Difference between revisions of "Course:SLU MATH 124: Math and Escher - Spring 2012 - Dr. Bryan Clair"

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===Week 14 (4/23-4/27)===
===Week 14 (4/23-4/27)===
[[Non-Euclidean Art Project]] due Monday. [[Hyperbolic Tessellations Exploration]].  Depth and perspective.  [[Depth Exploration]].
[[Non-Euclidean Art Project]] due Monday 4/23.
[[Hyperbolic Tessellations Exploration]].  Depth and perspective.  [[Depth Exploration]].
===Week 15 (4/30-5/4)===
===Week 15 (4/30-5/4)===

Latest revision as of 10:15, 17 May 2012


This course is over.


  1. Due Friday, January 27
    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, February 3
    Read Visions of Symmetry pg. 15-31.
    Read Frieze Patterns.
    Do Frieze Exercises # 1,2,3,5-10
  3. Due Friday, February 10
    Read Visions of Symmetry pg. 31-44, 77-78.
    Read Wallpaper Patterns.
    Do Wallpaper Exercises # 1-7,9,10,12
  4. Due Friday, February 17
    Read Visions of Symmetry pg. 44-52
    Do Symmetric Art Project
  5. Due Wednesday, February 22
    Read Fundamental Concepts (if needed), Introduction to Tessellations, begin Tessellations by Polygons
    Do Polygonal Tessellation Exercises # 2,3,4,6,12,13,14
  6. Due Friday, March 2
    Read Tessellations by Polygons, Tessellations by Recognizable Figures
    Do Polygonal Tessellation Exercises # 7, 8, 9, 10, 11, 15
  7. Due Friday, March 23
    Read Aperiodic Tessellations
    Do Aperiodic Tessellation Exercises # 1,2-8
  8. Due Friday, March 30
    Read Visions of Symmetry pg 243-247
    Begin reading Spherical Geometry.
    Do Spherical Geometry Exercises #1-5, 8-12, 16, 17, 19, 38, 43ab
  9. Due Monday, April 16
    Finish reading Spherical Geometry.
    Do Spherical Geometry Exercises #22-30, 13, 20, 32, 33, 39, 42, 44
  10. Due Monday, April 30
    Read Visions of Symmetry pg. 247-254
    Read Hyperbolic Geometry and The Three Geometries.
    Do Hyperbolic Geometry Exercises #1-9, 11*, 12*, 13*, 18. For the * exercises, skip the part about area.
  11. Not due - recommended to look over
    Read Depth and Perspective
    Do Depth and Perspective Exercises # 1, 2, 4-11

Course Information


  • Class Meets: MWF 12:00-12:50 in RH 316
  • Instructor:
    • Bryan Clair (http://math.slu.edu/~clair)
    • Office: Ritter Hall 110
    • Office Hours: Wed 1-2, Th 10:30-11:30, Fri 10-11 or by appointment.
    • Email: bryan@slu.edu
  • 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: Friday, Feb 24
    • Exam 2: Wednesday, April 4
    • Final exam: Friday, May 11, 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 http://math.slu.edu/escher

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 http://www.slu.edu/success. 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 (1/16-1/20)

Monday: No class, MLK. Rosette symmetry. Rotations, reflections. Symmetry groups. Symmetric Figures Exploration. Symmetry of Stars and Polygons Exploration.

Week 2 (1/23-1/27)

Composition Exploration and the classification of rosette symmetries. Frieze symmetry. Frieze Marking Exploration, Frieze Group Exploration.

Week 3 (1/30-2/3)

Frieze Names Exploration. Wallpaper symmetry. Wallpaper Exploration. Wallpaper Symmetry Exploration.

Week 4 (2/6-2/10)

Square Block Pattern Exploration. Potato Stamping Exploration.

Week 5 (2/13-2/17)

Islamic Patterns Exploration. Tessellations. Metamorphosis Exploration. Quadrilateral Tessellation Exploration.

Symmetric Art Project due Friday 2/17.

Week 6 (2/20-2/24)


Friday: Exam 1.

Week 7 (2/27-3/2)

Angles of Polygons and Regular Tessellations Exploration. Tessellations by Recognizable Figures.

Week 8 (3/5-3/9)

Non-periodic tessellations. Substitution Tessellation Exploration, Penrose Tiling Exploration

Tessellation Art Project Lite due Friday 3/9.

Spring Break (3/12-3/16)

Week 9 (3/19-3/23)

Spherical geometry. Spherical Geometry Exploration. Using Spherical Easel.

Week 10 (3/26-3/30)

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

Week 11 (4/2-4/6)

Wednesday: Exam 2. Friday: Good Friday, no class

Week 12 (4/9-4/13)

Monday: Easter, no class Euler characteristic and duality. Platonic Solids Exploration. Duality Exploration.

Week 13 (4/16-4/20)

Hyperbolic geometry. Hyperbolic Paper Exploration. Escher's Circle Limit Exploration.

Week 14 (4/23-4/27)

Non-Euclidean Art Project due Monday 4/23.

Hyperbolic Tessellations Exploration. Depth and perspective. Depth Exploration.

Week 15 (4/30-5/4)

Perspective Exploration. Flatness Exploration. Impossible Exploration.

Last day of class is Monday, 5/7. Review for final exam.

Final Exam Period (Friday, May 11, 12-1:50)

Visual Deception Project due.