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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 Pedoe's inequality ： ウィキペディア英語版 Pedoe's inequality In geometry, Pedoe's inequality, named after Daniel Pedoe, states that if ''a'', ''b'', and ''c'' are the lengths of the sides of a triangle with area ''ƒ'', and ''A'', ''B'', and ''C'' are the lengths of the sides of a triangle with area ''F'', then :$A^2(b^2+c^2-a^2)+B^2(a^2+c^2-b^2)+C^2(a^2+b^2-c^2)\backslash geq\; 16Ff,\backslash ,$ with equality if and only if the two triangles are similar with pairs of corresponding sides (''A, a''), (''B, b''), and (''C, c''). The expression on the left is not only symmetric under any of the six permutations of the set of pairs, but also—perhaps not so obviously—remains the same if ''a'' is interchanged with ''A'' and ''b'' with ''B'' and ''c'' with ''C''. In other words, it is a symmetric function of the pair of triangles. Pedoe's inequality is a generalization of Weitzenböck's inequality, which is the case in which one of the triangles is equilateral. ==See also== *List of triangle inequalities 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「Pedoe's inequality」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.