| 词条 | Hypersphere |
| 释义 |
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 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 {{nowrap|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. References1. ^{{cite book |first=D. M. Y. |last=Sommerville |authorlink=Duncan Sommerville |year=1914 |chapter-url=https://quod.lib.umich.edu/cache/a/b/n/abn6053.0001.001/00000201.tif.20.pdf#page=9 |title=The Elements of Non-Euclidean Geometry |chapter='Space Curvature' and the Philosophical Bearing of Non-Euclidean Geometry |page=193 |location=London |publisher=G. Bell and Sons |series=Bell's Mathematical Series for Schools and Colleges |editor-last=Milne |editor-first=William P. |via=University of Michigan Historical Math Collection}} Further reading
1 : Multi-dimensional geometry |
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