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 nothing in the world that I loathe more than group activity, that communal bath where the hairy and slippery mix in a multiplication of mediocrity.”
—Vladimir Nabokov (1899–1977)
“Don’t tell me what delusion he entertains regarding God, or what mountebank he follows in politics, or what he springs from, or what he submits to from his wife. Simply tell me how he makes his living. It is the safest and surest of all known tests. A man who gets his board and lodging on this ball in an ignominious way is inevitably an ignominious man.”
—H.L. (Henry Lewis)
“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)