Hairy ball theorem
The hairy ball theorem of algebraic topology (formally, the Sphere Vector Field Theory, sometimes called the hedgehog theorem) states that there is no non-vanishing continuous tangent vector field on even-dimensional n-spheres. For the ordinary sphere, or 2‑sphere, if f is a continuous function that assigns a vector in ℝ3 to every point p on a sphere such that f(p) is always tangent to the sphere at p, then there is at least one pole, a point where the field vanishes (a p such that f(p) = 0).