Up: The Shape of Space Curriculum Materials: Surfaces

Surfaces - Flatlander Games

The Shape of Space Curriculum Materials

Objectives

Students will discover how strategies of Tic-Tac-Toe change when played on a torus or a Klein bottle. The ability will be measured by answering several questions about the strategies.
Immeasureable outcomes: Students will get a feel for how flatlanders might feel living in a torus or klein bottle.

Materials

Torus Tic-Tac-Toe Activity Sheet

Activity

Play a sample game as a class (half the class against the other half) to remind the students of the notation used on gluing diagrams. Then let students play tic-tac-toe on their activity sheets in pairs. Consider the extensions to this activity listed below to further enrich the understanding of these surfaces.

Extensions

If you have a Web browser that runs Java applications (e.g. Netscape 3.0 or later), you can play Tic-Tac-Toe and other games on a torus or a Klein bottle at http://www.geometrygames.org/TorusGames/

Try playing games on other surfaces: You may wish to ask your students to think about whether their favorite board games, like chess, checkers or Othello, can be played on a torus or klein bottle.

Up: The Shape of Space Curriculum Materials: Surfaces

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