hairy ball  (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.
Last updated: 2002-01-07