| 翻訳と辞書 |
hypersphere
::''For spheres in hyperspace, see'' n-sphere.
In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center. The surface of the hypersphere is a manifold of one dimension less than the ambient space. As the radius increases the curvature of the hypersphere decreases; in the limit a hypersphere approaches the zero curvature of a hyperplane. Both hyperplanes and hyperspheres are hypersurfaces.
The term ''hypersphere'' was introduced by Duncan Sommerville in his discussion of models for non-Euclidean geometry.〔D. M. Y. Sommerville (1914) (The Elements of Non-Euclidean Geometry ), page 193, link from University of Michigan Historical Math Collection〕 The first one mentioned is a 3-sphere in four dimensions.
Some spheres are not hyperspheres: suppose ''S'' is a sphere in Em where ''m'' < ''n'' and the space had ''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==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「hypersphere」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|