# Course:SLU MATH 1240: Math and Escher - Fall 2015 - Dr. Anneke Bart

## Contents

## General Information

**Class Time:** 1:10 - 2:00 pm Monday, Wednesday, Friday

**Where:** TBD

**Contact Information:**
• **Office:** Ritter Hall 227
• **Email:** barta@slu.edu
• **Phone:** (314) 977-2852 (I prefer email!)

**Books:**

- M.C. Escher: Visions of Symmetry by D. Schattschneider. W.H. Freeman and Company (1990)

**Prerequisite:** A Math Index greater than or equal to 750 or a course at the level of College Algebra.

**Course Goals**

- Develop an intuitive understanding of geometry by looking at examples and applications in art (mainly Escher’s work, but also some other modern artists).
- Develop a thorough understanding of the concepts and techniques of geometry.
- Further develop the ability to apply your knowledge of geometry to solve unfamiliar problems.
- (Further) develop skills for working effectively with others on mathematics problems.

**Grading:**

- Two exam – 10% each
- Projects Portfolio – 20%
- Basilica Cathedral Fieldtrip
- 3 small creative projects based on the material for border patterns, wallpaper patterns, and non-Euclidean geometry.
- Saint Louis Museum Fieldtrip

- Homework and in-class work – 30% (Attendance is considered part of your in-class grade.)
- Final – 30%

**Final:**

- The schedule for all your final exams can be found online: final exam schedule
- For this course the Final is on
**Friday December 11 from 12 pm until 1:50 pm**.

**Grades:**
Grades are determined by your mastery of the material. The following cut-offs are the standard grades for mathematics courses.
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.

**Further Information:** See complete Syllabus.

## Schedule, Assignments, etc.

**Week 1 (Aug 24-28)**

- Go over syllabus, website and BBLearn
- Read Introduction to Symmetry
- Class: Symmetry of Stars and Polygons Exploration (Wednesday)
- Class: Rotational and Reflectional Symmetry in Escher’s Sketches
**Homework due Monday**: Rosette Exercises # 2, 3, 4, 5, 6. Write up your answers carefully. Explain your thinking. Usually just "yes", "no" or other short answers are not adequate. Homework should be stapled if there are multiple pages.

**Week 2 (Aug 31-Sep 4)**

- Monday:
- Symmetry and Celtic Knots Exploration Understand what Cn and Dn groups are.
- Symmetric Figures Exploration Use Silk - bottom of page - to explore the different patterns. Make sure to explore the controls.

- Wednesday
- We discussed the symmetry groups for Frieze patterns and how to find them.
- We started on Identifying Frieze Patterns Exploration

- Friday
- Discuss the Exploration that was due
- Homework: from Rosette Exercises do # 6, 7, 8, 13, 19 and from Frieze Exercises do # 1, 3, 6

**Week 3 (Sep 7 - 11)**

- Monday: Labor Day Holiday
- Wednesday: Do Frieze Group Exploration and Frieze Names Exploration problems 1 and 2.
- Friday: Due today are
- Identifying Frieze Patterns Exploration
- Rosette Exercises do # 6, 7, 8, 13, 19 and from Frieze Exercises do # 1, 3, 6
- Frieze Group Exploration

- Friday we will do Frieze Names Exploration problems 1 and 2 (left from last period) and start on Wallpaper Patterns
- Homework 2 is assigned: Rosette Exercises # 10, 12, 13 Frieze Exercises # 7, 8, 9 Wallpaper Exercises # 1 (due Monday)

**Week 4 (Sep 14 - 18)**

- Monday
: Rosette Exercises # 10, 12, 13 Frieze Exercises # 7, 8, 9 Wallpaper Exercises # 1**Homework 2 is due**- Go over Tessellations

- Wednesday: Polygonal tessellations. Discuss why all parallelograms tesselate the plane, why do all triangles tessellate the plane, etc.
- Friday: Polyominoes Exploration

**Week 5 (Sep 21 - 25)**

- Monday: Angles of Polygons and Regular Tessellations Exploration
- Wednesday: Tessellations by Recognizable Figures (see handout). Based on this page: Escher-Like Tessellations Explorations
- Friday: Islamic Patterns Exploration
- Homework Polygonal Tessellations is due.

**Week 6 (Sep 28 - Oct 2)**

- Monday: Read the section on Tessellations by Recognizable Figures
- Wednesday: Power outage - Class cancelled.
- Friday: Explore the regular and semi-regular tessellations on the Sphere. We used Kaleidotile.

**Week 7 (Oct 5 - Oct 9)**

- Monday:
- Short lecture on angle defects and fraction of a sphere covered by triangles.
- Spherical Triangles Exploration

- Wednesday:
**Tessellation project is due**- Spherical Geometry Exploration

- Friday:
- Regular Spherical Tessellations Exploration
**Reading assignment spherical geometry - Part 2 is due.****Homework Spherical geometry due: From Spherical Geometry Exercises # 3, 8, 11, 20, 22**

**Week 8 (Oct 12 - Oct 16)**

- Monday: Platonic Solids Exploration and Duality Exploration
- Wednesday: Exam 1 On general tessellations and topics covered in Spherical geometry.
- Friday: Euler Characteristic Exploration

**Week 8 (Oct 19 - Oct 23)**

- Monday:
**Fall Break - no class** - Wednesday:
- Friday: