Counting Zeros
From a more advanced point of view: every zero of a vector field has a (non-zero) "index", and it can be shown that the sum of all of the indices at all of the zeros must be two. (This is because the Euler characteristic of the 2-sphere is two.) Therefore there must be at least one zero. This is a consequence of the Poincaré–Hopf theorem. In the case of the torus, the Euler characteristic is 0; and it is possible to "comb a hairy doughnut flat". In this regard, it follows that for any compact regular 2-dimensional manifold with non-zero Euler characteristic, any continuous tangent vector field has at least one zero.
Read more about this topic: Hairy Ball Theorem
Famous quotes containing the word counting:
“What we commonly call man, the eating, drinking, planting, counting man, does not, as we know him, represent himself, but misrepresents himself. Him we do not respect, but the soul, whose organ he is, would he let it appear through his action, would make our knees bend.”
—Ralph Waldo Emerson (1803–1882)