Rubber-Sheet Geometry

A mug is a doughnut

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Topology allows stretching and bending, but not tearing or gluing.
• A mug and a doughnut are the same: both have one hole.
• Counting holes is a key topological invariant.

Steps

1. Forget lengths and angles
2. Squashing into a circle
3. Letters
4. Letters with a junction
5. Holes in things
6. Holes in a T-shirt