The hairy ball theorem of algebraic topology (sometimes called the hedgehog theorem in Europe) states that there is no nonvanishing 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).