Course:SLU MATH 124: Math and Escher - Fall 2008 - Dr. Anneke Bart

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Homework and Reading Assignments

  1. Due Friday, August 29:
    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 Friday, September 12:
    Read Visions of Symmetry pg. 15-31.
    Read Frieze Patterns.
    Do Frieze Exercises # 1-9
  3. Due Friday, September 19:
    Read Visions of Symmetry pg. 31-40.
    Do Wallpaper Exercises # 1, 3, 8, 9, 10
  4. Homework for Monday Sep 22: Read Fundamental Concepts. You are not responsible for the optional section on reciprocals at the very end.
  5. Printer.svg Printable version of the fieldtrip checklist, dimmed: File:Cathedral-Fieldtrip2008.pdf

    Cathedral Fieldtrip is scheduled for Friday October 3. (Or on your own time.) We will use this Field trip assignment St. Louis Cathedral Basilica
    This assignment is due on Friday October 17.

  6. Exam 1 is scheduled for Friday October 10. Study Guide - Exam 1 - Bart-Fall08
    Recommended reading:
  7. The Tessellation Project is due Friday October 24. Read Tessellation Art Project. We will follow the following rubric: Course:Art Project Rubric - Bart 2008
  8. Write up solutions to problems 1 - 7: Spherical Geometry Exploration (due Monday Oct 27)
  9. Turn in solutions to Spherical Geometry: Polygons Friday October 31
  10. Homework assignment #1 for Spherical Geometry - handed out in class. Due Monday November 3, 2007

Course Information


Math and the Art of M.C. Escher
MWF 9:00 am - 9:50 am
Ritter Hall 316

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.

Math and the Art of M.C. Escher is an inquiry based course. Inquiry based courses depend on a process called Cooperative Learning. Some helpful facts are described on this page that will help you succeed andexcel in this course.

Contact Information

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

The best way to contact the instructor is via email.

Office hours:

  • Monday, Wednesday, Friday 10:30 - 11:30 am
  • Thursday 10 - 11 am
  • By appointment
  • Remember that you can always ask questions via email.


  • The online textbook Math and the Art of MC Escher, at
  • 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). Note that Flatland can also be found in its entirety on the internet. You may of course buy a hard copy if you prefer a book.


  • Two exams – 15% each
  • Tessellation Project – 10%
  • Basilica Cathedral Fieldtrip - 10%
  • Saint Louis Museum Fieldtrip - 5%
  • Homework, in-class work, attendance – 20%
  • Final – 25%

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.


Week 1 (Aug 25 - Aug 29) Symmetry and Rozette Patterns

Introduction to the course; First topic is "Symmetry"
Wednesday we do the Symmetry of Stars and Polygons Exploration and Rozette Symmetry Groups with Kali Exploration.

On Friday: Rotational and Reflectional Symmetry in Escher’s Sketches

On Friday Homework #1 is due: Read Visions of Symmetry pg. 1-15.
Read M.C. Escher and Introduction_to_Symmetry.
Do Rosette Exercises # 1-5, 8-12, 14

Week 2 (Sep 1 - Sep 5) Symmetry, Isometries, and Frieze Patterns

Monday September 1 is Labor Day: Official University Holiday

Start on Frieze patterns - also known as Borderpatterns. Use examples from earlier work to define reflections and translations. Discuss the difference between a symmetry and an isometry. Define translations and glide-reflections.

  • Do Frieze Names Exploration (Wednesday)
  • On Friday we discussed homework. Some important points to remember:
    • The homework prepares you for the exams. You need to solve all the problems assigned.
    • Starting early so that you can ask for help is very important.
    • Write up nice detailed solutions. Complete sentences should be the rule. Remember that you will be referring to your work when you study for exams. Write down enough so that your answers will be clear to you several weeks from now.

Week 3 (Sep 8 - Sep 12) Frieze Patterns and Intro to Wallpaper Patterns

This week read: Frieze Patterns

  • Homework #2 is due on Friday.

Week 4 (Sep 15 - Sep 19) Wallpaper Patterns

This week read: Wallpaper Patterns

Week 5 (Sep 22 - Sep 26) Tessellations and Isometries

Homework for Monday Sep 22: Read Fundamental Concepts. You are not responsible for the optional section on reciprocals at the very end.
Note: there may be a quiz on this reading assignment!

  • Angles of Polygons and Regular Tessellations Exploration
  • On Wednesday: Discussion of some theorems we now have:
    • Theorem 1: All parallelograms tessellate the plane.
      • Corollary (result that follows from the theorem): All rectangles and squares tessellate the plane.
    • Theorem 2: All triangles tessellate the plane.
    • Theorem 3: There are exactly 3 regular tessellations.
  • Friday: We will start on the Polyominoes Exploration. This exploration is assigned as homework and is due on Monday.

Week 6 (Sep 29 - Oct 3) Escher-like Tessellations and Geometer Sketchpad

Recognizable Figure Tessellations: Do the new version:

Week 7 (Oct 6 - Oct 10) Tessellations with Sketchpad

Week 8 (Oct 13 - Oct 17) Art Project Assignment and intro to Spherical Geometry


  • Go over the Art Project assignment.
  • Do Sketches for the Art Project Exploration. This exploration will likely not been finished in class. It will become part of the Art project (the sketch component).

Friday: Spherical Easel Exploration

Week 9 (Oct 20 - Oct 24)Spherical Geometry

Monday and Tuesday October 21/22: Fall Break

Week 10 (Oct 27 - Oct 31)Spherical Geometry

Homework: Write up solutions to problems 1 - 7: Spherical Geometry Exploration (due Monday)

  • Worked on assignments in class - including starting the spherical homework assignment.
  • Friday: Short session. Explanation of some of the problems on the homework assignment.

Week 11 (Nov 3 - Nov 7) Spherical Geometry

  • Monday: Q&A session about homework about spherical geometry.
  • Monday: Discussed possible topics to be covered at the end of the course. The options are:
    • Depth and Perspective. (Including Impossible Figures)
    • The 4th dimension and fractals.
    • History of Mathematics (Ancient Egypt in particular)
  • Friday: Introduction to Hyperbolic Geometry. Discuss the axioms.

Week 12 (Nov 10 - Nov 14) Hyperbolic Geometry

Week 13 (Nov 17 - Nov 21) Hyperbolic Geometry

Final Stretch of the Course

During the last two weeks students will explore topics according to their personal interests.

  • Depth. perspective and impossible figures

Kate B., Adam C., Michelle E., Katherine J., Amanda K., Tiffany S., Chris W.

  • The 4th dimension and Fractals

Albert X., Tom C.

  • History of Mathematics

Sarah B., Molly B., Lauren B., Jess D., Cassie H., Lizzy L., Spencer L., Dania S.

Week 14 (Nov 24 - Nov 28)

Week 15 (Dec 1 - Dec 5)

Week 16 (Dec 8)

Week 17 (Dec 15)

  • Art Museum Fieldtrip. Due on the day of the final. Details
  • Final - Monday December 15 during the first block 8 - 9:50 in RH 316

The final will consist of two sections:

  • An essay question comparing and contrasting Euclidean, spherical and hyperbolic geometry.
  • Question(s) about the special topic you chose at the end of the semester.

I will not ask any further questions on the final based on homework or explorations. This was already covered on the two exams. This will hopefully make the study process a bit easier and help with time management.