Objectives:

The overall purpose of these games is for the students to famliarize themselves with the fundamental domains of various surfaces. The best way to accomplish this familiarity is through experience and discussion. In order to induce this kind of dicussion, you may want to break the students up into teams of three to six each. The strategic planning that will carry on while two teams compete against one another will cause the students to observe and discuss the properties of the surface on which they are playing.

The fundamental domain of a surface contains all the information about a surface that an inhabitant of that surface would have access to. Thus, the fundamental domain really does contain the fundamental (topological) properties of the surface, and to understand the fundamental domain is to understand the essence of the surface.

1. The students will learn the terminology associated with fundamental domain notation. Most importantly, they will learn how to use arrow notation to represent how two sides of a fundamental domain are glued together.

2. The students will learn what sort of properties are topological properties that an inhabitant can observe (such properties are called intrinsic.). These properties include (among others) boundaries, orientability, and Euler number.

3. The students will learn to use the intrinsic topological properties of surfaces to differentiate between two topoligcally distinct surfaces and to recognize when two surfaces are topologically equivalent.