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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\", \"you can't comb the hair on a coconut\", or sometimes \"every cow must have at least one cowlick.\" It can also be written as, \"Every 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 one-minute-math-why-you-cant-comb-a-hairy-ball.html.
- Hairy_ball_theorem wikiPageExternalLink www.eulersgem.com.
- Hairy_ball_theorem wikiPageID "485168".
- Hairy_ball_theorem wikiPageLength "8286".
- Hairy_ball_theorem wikiPageOutDegree "45".
- Hairy_ball_theorem wikiPageRevisionID "706823526".
- Hairy_ball_theorem wikiPageWikiLink Algebraic_topology.
- Hairy_ball_theorem wikiPageWikiLink Alternating_series.
- Hairy_ball_theorem wikiPageWikiLink Antipodal_point.
- Hairy_ball_theorem wikiPageWikiLink Betti_number.
- Hairy_ball_theorem wikiPageWikiLink Category:Differential_topology.
- Hairy_ball_theorem wikiPageWikiLink Category:Fixed_points_(mathematics).
- Hairy_ball_theorem wikiPageWikiLink Category:Theorems_in_algebraic_topology.
- Hairy_ball_theorem wikiPageWikiLink Compact_space.
- Hairy_ball_theorem wikiPageWikiLink Continuous_function.
- Hairy_ball_theorem wikiPageWikiLink Cowlick.
- Hairy_ball_theorem wikiPageWikiLink Cyclone.
- Hairy_ball_theorem wikiPageWikiLink Diffeomorphism.
- Hairy_ball_theorem wikiPageWikiLink Endomorphism.
- Hairy_ball_theorem wikiPageWikiLink Euclidean_vector.
- Hairy_ball_theorem wikiPageWikiLink Euler_characteristic.
- Hairy_ball_theorem wikiPageWikiLink File:Hairy_ball.png.
- Hairy_ball_theorem wikiPageWikiLink Fixed_point_(mathematics).
- Hairy_ball_theorem wikiPageWikiLink Function_(mathematics).
- Hairy_ball_theorem wikiPageWikiLink Henri_Poincaré.
- Hairy_ball_theorem wikiPageWikiLink Homology_(mathematics).
- Hairy_ball_theorem wikiPageWikiLink Homotopy.
- Hairy_ball_theorem wikiPageWikiLink Identity_function.
- Hairy_ball_theorem wikiPageWikiLink Irregularity_of_a_surface.
- Hairy_ball_theorem wikiPageWikiLink L._E._J._Brouwer.
- Hairy_ball_theorem wikiPageWikiLink Lefschetz_fixed-point_theorem.
- Hairy_ball_theorem wikiPageWikiLink Manifold.
- Hairy_ball_theorem wikiPageWikiLink N-sphere.
- Hairy_ball_theorem wikiPageWikiLink Null_vector.
- Hairy_ball_theorem wikiPageWikiLink One-parameter_group.
- Hairy_ball_theorem wikiPageWikiLink Poincaré–Hopf_theorem.
- Hairy_ball_theorem wikiPageWikiLink Stereographic_projection.
- Hairy_ball_theorem wikiPageWikiLink Tangent.
- Hairy_ball_theorem wikiPageWikiLink Torus.
- Hairy_ball_theorem wikiPageWikiLink Vector_field.
- Hairy_ball_theorem wikiPageWikiLink Vector_fields_on_spheres.
- Hairy_ball_theorem wikiPageWikiLink File:Hairy_ball_one_pole.jpg.
- Hairy_ball_theorem wikiPageWikiLink File:Hairy_doughnut.png.
- Hairy_ball_theorem wikiPageWikiLinkText "Hairy ball theorem".
- Hairy_ball_theorem wikiPageWikiLinkText "Lefschetz connection".
- Hairy_ball_theorem wikiPageWikiLinkText "hairy ball theorem".
- Hairy_ball_theorem wikiPageWikiLinkText "hairy".
- Hairy_ball_theorem wikiPageUsesTemplate Template:Cite_book.
- Hairy_ball_theorem wikiPageUsesTemplate Template:Cite_journal.
- Hairy_ball_theorem wikiPageUsesTemplate Template:Cite_web.
- Hairy_ball_theorem wikiPageUsesTemplate Template:Cn.
- Hairy_ball_theorem wikiPageUsesTemplate Template:More_footnotes.
- Hairy_ball_theorem wikiPageUsesTemplate Template:Redirect.
- Hairy_ball_theorem wikiPageUsesTemplate Template:Reflist.
- 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 Physic.
- Hairy_ball_theorem type Theorem.
- 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 sameAs Q1077741.
- Hairy_ball_theorem sameAs Sætningen_om_den_behårede_kugle.
- Hairy_ball_theorem sameAs Satz_vom_Igel.
- Hairy_ball_theorem sameAs Teoremo_pri_erinaco.
- Hairy_ball_theorem sameAs Teorema_de_la_bola_peluda.
- Hairy_ball_theorem sameAs نظریه_توپ_مودار.
- Hairy_ball_theorem sameAs Karvapallolause.
- Hairy_ball_theorem sameAs Théorème_de_la_boule_chevelue.
- Hairy_ball_theorem sameAs Sündisznótétel.
- 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 Теорема_о_причёсывании_ежа.
- Hairy_ball_theorem sameAs Q1077741.
- Hairy_ball_theorem sameAs 毛球定理.
- Hairy_ball_theorem wasDerivedFrom Hairy_ball_theorem?oldid=706823526.
- Hairy_ball_theorem depiction Hairy_ball.png.
- Hairy_ball_theorem isPrimaryTopicOf Hairy_ball_theorem.