Introduction
Macintosh users should make sure they have a recent Java implementation.
If you haven't played these games before, you should start with the Introduction. It explains what a torus and Klein bottle are, and shows you how to use the software.
Once you've done the first two pages of the Introduction, you may play the remaining six games in any order.
 Tic-Tac-Toe |
 Maze |
 Crossword |
 Word Search |
 Jigsaw |
 Chess |
The prize-winning Shape of Space video applies the idea of a torus to our 3-dimensional universe. More information is available upon request.
A 2-week Shape of Space unit for middle school math classes uses classroom games and activities, the Torus and Klein Bottle Games from this web site, and the aforementioned video to expand kids' concept of space. The unit has just been completed. More information is available upon request.
Questions? Suggestions? Please contact Jeff Weeks.
These applets were developed for Bolt, Beranek and Newman Inc. as part of the NSF-funded curriculum development project Teaching Mathematical Thinking through Computer-Assisted Space Explorations.
Download TorusGames.zip
(241KB) to play these games offline.
Download the Java source code.
Last revised May 14, 1999.