Course:SLU MATH 124: Math and Escher - Fall 2013 - Dr. Kim Druschel

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  • Class Meets: MWF 3:10-4:00 in RH 316
  • Instructor:
    • Dr. Kim Druschel
    • Office: RH 228
    • Office Hours: M,W,F 1:00 -2:00 or by appointment
    • You are always welcome to email me with questions or to set up an appointment.
    • Office Phone: 977-2804
    • 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 50% credit if the work is of reasonable quality.
  • Exams. I give makeup exams only for severe and documented reasons.
    • Exam 1:
    • Exam 2:
    • Final: Wednesday, December 11, 2:00-3:50
  • Grading Your letter grade is based on a percentage: 92% or greater earns an A, 88% or better an A-, 85% or better a B+, 82% or better a B, 78% or better a B- ,75% or better a C+,72% or better a C, 68% or better a C-, 60% or better a D, below 60% an F. Grading is tentatively weighted as follows:
    • Homework: 20%
    • Attendance and in-class work: 15%
    • Projects (3): 20%
    • Exams(2): 10% each
    • Final: 25%


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).

Classroom Policy

Any of the following could result in points deducted from your total score: The use of cell phones, computers, or other devices for any purpose other than the class. Rudeness to fellow students or the teacher. Tardiness or leaving early. If you have any concerns with the class or grading issues you are welcome to discuss this with me during my office hours.

Academic Integrity and Honesty

Students are expected to be honest in their academic work. The University reserves the right to penalize any student whose academic conduct at anytime is, in its judgment, detrimental to the University. The University is a community of learning, whose effectiveness requires an environment of mutual trust and integrity. Academic integrity is violated by any dishonesty such as soliciting, receiving, or providing any unauthorized assistance in the completion of work submitted toward academic credit. While not all forms of academic dishonesty can be listed here, examples include copying from another student, copying from a book or class notes during a closed book exam, submitting materials authored by or revised by another person as the student’s own work, copying a passage or text directly from a published source without appropriately citing or recognizing that source, taking a test or doing an assignment or other academic work for another student, securing or supplying in advance a copy of an examination or quiz without the knowledge or consent of the instructor, sharing or receiving the questions from an on-line quiz with another student, taking an on-line quiz with the help of another student, and colluding with another student or students to engage in academic dishonesty,the use of unapproved calculators or electronic devices on quizzes or exams.  All clear violations of academic integrity will be met with appropriate sanctions. In this course, academic dishonesty on an assignment will result in an automatic grade of 0 for that assignment and a report of academic dishonesty sent to the Academic Honesty Committee of the College of Arts and Sciences. In the case of Class B violations, the Academic Honesty Committee may impose a larger sanction including, but not limited to, assigning a failing grade in the course, disciplinary probation, suspension, and dismissal from the University. Students should refer to the following SLU website for more information about Class A and B violations and the procedures following a report of academic dishonesty:

Student Success Center Academic Support Statement

"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 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."

Undergraduate Grading Scale Grade Points

A 4.0 A- 3.7 B+ 3.3 B 3.0 B- 2.7 C+ 2.3 C 2.0 C- 1.7 D 1.0 F 0.0

Schedule / Assignments

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 (8/26-8/30)

Rosette symmetry. Rotations, reflections. Symmetry groups. Rotational and Reflectional Symmetry in Escher’s Sketches . Symmetric Figures Exploration. Symmetry of Stars and Polygons Exploration. Composition Exploration and the classification of rosette symmetries.

  • By Friday, August 30
    Read Visions of Symmetry pg. 1-15.
    Read M.C. Escher and Introduction to Symmetry.
  • Due Friday, September 6
    Do Rosette Exercises # 3,4,6,8,9,10,11,13,14

    Week 2 (9/2-9/6)

    Monday: Labor Day, no class. Frieze symmetry.Frieze Marking Exploration. Frieze Group Exploration.Frieze Names Exploration.

  • Due Friday, September 7
    Read Visions of Symmetry pg. 15-31.
    Read Frieze Patterns.
  • Hand in Friday, September 13 Frieze Exercises # 1,2,3,5-10

    Week 3 (9/9-9/13)

    Wallpaper symmetry. Wallpaper Exploration.Wallpaper Symmetry Exploration.

