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- noun A
theorem stating that, given asphere covered infur , one cannot brush all the hairs flat without creating at least twowhirls . - noun mathematics A
theorem stating that there is nononvanishing continuous tangent vector field on thesphere .
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sionnach commented on the word hairy ball theorem
The hairy ball theorem of algebraic topology states that there is no nonvanishing continuous tangent vector field on the 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.
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 billiard ball". It was first proved in 1912 by Brouwer, and is also known as Brouwer's fixed point theorem.
A failed attempt to comb a hairy ball flat, leaving a tuft at each pole.
October 27, 2008
bilby commented on the word hairy ball theorem
I was going to say something about Chuck Norris and hairy balls but am now disinclined to do so.
November 19, 2008
sionnach commented on the word hairy ball theorem
Were you looking for hairy Ball theorem?
No, I was not. And I speak as someone who actually used a functional analytical version of the Brouwer Fixed Point Theorem to prove one of the major* results in my dissertation.
*: well, it was major to me. And it seemed to impress the committee members.
May 9, 2011