Life on a Torus:
Some of the Mathematics 
from the World of Pacman
Warning: The links on this page do not work!

• Definitions and Background

 

 
 
 
 
 

• First encounters with a torus in the real world.

 

Bagel	Rings	Inner Tube/Life Saver
Donut	Wedding Bands	(Hoola) Hoops

• The Torus in Calculus Courses

 
• The shape of the Earth:

 
• How to make a Sphere.... How to make a Torus.
• Tiling the plane from the torus. Doubly Periodic Patterns.
• Moving (paths and networks) on the sphere and the torus.
• Games on the sphere and the torus.

Examples:
• Tic Tac Toe
• Chess
• Pacman (go to mapacman or games folder)

 
• The Euler Formula / Characteristic

 
• Utility Problem
 
• The Map Coloring Problem

 
• Graphs on a torus.

 
• group structures
• on the circle and the sphere
• on the torus

 
• Higher dimensional spheres and tori.
• Sⁿ ={ x : ||x||=1}a subset of Rⁿ⁺¹
• Tⁿ = { x : x = (x₁,  x₂,  x₃,... x_n )where x₁ is an element of S¹}.

 
• References:
• "A Dozen Questions About a Donut", James Tanton, Math Horizons, Volume VI, No.2, pp 26-31. ( November, 1998)
• Excursions in Mathematics, Bleck, Bleicher, and Crowe. (Worth, 1969)
• Experiments in Topology,  Stephen Barr, (Dover,1964, published 1989)
• The Geometry Junkyard. http://www.ics.uci.edu/~eppstein/junkyard/topic.html