Date 


(Assignments may change up until the date listed.) 
9/13/04  Introduction, Classification  The game Set 

9/20/04  Symmetry and Transformations  Transformations using Kali and the Geometer's Sketchpad 

9/27/04  Identifying Symmetries of Patterns  Identifying Symmetries of Patterns 
This assignment is due 10/18/04

10/4/04 
Proof that there are exactly 17 repeating patterns in the plane. Invariants (knot equivalence example) and the Euler Characteristic. 
Quiz 1 (symmetry types) Game introducing invariants. Calculation of Euler Characteristics. 
No homework assigned this week. If you're bored, try some of the games at http://www.cuttheknot.org/ctk/invexamples.shtml. Try to determine what invariant is illustrated by each game. 
10/18/04 
Euler's Theorem and fractional Euler characteristic Illustration of two kaledoscopic points on a sphere: *22. 
Euler's Theorem on a bagel and for 4*2  Write approximately one paragraph in your own words explaining why it doesn't matter what graph you choose to compute the Euler characteristic of any surface. (Theorem 2, pp. 7273.) 
10/25/04  Definition of Orbifold  Orbifolds of Repeating Patterns (bring scissors and tape) 

11/1/04  Turning orbifolds into patterns, and a hyperbolic pattern 
Quiz 2 (orbifolds) Making patterns by paper cutting. 
This assignment is due 11/15/04

11/8/03  Classification of Surfaces: Klein Bottles and games on the torus and Klein bottle. 
Presentations by: Jessica Lampert "Match Game" Lino Cabral "The Mystery of the m and b in y=mx+b". Will Kellogg "4x4 Set" (C code) 
Quiz 3 (takehome) In five pages or fewer, summarize the complete proof that there are exactly 17 symmetry types for repeating patterns in the plane. 
11/15/03  Logo Commands 
Presentations by: Pamela Walsh "Chaos and Fractals" Paul Canniff "Construction of a Pentagon" Getting started with Logo 
Print out or write down a logo program that draws a simple design then returns the turtle to its initial position and heading (use PRINT POS and PRINT HEADING to check that you're back to the home position) without using commands like HOME or CLEARSCREEN. If you're looking for more things for your turtle to do, try Logo for Kids. You may wish to follow the instructions at http://www.snee.com/logo/ for installing a logo.bat program in your Logo directory; if you use this program to start Logo you will be able to use notepad as your program editor rather than Jove. 
11/22/03  Drawing a frieze pattern with Logo. 
Presentations by: Patty Watters Nicole LoPilato Michelle LeBlanc 
Follow the outline provided in class to redo Quiz 3 for an improved grade. 
11/29/03  More Logo commands, a little bit about groups, and generators of frieze groups 
Presentations by: Jen Pineau "Fractals" Amy Cortright "Fibonacci Numbers and Spirals" (see web site) Coloring Frieze Patterns 
Quiz 4 (Takehome) Write a Logo program to display the seven different frieze patterns on your screen. Be prepared to run them during class. (If you can't fit all the frieze patterns on your screen, try experimenting with a combination of WAIT and CLEARSCREEN.) 
12/6/03  Colored Frieze Patterns  Coloring Frieze Patterns 

12/13/03  Review of the semester  Finding type symbols, coloring 2*∞, constructing orbifolds, and matching orbifolds to type symbols.  No Homework Assigned 
12/20/03  Discussion of Final Projects  Quiz 5 Quiz on classification systems, finding symmetry types, invariants and the Euler Characteristic and colored patterns.  Happy Holidays! 