Course:SLU MATH 124: Math and Escher - Fall 2009 - Philip Huling

From EscherMath

Contents 1 Course Information 1.1 General 1.2 Grading 1.3 Textbooks 1.4 Honesty 2 Schedule 2.1 Week 1: Introduction, Symmetry 2.2 Week 2: Symmetry, Isometries, and Frieze Patterns 2.3 Week 3: Frieze Patterns and Intro to Wallpaper Patterns 2.4 Week 4: Wallpaper Patterns 2.5 Week 5: Tessellations and Isometries 2.6 Week 6: Escher-like Tessellations and Geometer Sketchpad 2.7 Week 7: Spherical Geometry 2.8 Week 8: Art Project Assignment and Spherical Geometry 2.9 Week 9: Spherical Geometry 2.10 Week 10: Spherical Geometry 2.11 Week 11: Spherical Geometry 2.12 Week 12: Hyperbolic Geometry 2.13 Week 13: Hyperbolic Geometry 2.14 Week 14: TBD 2.15 Week 15: TBD 2.16 Week 16: Review for Final

Course Information

General

• Class Meets: MWF 1:10-2:00 PM in RH 316
• Instructor:
  • Philip Huling (http://math.slu.edu/~hulingpc)
  • Office: RH 23
  • Office Hours: W 11:10 AM - 1:00 PM and F 12:10 - 1:00 PM or by appointment.
  • Email: hulingpc@slu.edu
• Prerequisite: 3 years of high school mathematics or Math 120 (College Algebra).

Grading

• Attendance is required. You will have in-class work to be done in groups. One unexcused absence is allowed. Every subsequent unexcused absence will result in a 5% drop of your Attendance and in-class work grade. I only excuse absences when presented with official documentation.
• Homework will be due weekly. Your work should be neat, legible, stapled, and not have spiral edges attached. 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 4 (out of 10) if the work is of reasonable quality.
• Exams. Make-up exams will only be given if a severe emergency is occurs. I must receive contact about the situation within 24 hours of the start of the exam. Documentation will be required when the make-up is given.
  • Exam 1: TBA
  • Exam 2: TBA
  • Final: Friday December 11th, 2009 from noon until 1:50 PM in 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%
  • Escher Photo Scavenger Hunt: 10%
  • Final: 30% (the final is comprehensive)

Textbooks

The main text for this course is the Math and the Art of MC Escher online book, at http://math.slu.edu/escher

One traditional textbook is required for the course:

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

Honesty

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.

Schedule

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

• Monday: Introduction to the course; First topic is "Symmetry"
  
• Wednesday: Do the Symmetry of Stars and Polygons Exploration and Rozette Symmetry Groups with Kali Exploration.
• Friday: Rotational and Reflectional Symmetry in Escher’s Sketches and Symmetry, Escher and Architecture Exploration.

On Friday 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

Week 2: Symmetry, Isometries, and Frieze Patterns

August 31 - September 4

• Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration Frieze Marking Exploration

• Wednesday: Class canceled.

• Friday: Class with Dr. Bart.

CHANGE: Homework #2 is now due on Friday September 11th:

Read Visions of Symmetry pg. 15-31.
Read Frieze Patterns.
Do Frieze Exercises # 1-9

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

Week 3: Frieze Patterns and Intro to Wallpaper Patterns

September 7 - 11

• Monday: Labor Day: Official University Holiday

• Wednesday: Do Frieze Names Exploration, an introduction to wallpaper patterns, and do/start Tessellations, a first look Exploration

• Friday: Continue Tessellations, a first look Exploration

Homework #2 is due on Friday September 11th:

Read Visions of Symmetry pg. 15-31.
Read Frieze Patterns.
Do Frieze Exercises # 1-9

Week 4: Wallpaper Patterns

September 14 - 18

• Monday: Begin wallpaper groups discussion and do Wallpaper Exploration.

• Wednesday: Finish powerpoint, then do Tiling Worksheet and start Wallpaper Symmetry Exploration

• Friday: Escher's Wallpaper Groups Exploration

Homework #3 is due on Friday September 18th:

Read Visions of Symmetry pg. 31-44, 77-78.
Read Wallpaper Patterns.
Do Wallpaper Exercises # 1-7, 9, 10

Week 5: Tessellations and Isometries

September 21 - 25

• Monday: Short lecture about some terminology we need. Do Tessellation Exploration: The Basics
• Wednesday: Do Angles of Polygons and Regular Tessellations Exploration
• Friday: Short introduction to Tessellations by Recognizable figures, and do Escher-Like Tessellations Explorations

Week 6: Escher-like Tessellations and Geometer Sketchpad

September 28 - October 2

• Your assignment for this week is to do the following three Geometer Sketchpad Explorations at your own pace. The first part of the Introductions to GSP Exploration is heavily based on and inspired by materials developed by Mike Riedy.
• GSP Introduction Exploration
• GSP Quadrilateral Tessellation Exploration
• GSP Triangle Tessellation Exploration

• Exam 1 is scheduled for Monday October 5
  • Study Guide - Exam 1 - Bart-Fall09

Week 7: Spherical Geometry

October 5 - 9

• Friday - Weekend Group Scavenger Hunt Assignment and Spherical Geometry Exploration

Week 8: Art Project Assignment and Spherical Geometry

October 12 - 16

• Monday: Spherical Easel Exploration and project discussion

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

Week 9: Spherical Geometry

October 19 - 23

• Monday: Fall Break
• Wednesday: The Axioms of Spherical Geometry Exploration
• Friday: Catch-up day and short lecture/discussion

Homework: Read Spherical Geometry up to Platonic Solids

Week 10: Spherical Geometry

October 26 - 30

• Monday: Escher Photo Scavenger Hunt project DUE Definition discussion and exploration.
• Wednesday: Do/finish Spherical_versus_Euclidean_Polygons_Exploration and discuss Tessellation Art Project
• Friday: Angle defect discussion and then Regular Spherical Tessellations Exploration

Homework Sheet handed out. Will be due on Monday November 2nd

(Fri October 30 Last Day to Withdraw)

Week 11: Spherical Geometry

November 2 - 6

• Monday: Catch-up day and powerpoint presentation.
• Wednesday: Platonic Solids Exploration and Spherical Triangles Exploration
• Friday: Duality Exploration and Hyperbolic Geometry Powerpoint

Week 12: Hyperbolic Geometry

November 9 - 13

• Monday: Escher's Circle Limit Exploration
• Wednesday: Worksheet and Hyperbolic Geometry Exploration
• Friday: Hyperbolic Tessellations Exploration and Ideal Hyperbolic Tessellations Exploration

• Friday: Art Project Due

Week 13: Hyperbolic Geometry

November 16 - 20

Week 14: TBD

November 23 - 27

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

Week 15: TBD

November 30 - December 4

Week 16: Review for Final

• Monday December 7: Last Day of Class and Review