An eversion is a regular homotopy that turns a sphere inside out, taking an embedding
to one with the opposite orientation. The sphere may pass
through itself during the homotopy, but every stage
must remain an immersion. For a 2-sphere
in 
, this is sphere
eversion, whose existence follows from Smale's classification of immersions
(Smale 1959, p. 281).
The Season 1 episode "Sniper Zero" (2005) of the television crime drama NUMB3RS mentions eversion.
