======================================================================
=                            Hypersphere                             =
======================================================================

                             Introduction
======================================================================
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 oneāthat 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
discussion of models for non-Euclidean geometry. The first one
mentioned is a 3-sphere in four dimensions.

Some spheres are not hyperspheres: If 'S' is a sphere in E'm' where ,
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.


                           Further reading
======================================================================
* Kazuyuki Enomoto (2013) Review of an article in 'International
Electronic Journal of Geometry'.
* Jemal Guven (2013) "Confining spheres in hyperspheres", Journal of
Physics A 46:135201,


 License
=========
All content on Gopherpedia comes from Wikipedia, and is licensed under CC-BY-SA
License URL: http://creativecommons.org/licenses/by-sa/3.0/
Original Article: http://en.wikipedia.org/wiki/Hypersphere


.