Smale's Paradox
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In differential topology, Smale''s paradox states that it is possible to turn a sphere inside out in a three-dimensional space with possible self-intersections but without creating any crease, a process often called sphere eversion (eversion means "to turn inside out"). This is surprising, and is hence deemed a veridical paradox.This ''paradox'' was discovered by Stephen Smale (1958). It is difficult to visualize a particular example of such a turning, although some…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In differential topology, Smale''s paradox states that it is possible to turn a sphere inside out in a three-dimensional space with possible self-intersections but without creating any crease, a process often called sphere eversion (eversion means "to turn inside out"). This is surprising, and is hence deemed a veridical paradox.This ''paradox'' was discovered 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 easier. The first example was exhibited through the efforts of several mathematicians, including Arnold Shapiro and Bernard Morin who was blind. On the other hand, it is much easier to prove that such a "turning" exists and that is what Smale did.