The Hairy Ball Theorem

You can’t comb a coconut

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

• Hairy ball theorem: a continuous tangent field on a sphere vanishes somewhere.
• So there’s always a calm point in Earth’s horizontal wind.
• A torus (χ = 0) can be combed flat. The sphere (χ = 2) can’t.

Steps

1. Combing a sphere
2. Wind on Earth
3. Counting tufts
4. North to south
5. Vortices and saddles
6. A hairy doughnut