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.

(2002-01-07)