Course:SLU MATH 1240: Math and Escher - Fall 2015 - Dr. Bryan Clair

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Homework 9 is due Monday, December 7.

Exam 2 is Wednesday, December 9 from 12-1:50


  1. Due Wednesday, September 2
    Read M.C. Escher and Introduction to Symmetry.
    Do Rosette Exercises # 3,4,6,8,9,10,11,12,13,14,15,19,20
  2. Due Wednesday, September 16
    Read Frieze Patterns.
    Do Frieze Exercises # 1,2,3,6-11
  3. Due Wednesday, September 23
    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 9
    Read Fundamental Concepts (if needed), Introduction to Tessellations, Tessellations by Polygons,
    Do Polygonal Tessellation Exercises # 2,3,4,6-15.
  5. Due Wednesday, October 14
    Read Tessellations by Recognizable Figures, photocopied handout from Visions of Symmetry.
    Do Recognizable Tessellation Exercises #1, 2, 3, 4, 7
  6. Due Monday, November 2
    Begin reading Spherical Geometry.
    Do Spherical Geometry Exercises #1, 3, 4, 5, 8, 9, 10, 11, 12, 22, 23, 25, 26, 27, 60.
  7. Due Wednesday, November 11
    Finish reading Spherical Geometry.
    Do Spherical Geometry Exercises #31, 32-36, 38, 40-44, 50-53
  8. Due Friday, November 20
    Read Hyperbolic Geometry and The Three Geometries.
    Do Hyperbolic Geometry Exercises #1-9, 11, 12abce, 13abce, 16a, 18, 21-25.
  9. Due Monday, Dec. 7
    Read Depth and Perspective
    Do Depth and Perspective Exercises # 1-11

Course Information


  • Class Meets: MWF 12:00-12:50 in RH 323
  • 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.
    • Midterm: Friday, October 16
    • Final exam: Wednesday, December 9, 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: 20%
    • Attendance and in-class work: 20%
    • Art Projects: 30%
    • Exams: 30%


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 (8/24-8/28)

Rosette symmetry. Rotations, reflections. Symmetry groups.

Meet Escher Exploration. Symmetry of Stars and Polygons Exploration. Symmetry and Celtic Knots Exploration.

Week 2 (8/31-9/4)

Friday: Field trip to Pulitzer Arts

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

Week 3 (9/7-9/11)

Monday: Labor Day, no class.

Frieze Group Exploration. Frieze Names Exploration.

Week 4 (9/14-9/18)

Wallpaper symmetry. Wallpaper Exploration. Wallpaper Symmetry Exploration.

Week 5 (9/21-9/25)

Escher's Wallpaper Groups Exploration. Islamic Patterns Exploration. Potato Stamping Exploration.


Week 6 (9/28-10/2)

Monday: Symmetric Art Project due. Metamorphosis Exploration.

Wednesday: Power outage. Class cancelled.

Quadrilateral Tessellation Exploration.

Week 7 (10/5-10/9)

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

Week 8 (10/12-10/16)

Tessellations by Recognizable Figures.

Friday: Midterm Exam

Week 9 (10/19-10/23)

Monday: Fall Break, no class.

Spherical geometry. Spherical Geometry Exploration. Spherical Easel Exploration.

Week 10 (10/26-10/30)

Monday: Tessellation Art Project Lite due. Spherical tessellations. Spherical Triangles Exploration. Regular Spherical Tessellations Exploration.

Week 11 (11/2-11/6)

Platonic solids. Platonic Solids Exploration. Euler characteristic and duality. Duality Exploration.

Week 12 (11/9-11/13)

Hyperbolic geometry. Euler Characteristic Exploration. Hyperbolic Paper Exploration. Hyperbolic Geometry Exploration.

Week 13 (11/16-11/20)

Circle Limit Exploration. Hyperbolic Tessellations Exploration. The Schläfli Symbol Exploration.

Week 14 (11/23-11/27)

Monday: Non-Euclidean Art Project due. Rope Polyhedra Exploration

Wednesday, Friday: Thanksgiving break, no class.

Week 15 (11/30-12/4)

Depth Exploration. Perspective Exploration. Impossible Exploration.

Last day of class is Monday, 12/7. Evaluations. Review for final exam.

Final Exam Period (Wednesday, Dec 9, 12-1:50)

Exam 2