thumb|A [[Morin surface seen from "above"]]

[[File:Evshort2.webm|thumb| Sphere eversion process as described in

  • Combining the above methods, the complete sphere eversion can be described by a set of closed equations giving minimal topological complexity

Variations

  • A six-dimensional sphere <math>S^6</math> in seven-dimensional euclidean space <math>\mathbb{R}^7</math> admits eversion. With an evident case of an 0-dimensional sphere <math>S^0</math> (two distinct points) in a real line <math>\mathbb{R}</math> and described above case of a two-dimensional sphere in <math>\mathbb{R}^3 </math> there are only three cases when sphere <math>S^n</math> embedded in euclidean space <math>\mathbb{R}^{n+1}</math> admits eversion.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"

|+Surface plots

|

|

|

|-

|

| colspan="2" |

|}

See also

  • Whitney–Graustein theorem

References

Bibliography

  • A History of Sphere Eversions
  • "Turning a Sphere Inside Out"
  • Software for visualizing sphere eversion
  • Mathematics visualization: topology. The holiverse sphere eversion (Povray animation)
  • The deNeve/Hills sphere eversion: video and interactive model
  • Patrick Massot's project to formalise the proof in the Lean Theorem Prover
  • An interactive exploration of Adam Bednorz and Witold Bednorz method of sphere eversion
  • Outside In: A video exploration of sphere eversion, created by The Geometry Center of The University of Minnesota.