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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 Abouabdillah's theorem ： ウィキペディア英語版 Abouabdillah's theorem Abouabdillah's theorem refers to two distinct theorems in mathematics, proven by Moroccan mathematician Driss Abouabdillah: one in geometry and one in number theory. ==Geometry== In geometry, similarities of a Euclidean space preserve circles and spheres. Conversely, Abouabdillah's theorem states that every injective or surjective transformation of a Euclidean space that preserves circles or spheres is a similarity. More precisely: Theorem. Let $E$ be a Euclidean affine space of dimension at least 2. Then: 1. Every surjective mapping $f:\; E\; \backslash rightarrow\; E$ that transforms any four concyclic points into four concyclic points is a similarity. 2. Every injective mapping $f:\; E\; \backslash rightarrow\; E$ that transforms any circle into a circle is a similarity. 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「Abouabdillah's theorem」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.