Course:SLU MATH 124: Math and Escher - Fall 2010 - Philip Huling

Course Information

General

• Class Meets: MWF 9:00-9:50 PM in RH 225
• Instructor:
  • Dr. Philip Huling
  • Office: RH 23
  • Office Hours: MWF 10:00 am – 10:50 am and Noon – 12:50 pm or by appointment.
  • Email: hulingpc@slu.edu
• Prerequisite: 3 years of high school mathematics or Math 120 (College Algebra).

Grading

• Attendance. Attendance is required. You will have in-class work to be done in groups. Two unexcused absences are allowed. The next unexcused absence will result in a 1% drop of your Attendance and in-class work grade. The following unexcused absence will result in a 2% drop, 3% drop after that, and so on. I only excuse absences when presented with official documentation. Also, any in class work done on a day of unexcused absence will be given a zero.
• Homework/Quizzes. There will be problems attached to many, if not all, of the explorations. These will never be turned in, but will be used as part of an open note quiz given every other Friday. It is the expectation that the student will go over their explorations regularly to thoroughly understand the material outside of class. The quizzes will be made up of questions from the explorations, but complete sentences and thorough answers will be required. There will also be additional homework sets assigned periodically. All turned in homework must be either typed or neatly written up. Any spiral edges must be removed and pages must be stapled if there are more than 1. It is expected that you start the homeworks early enough to ask questions and spend enough time working on them to give sufficient answers.
• Exams. There will be 2 exams given throughout the semester. If you miss an exam, you will be given a 0 unless you can give strong written evidence, documenting an unavoidable emergency, presented within 24 hours of the start of the exam. PLEASE email me or have someone else email me as soon as possible if such an emergency arises. In such a situation, your grade on the final would be used to fill in the missing exam score.
  • Exam 1: TBA
  • Exam 2: TBA
  • Final: Monday December 13th, 2010 from 8:00 AM until 9:50 PM in RH 225
• Grading is on a straight scale, with 90%,80%,70%,60% guaranteeing A,B,C,D. Grading is weighted as follows:
  • Homework/Quizzes: 30%
  • Attendance and participation: 10%
  • Projects: two @15% each
  • Exams: three @10% each

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 23 - 27

• 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.

By Friday: Read M.C. Escher and Introduction_to_Symmetry

• Friday: Rotational and Reflectional Symmetry in Escher’s Sketches and Symmetry, Escher and Architecture Exploration.

Week 2: Symmetry, Isometries, and Frieze Patterns

August 30 - September 3

• Monday: Rosette Group recap & Introduction to Frieze patterns. Do exploration Frieze Marking Exploration. This is mainly a review of what we covered today.
• Wednesday: Do Frieze Names Exploration and Identifying Frieze Patterns Exploration.
• Friday: Quiz #1 then Frieze and Rosette Group Scavenger Hunt.

On Monday Homework #1 is due: Do Rosette Exercises # 1-5, 7-12, 14, 16 (omit 9a-c)

By Wednesday: Read Frieze Patterns

(Fri September 3 Last day to drop without a "W")

Week 3: Frieze Patterns and Intro to Wallpaper Patterns

September 6 - 10

• Monday: Labor Day: Official University Holiday

• Wednesday: Homework #1 review and Wallpaper Introduction

• Friday: Wallpaper Exploration and Wallpaper Symmetry Exploration

On Friday Homework #2 is due: Do Homework #2 distributed via email.

Note: Problem 4 will be discussed in class on Wednesday.

Week 4: Wallpaper Patterns

September 13 - 17

• Monday: Wallpaper Group Scavenger Hunt

• Wednesday: Tessellations, a first look Exploration

• Friday: City Museum 2010 and Angles of Polygons and Regular Tessellations Exploration

• Friday Night: Class Field Trip to City Museum

Week 5: Tessellations and Isometries

September 20 - 24

By Wednesday: Read Introduction_to_Tessellations and Tessellations by Polygons

• Friday: Escher's Wallpaper Groups Exploration

Read Wallpaper Patterns.
Homework #3: Do Wallpaper Exercises # 1-7, 9, 10, Polygonal Tessellation Exercises # 3,4,6,10-14

Week 6: Escher-like Tessellations and GeoGebra

September 27 - October 1

• Monday: Triangular Tessellations with GeoGebra

• Wednesday: Quadrilateral Tessellations with GeoGebra Also, use GeoGebra to construct an "equilateral triangle", "square", "kite", "rhombus", and "parallelogram." Email one file with all of them to the instructor by Monday October 4th.

• Friday: Art Project Discussion and Creating Tessellation Graph Paper

City Museum Poster is due Monday September 27th

Week 7: Introduction to Spherical Geometry

October 4 - 8

Exam 1 Study Guide

• Monday: Review for Exam 1.

Homework #3 is due on Monday October 4th

Exam #1 is on Wednesday October 6th

Friday: Rough sketches for art project due

Week 8: Art Project Assignment and Spherical Geometry

October 11 - 15

For Monday: Read Introduction to Non-Euclidean Geometry

• Monday: Spherical Easel Exploration and Spherical Geometry Exploration

• Wednesday: Spherical Easel Exploration and Spherical Geometry Exploration (Whichever one you did not do on Monday.)

For Friday: Read Spherical Geometry until you get to Spherical Tessellations and...

• Friday: Spherical Triangles Exploration

Friday: Rough draft of art project due

(October 11-15 Midterm Exams - Note: we do not necessarily have an exam this week)

Week 9: Spherical Geometry

October 18 - 22

• Monday: Fall Break: No Class

• Wednesday: Spherical versus Euclidean Polygons Exploration and last chance to get input on Art Project.

Friday: Art project due

Week 10: Spherical Geometry

October 25 - 29

• Monday: Duality Discussion and Duality Exploration

• Wednesday: Platonic Solids Exploration

(Fri October 30 Last Day to Withdraw)

Week 11: Hyperbolic Geometry

November 1 - 5

• Wednesday: Intro to Hyperbolic Geometry and Escher's Circle Limit Exploration

Week 12: Hyperbolic Geometry

November 8 - 12

• Monday: Class cancelled. Please complete Hyperbolic Paper Exploration by Wednesday and bring your finished Hyperbolic paper and answers (and possibly questions) to class.

• Wednesday: Review of Hyperbolic Paper Exploration and Hyperbolic Geometry Exploration

• Friday: Hyperbolic Geometry II with NonEuclid Exploration

For Friday Read Hyperbolic Geometry until Hyperbolic Tessellations

Spherical Geometry Homework Due Wednesday: Spherical Geometry Exercises #1,6,9,13,16,21,28,30,36

Week 13: Hyperbolic Geometry

November 15 - 19

• Monday: Catch-up and Hyperbolic Tessellations Exploration

• Wednesday: Hyperbolic Escher Exploration

• Friday: Ideal Hyperbolic Tessellations Exploration

Week 14: TBD

November 22 - 26

• Wednesday: Thanksgiving Break: No Class
• Friday: Thanksgiving Break: No Class

Week 15: Fourth Dimension and Topology

November 29 - December 3

• Monday: Flatland Exploration and discussion

• Wednesday: Dimensions Exploration and Hypercube Discussion

• Friday: Fractals Discussion and Review

Extra Credit: Read (And he built a crooked house… , Short story by Robert A. Heinlein) and write a two page "book report" on it. Submit it Monday.

Week 16: Exam 2

• Monday: Exam 2 See Exam 2 Outline for information