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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 Comparison triangle ： ウィキペディア英語版 Comparison triangle Define $M\_^$ as the 2-dimensional metric space of constant curvature $k$. So, for example, $M\_^$ is the Euclidean plane, $M\_^$ is the surface of the unit sphere, and $M\_^$ is the hyperbolic plane. Let $X$ be a metric space. Let $T$ be a triangle in $X$, with vertices $p$, $q$ and $r$. A comparison triangle $T$ * in $M\_^$ for $T$ is a triangle in $M\_^$ with vertices $p\text{'}$, $q\text{'}$ and $r\text{'}$ such that $d(p,q)\; =\; d(p\text{'},q\text{'})$, $d(p,r)\; =\; d(p\text{'},r\text{'})$ and $d(r,q)\; =\; d(r\text{'},q\text{'})$. Such a triangle is unique up to isometry. The interior angle of $T$ * at $p\text{'}$ is called the comparison angle between $q$ and $r$ at $p$. This is well-defined provided $q$ and $r$ are both distinct from $p$. ==References== * M Bridson & A Haefliger - ''Metric Spaces Of Non-Positive Curvature'', ISBN 3-540-64324-9 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「Comparison triangle」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.