hey! check out some Neat Stuff

Also: some new movies, etc regarding hyperbolic space!

Symmetry and the Shape of Space

by Chaim Goodman-Strauss

Without further ado, welcome...

Part 1

• Symmetry

  Motion in the plane

  Isometries

  Regular patterns

• Rules of the Game

  Visual Notation

  Gallery to Analyze

• Additional Theorems
  ....aka "What Patterns Can Arise"
• More Planar Motifs
• Homework

Caution

Part 2

• Kali

  How many ways...?

  How to Cheat at Lori's Worksheet

  A Translation

  Frieze!

  A Technical Question

• So what do all these names mean anyway?
• Paperdolls!
• Orbifolds!
• Homework!

Part 3

• Paper Surfaces

  The mobius band and the Annulus

  The Torus and the Klein Bottle

  More about the Klein Bottle

  Cutting Open an Orbifold

  Subsymmetries Revealed

  Homework for week 3

Part 4

• Kaleidotile
• An amazing formula for the sphere
• Euler characteristic of other surfaces
• The Orbifold Shop
• Proof
• Homework list

  Chaim Goodman-Strauss
  Dept. Mathematics
  Univ. Arkansas
  Fayetteville, AR 72701
  strauss@comp.uark.edu
  479-575-6332

Caution

Seeded throughout these materials are interactive demos using Geometer's Sketchpad. To use these demos, you must be at a Macintosh, with Sketchpad installed, and with your web browser properly configured to accept the sketches. For more information... However there's lots to do even without sketchpad! So come on in... Return to outline