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 culture lacks is the taste for anonymous, innumerable germination. Culture is smitten with counting and measuring; it feels out of place and uncomfortable with the innumerable; its efforts tend, on the contrary, to limit the numbers in all domains; it tries to count on its fingers.”
—Jean Dubuffet (1901–1985)