ABSTRACT
A popular video game pits two players in biplanes in aerial combat on a TV screen. An interesting feature of the game is that when a biplane flies off one edge of the screen it doesn’t crash, but rather it comes back from the opposite edge of the screen (Figure 2.1). Mathematically speaking, the screen’s edges have been “glued” together. (The gluing is purely abstract: there is no need to physically connect the edges.) A square or rectangle whose opposite edges are ab stractly glued in this fashion is called a torus or, more precisely, a flat two-dimensional torus. There is a con-
nection between this flat two-dimensional torus and the doughnut-surface torus of Chapter 1, but for the time being you should forget the doughnut surface en tirely.
