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Hairy Ball Theorem

There does not exist an everywhere Nonzero tangent Vector Field on the 2-Sphere $\Bbb{S}^2$. This implies that somewhere on the surface of the Earth, there is a point with zero horizontal wind velocity. The theorem can be generalized to the statement that the $n$-sphere $\Bbb{S}^n$ has a nonzero tangent vector field Iff $n$ is Odd.

© 1996-9 Eric W. Weisstein