:50 in RH 316
  • Instructor:
  • Prerequisite: 3 years of high school mathematics or MT A 120 (College Algebra).


  • Attendance is required. You will have in-class work to be done in groups. You can lose up to two letter grades by missing class.
  • 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, February 29
    • Exam 2: Friday, April 11
    • Exam 3: Friday May 9, 12:00–1:50 pm
  • 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. Plagiarism, cheating and dishonesty will be reported to the dean and may result in probation, expulsion, or worse.


Week 1 (1/21-1/25)

Monday, 1/21: MLK - NO CLASS

Rosette symmetry. Rotations, reflections. Symmetry groups. Did a loose variant of Symmetric Figures Exploration on Monday Symmetry of Stars and Polygons Exploration on Wednesday.

Week 2 (1/28-2/1)

Composition Exploration and the classification of rosette symmetries on Monday. Wednesday, began frieze symmetry with Frieze Marking Exploration. Translation. Glide reflection. Friday: snow day, no class.

Week 3 (2/4-2/8)

Frieze symmetry groups. Frieze Group Exploration. Begin wallpaper groups with Wallpaper Exploration.

Week 4 (2/11-2/15)

Continue wallpaper symmetry. Wallpaper Symmetry Exploration. Begin tessellations, Metamorphosis Exploration

Week 5 (2/18-2/22)

Monday, Feb 18: Field trip to Cathedral from 4:10-5pm, instead of usual class meeting. Triangle tessellations. Quadrilateral tessellations. Quadrilateral Tessellation Exploration.

Week 6 (2/25-2/29)

Angles of Polygons and Regular Tessellations Exploration, classification of convex polygon tessellations. Regular polygons and regular tessellations. Friday, 2/29: EXAM 1

Week 7 (3/3-3/7)

Creating shapes that tessellate. Techniques from Tessellations by Recognizable Figures.

Week 8 (3/10-3/14)

Dilations, Dilation Exploration. Iterations, Iteration Exploration. Fractals, Print Gallery, and the Droste effect, Self-Similarity Exploration.

Friday, 3/14: Tessellation art project due.

SPRING BREAK (3/19-3/21)

Week 9 (3/24-3/28)

Monday, 3/24: NO CLASS.

Spherical geometry. Geodesics. Triangles. Spherical Geometry Exploration.

Week 10 (3/31-4/4)

Spherical triangles: Angle sum, defect, area fraction. Spherical Triangles Exploration. Regular Spherical Tessellations Exploration. Introduce Platonic Solids.

Week 11 (4/7-4/11)

Polyhedra, duality, Euler characteristic. Platonic Solids Exploration. Review. Friday, 4/11: EXAM 2

Week 12 (4/14-4/18)

Hyperbolic Paper Exploration. Hyperbolic Geometry Exploration. The Poincaré Disk. Geodesics. Hyperbolic triangles. Escher's Circle Limit Exploration.

Week 13 (4/21-4/25)

Hyperbolic Tessellations Exploration. The classification of regular tessellations in the three geometries. Depth Exploration.

Week 14 (4/28-5/2)

Perspective Exploration. Impossible figures, Impossible Exploration. 2D vs. 3D, Flatness Exploration.

Week 15 (5/5-5/9)

Monday 5/5: Last day of class. Review.

Friday 5/9: The final exam period is 12:00–1:50 pm. The final art project is due at this time. There will be a one hour (not comprehensive) exam.