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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 iff n is odd.

    Related term

    fixed point theorem

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