Course:SLU MATH 124: Math and Escher - Spring 2011 - Dr. Anneke Bart

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Course Information


  • Class Meets: TTh 2:15-3:30 in RH 316
  • Instructor:
    • Anneke Bart
    • Office: Ritter Hall 115
    • Office Hours: TTh 1-2 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.
  • 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:
    • Exam 2:
    • Final: Thursday May 12, 2:00-3:50
  • Grading is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. Grading is weighted as follows (a total of 1200 points):
    • Homework: 200 points
    • Attendance and in-class work: 200 points
    • Projects (2): 100 points each
    • Exams(2): 150 points each
    • Final: 300 points


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

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.


Schedule for MATH 124 - Spring 2011
Week Date Explorations Homework Comments
1 Jan 18-20 1) Symmetric Figures Exploration
2) Symmetry of Stars and Polygons Exploration
3) Symmetry in Escher's Work
Read M.C. Escher and Introduction to Symmetry
Homework Rosette Exercises nrs 2-6,8,10,11,14,18 (Due Tue Jan 25)
The goal for this week is to understand the classification of rosette symmetries.
2 Jan 25-27 1) Symmetry, Escher and Architecture Exploration
2) Frieze Group Exploration
3) Identifying Frieze Patterns Exploration
In Frieze Exercises do problems 1, 4, 6, 7, 8, 9
(Due Tue Feb 1)
This week we finish the rosette symmetry section and start on frieze groups (also known as border patterns).
3 Feb 1-3 1) Wallpaper Exploration
2) Wallpaper Symmetry Exploration
Read Frieze Patterns and Wallpaper Patterns. Tuesday class canceled due to inclement weather.
4 Feb 8-10 1) Tessellations, a first look Exploration
Tessellation Exploration: The Basics
Read Introduction to Tessellations and Tessellations by Polygons
5 Feb 15-17 1) Triangular Tessellations with GeoGebra
2) Quadrilateral Tessellations with GeoGebra
Homework for the Introduction to Tessellations handed out (due next Tuesday) Discuss the worksheets from last week. Some important results we have seen: * There are 3 regular tessellations (we will prove this later) * All parallelograms tessellate (and hence all squares and rectangles) * All triangles tessellate
6 Feb 22-24 1) Angles of Polygons and Regular Tessellations Exploration
2) Polyominoes Exploration
3) Escher-Like Tessellations Explorations
Read Tessellations by Recognizable Figures Thursday: Short reading quiz on Tessellations by Recognizable Figures
7 Mar 1-3 1)Tessellation Art Project Read Introduction to Non-Euclidean Geometry Tuesday: we will start on the Art Project.
Thursday: Exam I
8 Mar 8-10 1) Spherical Easel Exploration
2) Spherical Geometry: Polygons
3) Regular Spherical Tessellations Exploration
Read Spherical Geometry This is officially Midterm week, but there are no exams in MATH 124 this week. I may give a reading quiz.
9 Mar 15-17 No Class Spring Break' Midterm grades due March 15.
10 Mar 22-24 1) Polygons in Spherical and Euclidean Geometry Exploration Tessellation Art Project Due on Thursday.
11 Mar 29-31 1) Euler Characteristic Exploration
2) Platonic Solids Exploration
Spherical Geometry homework is due. Introduction to Hyperbolic Geometry
12 Apr 5-7 1) Escher's Circle Limit Exploration
2) Hyperbolic Paper Exploration
3) Hyperbolic Geometry Exploration
Read Hyperbolic Geometry
13 Apr 12-14 1) Start on Hyperbolic Homework
2) Perspective Exploration
Introduction to Depth and Perspective
14 Apr 19-21 1) Flatness Exploration
2) Impossible Figures and Escher Exploration
Read Depth and Perspective No class on Holy Thursday
15 Apr 26-28 No explorations this week Introduction to Egyptian Mathematics: History and Numbers, The Mathematical Papyri, and The Pyramids
Exam 2 on Thursday April 28
16 May 3-5 1. Egyptian Numbers Exploration Introduction to The Fourth Dimension
Showed a video of Dr Tom Banchoff speaking about Dali and the fourth dimension.
  • Copy of a previous Final This is a copy of the old final. Your final will of course look different, but this gives you some idea of the types of questions.