<topology> A result in topology
stating that a continuous vector field on a sphere is always zero somewhere.
The name comes from the fact that you can't flatten all the hair on a hairy ball, like a tennis ball, there will always be a tuft somewhere (where the tangential projection of the hair is zero).
An immediate corollary to this theorem is that for any continuous map f of the sphere into itself there is a point x such that f(x)=x or f(x) is the antipode of x.
Another corollary is that at any moment somewhere on the Earth there is no wind.