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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 Dilation theory ： ウィキペディア英語版 Dilation (metric space) In mathematics, a dilation is a function $f$ from a metric space into itself that satisfies the identity :$d(f(x),f(y))=rd(x,y)$ for all points $(x,\; y)$, where $d(x,\; y)$ is the distance from $x$ to $y$ and $r$ is some positive real number.〔.〕 In Euclidean space, such a dilation is a similarity of the space.〔. See in particular (p. 110 ).〕 Dilations change the size but not the shape of an object or figure. Every dilation of a Euclidean space that is not a congruence has a unique fixed point〔.〕 that is called the center of dilation.〔.〕 Some congruences have fixed points and others do not.〔.〕 ==See also== * Homothety * Dilation (operator theory) 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「Dilation (metric space)」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.