Hairy Theorem

Hairy Ball

This one’s a new one for me. It is definitely intuitive but I would have never thought of name for it!

You cannot comb a hairy ball.

The Hairy Ball Theorem states that if you take a ball that is evenly covered with hairs, no matter how you comb the ball, there must be a part somewhere. In other words, the orientation of the hairs must be discontinuous. Compare this to a hairy cylinder which you could comb all the hairs in on direction around the outside of the cylinder with no part. Sorry, I have no picture of a hairy cylinder.

To think of the theorem in another way, let the hairs represent the velocity of the wind blowing across the surface of the Earth. Then, if the wind velocity is continuous, there must be a point where the wind speed is zero.

Koosh!

cf, Mathsnacks: Hairy Theorem

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