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)
“The world was a huge ball then, the universe a might harmony of ellipses, everything moved mysteriously, incalculable distances through the ether.
We used to feel the awe of the distant stars upon us. All that led to was the eighty-eight naval guns, ersatz, and the night air-raids over cities. A magnificent spectacle.
After the collapse of the socialist dream, I came to America.”
—John Dos Passos (1896–1970)
“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)