A donut is not a sphere | Things you can do on one surface but not the other

The video explores the topological differences between a torus and a sphere, using the game Asteroids as an example. It explains why the universe in Asteroids is a torus, not a sphere, by examining movement patterns. The video also highlights unique properties of a torus, such as non-contractible loops and vector fields, and discusses graph theory problems that can be solved on a torus but not on a sphere.

What are some surprising properties of a torus that do not apply to a sphere?

Discuss the implications of having a continuous tangent vector field on a torus compared to a sphere.

How does the three utilities problem illustrate the differences between a torus and a sphere?