Hairy ball theorem
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.
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Hairy ball theorem
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.
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Der Satz vom Igel, auch Igelsa ...... des globalen Windes verknüpft.
@de
Em topologia algébrica, o teor ...... monstrado em 1912 por Brouwer.
@pt
En matemática, y más precisame ...... ogía o la computación gráfica.
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En mathématiques, le théorème ...... théorème de la boule chevelue.
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Il teorema della palla pelosa ...... partire dal lemma di Sperner.
@it
The hairy ball theorem of alge ...... rst proved in 1912 by Brouwer.
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Теорема о причёсывании ежа утв ...... бязательно должен быть циклон.
@ru
在代数拓扑中，毛球定理（英語：Hairy ball theo ...... ，若其欧拉示性数不为0，则其上的连续的切向量场必然存在零点。
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Der Satz vom Igel, auch Igelsa ...... des globalen Windes verknüpft.
@de
Em topologia algébrica, o teor ...... monstrado em 1912 por Brouwer.
@pt
En matemática, y más precisame ...... brá zonas vacías (o calvicie).
@es
En mathématiques, le théorème ...... s'annule en au moins un point.
@fr
Il teorema della palla pelosa ...... nte: data una sfera tale che .
@it
The hairy ball theorem of alge ...... caré in the late 19th century.
@en
Теорема о причёсывании ежа утв ...... казанной в 1912 году Брауэром.
@ru
在代数拓扑中，毛球定理（英語：Hairy ball theo ...... ，若其欧拉示性数不为0，则其上的连续的切向量场必然存在零点。
@zh
label
Hairy ball theorem
@en
Satz vom Igel
@de
Teorema da bola cabeluda
@pt
Teorema de la bola peluda
@es
Teorema della palla pelosa
@it
Théorème de la boule chevelue
@fr
Теорема о причёсывании ежа
@ru
毛球定理
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