Course:SLU MATH 124: Math and Escher - Fall 2009 - Dr. Anneke Bart

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Course Information


  • Class Meets: MWF 9:00-9:50 in RH 316
  • Instructor:
    • Anneke Bart (
    • Office: Ritter Hall 115
    • Office Hours: MW 1-2 and Tue 9-10 or by appointment.
    • Email:
  • 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. Being late twice or leaving early counts as an absence.
  • 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: TBA
    • Exam 2: TBA
    • Final: Monday December 14. Time: 8:00 - 9:50. Place: RH 316
  • Grading is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. Grading is weighted as follows:
    • Exams: two @15% each
    • Homework and in-class work: 20%
    • Tessellation Project: 10%
    • Cathedral Poster Assignment: 10%
    • Final: 30% (the final is comprehensive)


The main text for this course is the Math and the Art of MC Escher online book, at

One traditional textbook is required for the course:

  • D. Schattschneider, Visions of Symmetry. H. Abrams 2004. (The paperback 1990 edition is also acceptable).


Students are expected to be honest in their academic work, as per the 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.

Homework Assignments

On Friday August 28, 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 (Extension given)

Due Wednesday, September 9: Homework #2
Read Visions of Symmetry pg. 15-31.
Read Frieze Patterns.
Do Frieze Exercises # 1-9

Homework #3: Due Wednesday September 23, 2009
File:Homework3-wallpaper.pdf Available for download.

Homework #4: Due Monday September 28

  • Create 2 interesting tessellations using the techniques described on the page. Use two different techniques, and do not just copy what is used as an example on the page. The tessellation should show recognizable figures: plants, animals, objects, etc.
  • Give a short 1 paragraph description of how you made each of the tessellations.
  • Identify the Symmetry Group.

Cathedral Basilica Project: Due Friday October 23.
for details see: Cathedral Basilica Field Trip and Poster Assignment

Tessellation Project: Due Monday November 3.
for details see: Tessellation Project Fall 2009 - Bart

Spherical Geometry: Homework Part I
Due Wednesday November 4. Download pdf here: File:SphericalHW-P1.pdf
Note that the handout gives the due date as being Monday. This was extended to Wednesday.

Spherical Geometry: Homework Part II
Due Monday November 9. Download pdf here: File:Spherical Geometry Homework2.pdf


This tentative schedule will give you some idea of what topics to expect. As the course develops, adjustments will be made if necessary.

Week 1: Introduction, Symmetry

August 24 - 28

Week 2: Symmetry, Isometries, and Frieze Patterns

August 31 - September 4

(Fri September 4 Last day to drop without a "W")

Week 3: Wallpaper Patterns

September 7 - 11

  • Monday: Labor Day: Official University Holiday
  • Wednesday: An introduction to wallpaper patterns Tessellations, a first look Exploration
  • Friday: Went over border patterns and discussed some problems from homework 2.

Some points to remember:

  • Start homework early, so you have time to ask questions.
  • Anything on homework or explorations can show up on an exam.
  • Always explain your answer. You will need to explain yourself on any exam to get full credit, but apart from that it is a good idea to explain how you arrived at your conclusions. It will be easier to assign partial credit if more information is given, and it will also be easier for the instructor to give feedback in case there is some confusion.

Week 4: Wallpaper Patterns

September 14 - 18

Week 5: Tessellations and Isometries

September 21 - 25

Week 6: Escher-like Tessellations and Geometer Sketchpad

September 28 - October 2

  • Friday we start on Sketches for the Art Project Exploration. The precise assignment will be given later. This exploration will help you create a collection of sketches to choose your final art project from.

Week 7: Exam I, Field Trip and Intro to Spherical Geometry

October 5 - 9

Week 8: Art Project Assignment and intro to Spherical Geometry

October 12 - 16

(October 12-17 Midterm Exams - Note: we do not necessarily have an exam this week)

Week 9: Spherical Geometry

October 19 - 23

Week 10: Spherical Geometry

October 26 - 30

(Fri October 30 Last Day to Withdraw)

Week 11: Spherical Geometry

November 2 - 6

  • Spherical Triangles Exploration
  • We went over Spherical versus Euclidean Polygons Exploration and looked at the different definitions from Euclidean geometry and compared them to the definitions we (could) use in spherical geometry.
  • We looked at Kaleidotile in class. We found regular and semi-regular tessellations on the sphere. There are 5 regular tessellations on the sphere (as opposed to 3 in the plane), and we found at least 10 semi-regular tessellations (as opposed to only 8 in the plane).
  • We did the Platonic Solids Exploration

Week 12: Hyperbolic Geometry

November 9 - 13

Week 13: Hyperbolic Geometry

November 16 - 20

During this week we worked on a variety of explorations:

And we worked on the homework.

Week 14: Hyperbolic Geometry

November 23 - 27

  • Monday:
  • Wednesday: Thanksgiving: Official University Holiday
  • Friday: Thanksgiving: Official University Holiday

Week 15: Depth, Perspective and Impossible Figures

November 30 - December 4

Week 16: Review for Final

  • Monday December 7: Last Day of Class and Review