First proved by Brouwer in 1912, this theorem can be shown to be a consequence of the more general Poincare-Hopf theorem.
First proved by Brouwer in 1912, this theorem can be shown to be a consequence of the more general Poincare-Hopf theorem. A consequence of it is that any continuous function that maps a sphere into itself has either a fixed point or a point that maps onto its own antipodal point. One corollary of this theorem is that an any moment in time, there is at least one point on Earth where there is no wind, which therefore means that there must always be a cyclone on earth. FTP, name this theory of algebraic topology which states that given a vector field on the sphere there must be at least one point of the sphere for which the vector is zero, and which is usually visualized by thinking of a tennis ball.
First proved by Brouwer in 1912, this theorem can be shown to be a consequence of the more general Poincare-Hopf theorem.
hairy ball theorem (prompt on "ball")