Course:SLU MATH 124: Math and Escher - Fall 2007 - Dr. Anneke Bart

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General Information

Class Time: 9:00 am - 9:50 am MWF

Where: Ritter Hall 225

Contact Information: • Office: Ritter Hall 115 • Email: • Phone: (314) 977-2852


  • M.C. Escher: Visions of Symmetry by D. Schattschneider. W.H. Freeman and Company (1990)
  • Flatland: A romance of many dimensions by E.A. Abbott, Dover Publ. (1992).
  • Recommended: The Magic of M.C. Escher. (On sale in the bargain section of Barnes and Nobles for $20.)

Prerequisite: 3 years of high school mathematics or MT A 120 (College Algebra).

Course Goals

  1. Develop an intuitive understanding of geometry by looking at examples and applications in art (mainly Escher’s work, but also some other modern artists).
  2. Develop a thorough understanding of the concepts and techniques of geometry.
  3. Further develop the ability to apply your knowledge of geometry to solve unfamiliar problems.
  4. (Further) develop skills for working effectively with others on mathematics problems.


  • One exam – 20%
  • Tessellation Project – 10%
  • Basilica Cathedral Fieldtrip - 10%
  • Flatland and the fourth dimension project - 7%
  • Saint Louis Museum Fieldtrip - 8%
  • Homework and in-class work – 20%
  • Final – 25%

Final: Monday December 17 8:00 am – 9:50 am

Grades: 93-100 A, 89-92 A-, 86-88 B+, 82-85 B, 80-81 B- 77-79 C+, 70-76 C, 60-69 D, 0-59 F

Curve: I do not technically grade on a curve, but your work will of course be compared to that of your classmates, and even to students who have taken the class before you. To give an example: when evaluating answers that require an explanation, I will collect all the answers I consider “A-level” and then rank them. If the question is worth 20 points, an A is somewhere between 18 and 20 points. The best answers will receive 20 points, the next best group will receive 19 points, and the others 18. They are all awarded an A, but the best answers receive a few more points. If someone writes answers that are truly excellent, then I will award extra credit.

How to do well: Attendance and participation is extremely important. Missing class regularly causes students quite a bit of trouble. It is very hard to make up this material on ones own.

Further Information: See complete Syllabus.

Homework and Reading Assignments


The schedule below is a tentative schedule.

Week of August 27 - Euclidean Geometry

Introduction to the course. The first week we will do some exploration that will show you how to explore mathematics in this course. We will look at some triangles and quadrilaterals and finish the week by taking a first look at geometric tessellations.



  • Read the Fundamental Concepts with special attention to triangles, quadrilaterals and convexity.
  • Read Schattschneider page 1-19

Week of September 3 - Symmetry

One of the first topics we will cover is symmetry. We will discuss bilateral (reflectional) and rotational symmetry. We will examine some of Escher's prints and discover that symmetry is often present in his artwork.




  • Monday September 3 Labor Day: Official University Holiday
  • Friday September 7 Last day to drop without a "W"

Week of September 10 - Introduction to Border Patterns and Wallpaper Groups



Week of September 17 - Basic Tessellations


  • Read Schattschneider page 19-34

Week of September 24 - More Tessellations


Week of October 1 - Escher’s tessellation



Week of October 8 - Tessellation Art Project

  • Monday: Come up with ideas for the Tessellation Art Project. Have students start on the set of preliminary sketches that are part of the assignment. We will use the Sketches for the Art Project Exploration
  • Wednesday: Answer any remaining questions about the Tessellation Art Project. Introduce Non-Euclidean Geometry. Discuss Axioms.
  • Friday: Spherical Easel Exploration

Week of October 15 - Non-Euclidean Geometry: Spherical Geometry

Read: Spherical Geometry

Week of October 22 Spherical Geometry Continued

Week of October 29 Hyperbolic Geometry

Fri November 2 Last Day to Withdraw

Week of November 5 Hyperbolic Geometry Continued

Week of November 12 Hyperbolic Geometry, Similarity and Fractals

Week of November 19 More Fractals

Week of November 26 Fractals and Flatland

Week of December 3 The Fourth Dimension and the Möbius Strip

  • Monday, December 10th: No Class.

The Saint Louis Art Museum paper is due on the day of the Final - December 17, 2007.

Final Exam

The final exam is on Monday December 17, 2007 8 a.m. - 9:50 a.m. in Ritter Hall 225 The exam is cumulative. It may help to follow this study guide: Study Guide - Final - Bart-Fall07