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.