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Lexikon


hairy ball


A result in ref="module.php?name=Lexikon&file=search&eid=1&query=topology">topology stating that a continuous ref="module.php?name=Lexikon&file=search&eid=1&query=vector field">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 ref="module.php?name=Lexikon&file=search&eid=1&query=continuous map">continuous map f of the sphere into itself there is a point x such that f(x)=x or f(x) is the ref="module.php?name=Lexikon&file=search&eid=1&query=antipode">antipode of x. Another corollary is that at any moment somewhere on the Earth there is no wind. (2002-01-07)

In addition suitable contents:
[ ref="module.php?name=Lexikon&op=content&tid=31">2 ] [ ref="module.php?name=Lexikon&op=content&tid=134">= ] [ ref="module.php?name=Lexikon&op=content&tid=411">ai ] [ ref="module.php?name=Lexikon&op=content&tid=433">al ] [ ref="module.php?name=Lexikon&op=content&tid=544">am ] [ ref="module.php?name=Lexikon&op=content&tid=592">an ] [ ref="module.php?name=Lexikon&op=content&tid=740">ar ] [ ref="module.php?name=Lexikon&op=content&tid=743">arc ] [ ref="module.php?name=Lexikon&op=content&tid=894">at ] [ ref="module.php?name=Lexikon&op=content&tid=1026">b ] [ ref="module.php?name=Lexikon&op=content&tid=1034">ba ] [ ref="module.php?name=Lexikon&op=content&tid=1181">be ] [ ref="module.php?name=Lexikon&op=content&tid=1724">ca ] [ ref="module.php?name=Lexikon&op=content&tid=2001">ch ] [ ref="module.php?name=Lexikon&op=content&tid=2247">co ] [ ref="module.php?name=Lexikon&op=content&tid=2330">com ] [ ref="module.php?name=Lexikon&op=content&tid=2545">con ] [ ref="module.php?name=Lexikon&op=content&tid=3151">de ] [ ref="module.php?name=Lexikon&op=content&tid=3752">du ] [ ref="module.php?name=Lexikon&op=content&tid=3834">E ] [ ref="module.php?name=Lexikon&op=content&tid=3865">ec ] [ ref="module.php?name=Lexikon&op=content&tid=3896">ed ] [ ref="module.php?name=Lexikon&op=content&tid=4148">er ] [ ref="module.php?name=Lexikon&op=content&tid=4171">es ] [ ref="module.php?name=Lexikon&op=content&tid=4379">fact ] [ ref="module.php?name=Lexikon&op=content&tid=4497">fi ] [ ref="module.php?name=Lexikon&op=content&tid=4508">field ] [ ref="module.php?name=Lexikon&op=content&tid=4520">file ] [ ref="module.php?name=Lexikon&op=content&tid=4631">flat ] [ ref="module.php?name=Lexikon&op=content&tid=4635">flatten ] [ ref="module.php?name=Lexikon&op=content&tid=4700">fo ] [ ref="module.php?name=Lexikon&op=content&tid=4727">for ] [ ref="module.php?name=Lexikon&op=content&tid=4828">fr ] [ ref="module.php?name=Lexikon&op=content&tid=5057">ge ] [ ref="module.php?name=Lexikon&op=content&tid=5070">gen ] [ ref="module.php?name=Lexikon&op=content&tid=5430">gy ] [ ref="module.php?name=Lexikon&op=content&tid=5434">h ] [ ref="module.php?name=Lexikon&op=content&tid=5458">hair ] [ ref="module.php?name=Lexikon&op=content&tid=5459">hairy ] [ ref="module.php?name=Lexikon&op=content&tid=5540">hat ] [ ref="module.php?name=Lexikon&op=content&tid=5768">hr ] [ ref="module.php?name=Lexikon&op=content&tid=5931">id ] [ ref="module.php?name=Lexikon&op=content&tid=5956">ie ] [ ref="module.php?name=Lexikon&op=content&tid=6013">il ] [ ref="module.php?name=Lexikon&op=content&tid=6064">in ] [ ref="module.php?name=Lexikon&op=content&tid=6194">int ] [ ref="module.php?name=Lexikon&op=content&tid=6413">io ] [ ref="module.php?name=Lexikon&op=content&tid=6449">ir ] [ ref="module.php?name=Lexikon&op=content&tid=6482">is ] [ ref="module.php?name=Lexikon&op=content&tid=6558">it ] [ ref="module.php?name=Lexikon&op=content&tid=6789">ke ] [ ref="module.php?name=Lexikon&op=content&tid=6918">la ] [ ref="module.php?name=Lexikon&op=content&tid=7023">ld ] [ ref="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ ref="module.php?name=Lexikon&op=content&tid=7107">li ] [ ref="module.php?name=Lexikon&op=content&tid=7410">lt ] [ ref="module.php?name=Lexikon&op=content&tid=7463">ma ] [ ref="module.php?name=Lexikon&op=content&tid=7607">map ] [ ref="module.php?name=Lexikon&op=content&tid=8019">mm ] [ ref="module.php?name=Lexikon&op=content&tid=8032">mo ] [ ref="module.php?name=Lexikon&op=content&tid=8040">mod ] [ ref="module.php?name=Lexikon&op=content&tid=8079">module ] [ ref="module.php?name=Lexikon&op=content&tid=8386">na ] [ ref="module.php?name=Lexikon&op=content&tid=8627">ng ] [ ref="module.php?name=Lexikon&op=content&tid=8630">ni ] [ ref="module.php?name=Lexikon&op=content&tid=8672">nn ] [ ref="module.php?name=Lexikon&op=content&tid=8675">no ] [ ref="module.php?name=Lexikon&op=content&tid=8787">nu ] [ ref="module.php?name=Lexikon&op=content&tid=8964">om ] [ ref="module.php?name=Lexikon&op=content&tid=9014">op ] [ ref="module.php?name=Lexikon&op=content&tid=9550">ph ] [ ref="module.php?name=Lexikon&op=content&tid=9757">pod ] [ ref="module.php?name=Lexikon&op=content&tid=9762">point ] [ ref="module.php?name=Lexikon&op=content&tid=9908">pr ] [ ref="module.php?name=Lexikon&op=content&tid=10058">projection ] [ ref="module.php?name=Lexikon&op=content&tid=10253">query ] [ ref="module.php?name=Lexikon&op=content&tid=10364">rc ] [ ref="module.php?name=Lexikon&op=content&tid=10385">re ] [ ref="module.php?name=Lexikon&op=content&tid=10767">ro ] [ ref="module.php?name=Lexikon&op=content&tid=11150">se ] [ ref="module.php?name=Lexikon&op=content&tid=11651">so ] [ ref="module.php?name=Lexikon&op=content&tid=11934">st ] [ ref="module.php?name=Lexikon&op=content&tid=12133">su ] [ ref="module.php?name=Lexikon&op=content&tid=12359">T ] [ ref="module.php?name=Lexikon&op=content&tid=12588">th ] [ ref="module.php?name=Lexikon&op=content&tid=12721">to ] [ ref="module.php?name=Lexikon&op=content&tid=12752">topology ] [ ref="module.php?name=Lexikon&op=content&tid=12896">tt ] [ ref="module.php?name=Lexikon&op=content&tid=13175">us ] [ ref="module.php?name=Lexikon&op=content&tid=13310">ve ] [ ref="module.php?name=Lexikon&op=content&tid=13311">vector ] [ ref="module.php?name=Lexikon&op=content&tid=13725">win ] [ ref="module.php?name=Lexikon&op=content&tid=14102">zero ]






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