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.

**References**

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

© 1996-9

1999-05-25