By today's standards, the classic video game Asteroids is almost primitive. In the game, the player flys a wedge-shaped spaceship and destroys asteroids. Outer space is represented by a 2-dimensional map which is superficially similar to the map of Earth. While the game play of Asteroids is rather simple, the underlying mathematics is not!

In my talk, I will use the example of the game Asteroids to explore the nature of abstract shapes in 2 dimensions and beyond. I'll discuss some interesting aspects of “Asteroids space” and compare these properties to the properties of more familiar shapes.