Sphere eversion
Topological operation of turning a sphere inside-out without creasing
Sphere eversion
In differential topology, sphere eversion is a theoretical process of turning a sphere inside out in a three-dimensional space (the word eversion means "turning inside out"). It is possible to smoothly and continuously turn a sphere inside out in this way (allowing self-intersections of the sphere's surface) without cutting or tearing it or creating any crease. This is surprising, both to non-mathematicians and to those who understand regular homotopy, and can be regarded as a veridical paradox; that is something that, while being true, on first glance seems false. More precisely, let f : S 2 → R 3 {\displaystyle f\colon S^{2}\to \mathbb {R} ^{3}} be the standard embedding; then there is a regular homotopy of immersions f t...
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