Course:SLU MATH 124: Math and Escher - Fall 2012 - Dr. Kim Druschel

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  • Class Meets: MWF 1:10-2:00 in RH 316
  • Instructor:
    • Dr. Kim Druschel
    • Office: RH 228
    • Office Hours: M 12:00 – 12:50, W,F 2:10-3:00 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 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: December 14, 12:00-1:50
  • 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 weighted as follows:
    • Homework: 15%
    • Attendance and in-class work: 15%
    • Projects (4): 25%
    • 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 (8/27-8/31)

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 31
    Read Visions of Symmetry pg. 1-15.
    Read M.C. Escher and Introduction to Symmetry.
  • Due Friday, September 7
    Do Rosette Exercises # 3,4,6,8,9,10,11,13,14

    Week 2 (9/3-9/7)

    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 Wednesday, September 12 Frieze Exercises # 1,2,3,5-10

    Week 3 (9/10-9/14)

    Wallpaper symmetry. 
    Wallpaper Exploration.Wallpaper Symmetry Exploration.
  • Due Friday, September 14
    Read Visions of Symmetry pg. 31-44, 77-78.
    Read Wallpaper Patterns.

    Week 4 (9/17-9/21)

    Continue work with Wallpaper symmetry.
  • Monday: Looked at flowchart for wallpaper groups; Did Wallpaper Symmetry Exploration.
  • Wednesday Bring your book. Bring your flowcharts with sketches of the wallpaper patterns.
  • Friday: Stamping (II) and wallpaper symmetry-wear something you don't mind getting ink on. Bring your sketches of four different wallpaper patterns from the same basic tile.Include something with a glide; something with three or six fold symmetry. You may want to use Escher Web Sketch.
  • Rosette Art project: Due Wednesday, October 3. Create two rosettes.See Symmetric Art Project for instructions.
  • Due Wednesday, September 26 Wallpaper Exercises # 1,4-9,10,12. Note change of due date and exercise numbers.

    Week 5 (9/24-9/28)

    Tessellations. Tessellations, a first look Exploration, Tessellation Exploration: The Basics. Angles of Polygons and Regular Tessellations Exploration.

  • By Friday. Read Fundamental Concepts, Introduction to Tessellations, Tessellations by Polygons
  • Rosette Art project: Due Friday, October 5. Create two rosettes.See Symmetric Art Project for instructions.
  • Homework, Due October 8,Polygonal Tessellation Exercises, 1-10

    Week 6 (10/1-10/5)

    Tessellations. Pattern Block Exploration.Archimedean Exploration.Polyominoes Exploration

  • 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 12.

    Week 7 (10/8-10/12)

  • Finish Polyomino Worksheet-due Wednesday 10/17
  • Read Tessellations by Polygons
  • Read Tessellations by Recognizable Figures.
  • In-class sketching. Escher-Like Tessellations Explorations
  • Escher Web Sketch applet from the Ecole Polytechnique Fédérale de Lausanne.
  • Project Due October 29. Make two friezes of different patterns and one wallpaper pattern. Frieze/Wallpaper Art Project
  • Due Monday, 10/15- two sketches of tessellations by recognizable figures from two different wallpaper groups
  • Due Friday, 10/19- six sketches of tessellations by recognizable figures from p1, p2, p4,p6 and two more different wallpaper groups. You can use the two you turned in on Monday as part of this group.

    Week 8 (10/15-10/19)

  • Spherical geometry. Spherical Geometry Exploration.
  • read Spherical Geometry
  • Quiz Wednesday
  • Six sketches due Friday

    Week 9 (10/22-10/26)

    Monday: Fall Break, no class.

  • Wednesday Spherical Easel Exploration
  • Exam Friday October 26
  • Remember project is due October 29

    Week 10 (10/29-11/2)

    Spherical Triangles Exploration. Spherical tessellations. Regular Spherical Tessellations Exploration. Spherical Geometry: Isometry Exploration. Platonic solids.

  • Tessellation by Recognizable Figures F2012 Due Friday November 16
  • Spherical Geometry Exercises 1-21 Due Friday November 9

    Week 11 (11/5-11/9)

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

    Week 12 (11/12-11/16)

    Hyperbolic geometry. Hyperbolic Geometry Exploration.

    Week 13 (11/19-11/23)

    Wednesday, Friday: Thanksgiving break, no class.Happy Thanksgiving! Hyperbolic geometry. Escher's Circle Limit Exploration.Hyperbolic Geometry II with NonEuclid Exploration
    Homework from hyperbolic geometry due Wednesday 12/5:problems 1-25:Hyperbolic Geometry Exercises. Project 4 Due December 10 (last day of class) Non-Euclidean Art Project

    Week 14 (11/26-11/30)

    Hyperbolic Tessellations Exploration. Ideal Hyperbolic Tessellations Exploration. Depth and perspective. Depth Exploration.

    Week 15 (12/3-12/7)

    Perspective Exploration. Impossible Exploration. Flatness Exploration. Wednesday: Exam 2 Homework from hyperbolic geometry due Wednesday 12/5:problems 1-25:Hyperbolic Geometry Exercises. Last day of class is Monday, 12/10.

    Final Exam (Friday, December 14, 12-1:50)