To most people, a torus is a donut-like shape. Topologists like to describe the torus differently: you start with a square, and "identify opposite sides". We can imagine gluing together one pair of opposite sides to get a cylinder, and then gluing together opposite ends of the cylinder to get a torus. (Provided that our material is stretchy enough, which isn't an issue topologists concern themselves with.)
In the past, I've described this description of the torus by analogy with Pac-Man. In this video game, Pac-Man can leave the screen on one edge, and come back onto the screen from the same position on the other side.
But I want to abandon this analogy, and come up with something better, because:
- If you haven't played Pac-Man, it's not very helpful - and how many people these days have? I think I've played Pac-Man on a TI calculator a total of once or twice in high school.
- If you have played Pac-Man, it's not very helpful, because in a typical Pac-Man maze, the "tunnels" that allow this wrapping-around behavior only go one way: from left to right. So a Pac-Man level is more like a cylinder than a torus.
Are there better analogies?