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What (who) is hairy ball - definition

THEOREM WHICH STATES THAT THERE IS NO NONVANISHING CONTINUOUS TANGENT VECTOR FIELD ON EVEN-DIMENSIONAL N-SPHERES

Hairy billiard ball theorem; Hairy billiard ball; Hairy ball; Hairy dog theorem

hairy ball

<topology> A result in topology stating that a continuous vector field on a sphere is always zero somewhere. The name comes from the fact that you can't flatten all the hair on a hairy ball, like a tennis ball, there will always be a tuft somewhere (where the tangential projection of the hair is zero). An immediate corollary to this theorem is that for any continuous map f of the sphere into itself there is a point x such that f(x)=x or f(x) is the antipode of x. Another corollary is that at any moment somewhere on the Earth there is no wind. (2002-01-07)

Hairy ball theorem

The hairy ball theorem of algebraic topology (sometimes called the hedgehog theorem in Europe) 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 pole, a point where the field vanishes (a p such that f(p) = 0).

https://en.wikipedia.org/wiki/Hairy_ball_theorem

Hairy Maclary and Friends

SERIES OF CHILDREN'S BOOKS

Hairy Maclary's Bone; Slinky Malinki Open The Door; Hairy McLary; Schnitzel Von Krumm; Hairy MacLary; Hairy Maclary’s Bone; Hairy Maclary, Scattercat; Hairy Maclary's Showbusiness; Rumpus at the Vet; Zachary Quack Minimonster; Slinky Malinki's Christmas Crackers; Hairy Maclary's Hat Tricks; Hairy Maclary, Shoo; Slinky Malinki - Early Bird; Hairy Maclary - Shoo; Hairy Maclary Scattercat; Scarface Claw, Hold Tight; Hairy Maclary's Rumpus at the Vet; Caterwaul Caper; Hairy Maclary

Hairy Maclary and Friends is a series of children's picture books created by New Zealand author and illustrator Dame Lynley Dodd. The popular series has sold over five million copies worldwide.

https://en.wikipedia.org/wiki/Hairy_Maclary_and_Friends

Wikipedia

Hairy ball theorem

The hairy ball theorem of algebraic topology (sometimes called the hedgehog theorem in Europe) 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 pole, a point where the field vanishes (a p such that f(p) = 0).

The theorem was first proved by Henri Poincaré for the 2-sphere in 1885, and extended to higher even dimensions in 1912 by Luitzen Egbertus Jan Brouwer.

The theorem has been expressed colloquially as "you can't comb a hairy ball flat without creating a cowlick" or "you can't comb the hair on a coconut".

https://en.wikipedia.org/wiki/Hairy ball theorem