The hairy ball theorem of algebraic topology 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 p such that f(p) = 0. In other words, whenever one attempts to comb a hairy ball flat, there will always be at least one tuft of hair at one point on the ball. The theorem was first stated by Henri Poincaré in the late 19th century.
This is famously stated as "you can't comb a hairy ball flat without creating a cowlick", or sometimes "you can't comb the hair on a coconut". It was first proved in 1912 by Brouwer.
Read more about Hairy Ball Theorem: Counting Zeros, Cyclone Consequences, Application To Computer Graphics, Lefschetz Connection, Corollary, Higher Dimensions
Famous quotes containing the words hairy, ball and/or theorem:
“There is the old brute, too, the savage, the hairy man who dabbles his fingers in ropes of entrails; and gobbles and belches; whose speech is guttural, visceral—well, he is here. He squats in me.”
—Virginia Woolf (1882–1941)
“It may be possible to do without dancing entirely. Instances have been known of young people passing many, many months successively, without being at any ball of any description, and no material injury accrue either to body or mind; Mbut when a beginning is made—when felicities of rapid motion have once been, though slightly, felt—it must be a very heavy set that does not ask for more.”
—Jane Austen (1775–1817)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)