Eversion

A curve on the unit sphere  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  forms an immersion of the circle into the sphere iff, for all ,

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.

REFERENCES:

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