Wiki.RIP

Hypersphere

From Wikipedia, the free encyclopedia
Graphs of volumes (V) and surface areas (S) of n-balls of radius 1. In the SVG file, hover over a point to highlight it and its value.

In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its centre. It is a manifold of codimension one—that is, with one dimension less than that of the ambient space.

As the hypersphere's radius increases, its curvature decreases. In the limit, a hypersphere approaches the zero curvature of a hyperplane. Hyperplanes and hyperspheres are examples of hypersurfaces.

The term hypersphere was introduced by Duncan Sommerville in his 1914 discussion of models for non-Euclidean geometry.[1] The first one mentioned is a 3-sphere in four dimensions.

Some spheres are not hyperspheres: If S is a sphere in Em where m < n, and the space has n dimensions, then S is not a hypersphere. Similarly, any n-sphere in a proper flat is not a hypersphere. For example, a circle is not a hypersphere in three-dimensional space, but it is a hypersphere in the plane.

References

Further reading

  • Kazuyuki Enomoto (2013) Review of an article in International Electronic Journal of Geometry.MR3125833
  • Jemal Guven (2013) "Confining spheres in hyperspheres", Journal of Physics A 46:135201, doi:10.1088/1751-8113/46/13/135201
What is Wiki.RIP There is a free information resource on the Internet. It is open to any user. Wiki is a library that is public and multilingual.

The basis of this page is on Wikipedia. Text licensed under CC BY-SA 3.0 Unported License..

Wikipedia® is a registered trademark of Wikimedia Foundation, Inc. wiki.rip is an independent company that is not affiliated with the Wikimedia Foundation (Wikimedia Foundation).

E-mail: wiki@wiki.rip
WIKI OPPORTUNITIES
Privacy Policy      Terms of Use      Disclaimer