Smale's Theorem on Sphere Eversion is a result of differential topology showing that an ordinary sphere can be turned inside out through a continuous, smooth motion in three-dimensional space without ever cutting, tearing, or creasing its surface, a process called sphere eversion. The result is considered a veridical paradox, since it is true despite seeming, on first encounter, to contradict intuition about surfaces; it follows from Stephen Smale's more general classification of immersions up to regular homotopy.
Facts
StatementA sphere can be turned inside out through a continuous, smooth motion in three dimensional space, allowing self intersections, without cutting, tearing, or creasing its surface. 1 Classification
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Source Sphere eversion, Wikipedia
Proved By
Source Sphere eversion, Wikipedia
Sources
1. Sphere eversion, Wikipedia
Introduction
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.
History
An existence proof for crease-free sphere eversion was first created by Stephen Smale (1958).
In Branch: Differential Topology, Lead sentence
In differential topology, sphere eversion is a theoretical process of turning a sphere inside out in a three-dimensional space (th
Proved By: Stephen Smale, Lead
An existence proof for crease-free sphere eversion was first created by Stephen Smale (1958).
In Group: Geometric and Differential Topology, Lead paragraph
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").
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