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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Singularity theory ： ウィキペディア英語版 Singularity theory In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it. In some places the flat string will cross itself in an approximate ''X'' shape. The points on the floor where it does this are one kind of singularity, the double point: one bit of the floor corresponds to more than one bit of string. Perhaps the string will also touch itself without crossing, like an underlined 'U'. This is another kind of singularity. Unlike the double point, it is not ''stable'', in the sense that a small push will lift the bottom of the 'U' away from the 'underline'. ==How singularities may arise== In singularity theory the general phenomenon of points and sets of singularities is studied, as part of the concept that manifolds (spaces without singularities) may acquire special, singular points by a number of routes. Projection is one way, very obvious in visual terms when three-dimensional objects are projected into two dimensions (for example in one of our eyes); in looking at classical statuary the folds of drapery are amongst the most obvious features. Singularities of this kind include caustics, very familiar as the light patterns at the bottom of a swimming pool. Other ways in which singularities occur is by degeneration of manifold structure. That implies the breakdown of parametrization of points; it is prominent in general relativity, where a gravitational singularity, at which the gravitational field is strong enough to change the very structure of space-time, is identified with a black hole. In contrast, a tear in the structure of a manifold is a topological anomaly in which no field - embedded in the manifold - can converge. The presence of symmetry can be good cause to consider orbifolds, which are manifolds that have acquired 'corners' in a process of folding up resembling the creasing of a table napkin. 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「Singularity theory」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.