A curve on the unit sphere S^2 is an eversion if it has no corners or cusps (but it may be self-intersecting). These properties are guaranteed by requiring that the curve's velocity never vanishes. A mapping sigma:S^1->S^2 forms an immersion of the circle into the sphere iff, for all theta in R,


Smale (1958) showed it is possible to turn a sphere inside out (sphere eversion) using eversion.

The Season 1 episode "Sniper Zero" (2005) of the television crime drama NUMB3RS mentions eversion.

See also

Sphere Eversion

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Smale, S. "A Classification of Immersions of the Two-Sphere." Trans. Amer. Math. Soc. 90, 281-290, 1958.

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Cite this as:

Weisstein, Eric W. "Eversion." From MathWorld--A Wolfram Web Resource.

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