Hypersphere
Get Hypersphere essential facts below. View Videos or join the Hypersphere discussion. Add Hypersphere to your PopFlock.com topic list for future reference or share this resource on social media.
Hypersphere
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 , 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

  This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

Hypersphere
 



 



 
Music Scenes