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erversions
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There are 10 letters in ERVERSIONS ( E1I1N1O1R1S1V4 )
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| Erversions might refer to |
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In differential topology, Sphere eversion is the process of turning a sphere inside out in a three-dimensional space. (The word eversion means "turning inside out".) Remarkably, it is possible to smoothly and continuously turn a sphere inside out in this way (with possible self-intersections) 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 * * * : * * S * * 2 * * * → * * * R * * * 3 * * * * * {\displaystyle f_{t}\colon S^{2}\to \mathbb {R} ^{3}} * such that ƒ0 = ƒ and ƒ1 = −ƒ. |