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:
“Down came the hairy talons
and horrible poison blade
And none of the garden noticed
that fizzing, hopeless fight.”
—Sir John Betjeman (1906–1984)
“I never knew anyone yet who got up at six who did anything more useful between that time and breakfast than banging a tennis ball up against the side of the house, waiting for the more civilized members of the party to get up.”
—Robert Benchley (1889–1945)
“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)