  • Due Friday, September 13
    Read Visions of Symmetry pg. 31-44, 77-78.
    Read Wallpaper Patterns.

    Week 4 (9/16-9/20)

    Continue work with Wallpaper symmetry.
  • Monday: Looked at flowchart for wallpaper groups; Did Wallpaper Symmetry Exploration.
  • Wednesday Worked on worksheet for Wallpaper groups with order three, four, or six symmetry. Did "dance" for two WP groups-need more space!
  • Friday: Stamping (II) and wallpaper symmetry-wear something you don't mind getting ink on. Bring your sketches of two different wallpaper patterns and two basic motifs. Write a recipe for how you would create the wallpaper pattern from the basic motif. You may want to use Escher Web Sketch.
  • Rosette/Frieze Art project: Due Friday, October 11. Create two rosettes and one frieze.See Symmetric Art Project for instructions.
  • Due Friday, September 27 Wallpaper Exercises # 1-3,5-11,13,14.

    Week 5 (9/23-9/27)

    Finish printmaking Tessellations. Tessellations, a first look Exploration, Tessellation Exploration: The Basics.

  • By Friday. Read Fundamental Concepts, Introduction to Tessellations, Tessellations by Polygons
  • Rosette/Frieze Art project: Due Friday, October 11. Create two rosettes and one Frieze.See Symmetric Art Project for instructions.

    Week 6 (9/30-10/4)

    Tessellations. Angles of Polygons and Regular Tessellations Exploration.Pattern Block Exploration.Archimedean Exploration

    Week 7 (10/7-10/11)

  • Read Tessellations by Polygons
  • Read Tessellations by Recognizable Figures.
  • Wednesday -trip to the Cathedral Basilica of Saint Louis [1] [2] Meet outside the Cathedral at around 1:00. You can take the Lindell bus to and from the Cathedral. Worksheet for Cathedral trip. Be sure to bring a camera.Report due October 18.
  • Homework, Due Wednesday, October 23,Polygonal Tessellation Exercises, 1-13

    Week 8 (10/14-10/18)

    Finish semi-regular tessellation worksheet
  • In-class sketching. Escher-Like Tessellations Explorations
  • Escher Web Sketch applet from the Ecole Polytechnique Fédérale de Lausanne.
  • Due Friday, 10/1618- two sketches of tessellations by recognizable figures from two different wallpaper groups
  • Spherical geometry. Spherical Geometry Exploration.
  • read Spherical Geometry

    Week 9 (10/21-10/25)

    Monday: Fall Break, no class.

  • Spherical Easel Exploration

    Week 10 (10/28-11/1)

  • Exam Monday, October 28 Spherical Triangles Exploration. Spherical tessellations. Regular Spherical Tessellations Exploration. Spherical Geometry: Isometry Exploration. Platonic solids.
  • Tessellation by Recognizable Figures F2012 Due Friday November 15
  • Spherical Geometry Exercises 1,3-8,11,13-20,23,40 Due Wednesday November 13

    Week 11 (11/4-11/8)

    Euler characteristic and duality. Platonic Solids Exploration. Duality Exploration.Euler Characteristic Exploration.

    Week 12 (11/11-11/15)

    Hyperbolic geometry. Hyperbolic Geometry Exploration.

    Week 13 (11/18-11/22)

    Hyperbolic geometry. Escher's Circle Limit Exploration.Hyperbolic Geometry II with NonEuclid Exploration
    Homework from hyperbolic geometry due Wednesday 12/4:problems 1-25:Hyperbolic Geometry Exercises. Project 3 Due December 11 (last day of class) Non-Euclidean Art Project

    Week 14 (11/25-11/29)

    Wednesday, Friday: Thanksgiving break, no class.Happy Thanksgiving! [[Hyperbolic Tessellations Exploratio n]]. Ideal Hyperbolic Tessellations Exploration. Depth and perspective. Depth Exploration.

    Week 15 (12/2-12/6)

    Perspective Exploration. Impossible Exploration. Flatness Exploration. Wednesday: Exam 2 Homework from hyperbolic geometry due Wednesday 12/4 :problems 1-25:Hyperbolic Geometry Exercises. Last day of class is Monday, 12/9.

    Final Exam (Wednesday, December 11, 2:00-3:50)