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- Hairy_ball_theorem abstract "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 can also be written as, "Any smooth vector field on a sphere has a singular point." It was first proved in 1912 by Brouwer.".
- Hairy_ball_theorem thumbnail Hairy_ball.png?width=300.
- Hairy_ball_theorem wikiPageExternalLink sperner.pdf.
- Hairy_ball_theorem wikiPageExternalLink www.eulersgem.com.
- Hairy_ball_theorem wikiPageExternalLink one-minute-math-why-you-cant-comb-a-hairy-ball.html.
- Hairy_ball_theorem wikiPageID "485168".
- Hairy_ball_theorem wikiPageRevisionID "606716752".
- Hairy_ball_theorem hasPhotoCollection Hairy_ball_theorem.
- Hairy_ball_theorem subject Category:Differential_topology.
- Hairy_ball_theorem subject Category:Fixed_points_(mathematics).
- Hairy_ball_theorem subject Category:Theorems_in_algebraic_topology.
- Hairy_ball_theorem type Abstraction100002137.
- Hairy_ball_theorem type Communication100033020.
- Hairy_ball_theorem type Message106598915.
- Hairy_ball_theorem type Proposition106750804.
- Hairy_ball_theorem type Statement106722453.
- Hairy_ball_theorem type Theorem106752293.
- Hairy_ball_theorem type TheoremsInAlgebraicTopology.
- Hairy_ball_theorem comment "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.".
- Hairy_ball_theorem label "Hairy ball theorem".
- Hairy_ball_theorem label "Satz vom Igel".
- Hairy_ball_theorem label "Teorema da bola cabeluda".
- Hairy_ball_theorem label "Teorema de la bola peluda".
- Hairy_ball_theorem label "Teorema della palla pelosa".
- Hairy_ball_theorem label "Théorème de la boule chevelue".
- Hairy_ball_theorem label "Теорема о причёсывании ежа".
- Hairy_ball_theorem label "毛球定理".
- Hairy_ball_theorem sameAs Satz_vom_Igel.
- Hairy_ball_theorem sameAs Teorema_de_la_bola_peluda.
- Hairy_ball_theorem sameAs Théorème_de_la_boule_chevelue.
- Hairy_ball_theorem sameAs Teorema_della_palla_pelosa.
- Hairy_ball_theorem sameAs Teorema_da_bola_cabeluda.
- Hairy_ball_theorem sameAs m.02g43n.
- Hairy_ball_theorem sameAs Q1077741.
- Hairy_ball_theorem sameAs Q1077741.
- Hairy_ball_theorem sameAs Hairy_ball_theorem.
- Hairy_ball_theorem wasDerivedFrom Hairy_ball_theorem?oldid=606716752.
- Hairy_ball_theorem depiction Hairy_ball.png.
- Hairy_ball_theorem isPrimaryTopicOf Hairy_ball_theorem.
