Sphere eversion
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In differential topology, sphere eversion is a theoretical process of turning a sphere inside out in a three-dimensional space. It is possible to smoothly and continuously turn a sphere inside out in
Paper sphere eversion and Morin surface
Paper Morin surface (sphere eversion halfway) with hexagonal symmetry
halfway top
halfway side
Stephen Smale
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Stephen Smale is an American mathematician, known for his research in topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades
Sphere eversion
…such that f0 = f and f1 = −f. An existence proof for crease-free sphere eversion was first created by Stephen Smale (1958). It is difficult to visualize a particular example of such a turning, although some digital animations have been produced that make it somewhat…
Smale in 2008