This theo- rem implies that some point on the Earth has zero wind velocity, and has been summarized as  you can't comb a coconut .
This result fails for odd-dimensional surfaces because the alternating sum of their Betti numbers is zero instead of two. As a result of this non-eponymous theorem, any continuous mapping from the surface of a sphere to itself must either have a    xed point or a point that maps to its antipode. This theo- rem implies that some point on the Earth has zero wind velocity, and has been summarized as  you can't comb a coconut . For ten points, identify this re- sult stating that every continuous vector  eld on an even-dimensional spherical surface must have at least one point where the vector is zero.
This result fails for odd-dimensional surfaces because the alternating sum of their Betti numbers is zero instead of two.
hairy ball theorem