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Hairy smooth

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The hairy ball theorem of algebraic topology sometimes called the hedgehog theorem in Europe [1] states that there is no nonvanishing continuous tangent vector field on even-dimensional n -spheres.

Lvs. lanc. rather soft serrated...

In other words, whenever one attempts to comb a hairy ball flat, there will always be at least one tuft of hair at one point on the ball.

This is famously stated as "you can't comb a hairy ball flat without creating a cowlick ", "you can't comb the hair on a coconut", or sometimes "every cow must have at least one cowlick. From a more advanced point of view: This is because the Euler characteristic of the 2-sphere is Hairy smooth.

Therefore, there must be at least one zero. In Hairy smooth case of the torusthe Euler characteristic is 0; and it is possible to "comb a hairy doughnut flat".


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