The optimal sphere eversion, or optiverse, is now the star of a vivid, computer-generated video, titled The Optiverse, produced by Sullivan and his Illinois colleagues George K.
The sphere eversion problem is perenially intriguing," says Anthony V.
That uncertainty vanished when Stephen Smale, now at the University of California, Berkeley, proved a theorem in the field of differential topology demonstrating the feasibility of a sphere eversion.
The extraordinary difficulty of visualizing the details of a sphere eversion made it a tremendous challenge to mathematicians and inspired some of the first applications of computer graphics to mathematics.
In 1977, Morin's sphere eversion became the basis of an animated film by Nelson L.
The trick is performing the entire eversion without letting a crease enter the picture.
Now French mathematician Bernard Morin of the Universite Louis-Pasteur in Strasbourg has found the simplest possible route for a sphere eversion.
In fact, his proof laid out a step-by-step path for accomplishing a sphere eversion, but in such a complicated argument that no one could visualize his procedure.
A sequence of six elementary moves carries the central model through the tricky stages of the eversion.