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Hairy Ball Theorem

  • Definition: There does not exist an everywhere nonzero tangent vector field on the 2-sphere 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 S^n has a nonzero tangent vector field if and only if n is odd.

    Source: http://mathworld.wolfram.com

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