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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 Hadwiger–Finsler inequality ： ウィキペディア英語版 Hadwiger–Finsler inequality In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane. It states that if a triangle in the plane has side lengths ''a'', ''b'' and ''c'' and area ''T'', then :$a^\; +\; b^\; +\; c^\; \backslash geq\; (a\; -\; b)^\; +\; (b\; -\; c)^\; +\; (c\; -\; a)^\; +\; 4\; \backslash sqrt\; T\; \backslash quad\; \backslash mbox.$ Weitzenböck's inequality is a straightforward corollary of the Hadwiger–Finsler inequality: if a triangle in the plane has side lengths ''a'', ''b'' and ''c'' and area ''T'', then :$a^\; +\; b^\; +\; c^\; \backslash geq\; 4\; \backslash sqrt\; T\; \backslash quad\; \backslash mbox.$ Weitzenböck's inequality can also be proved using Heron's formula, by which route it can be seen that equality holds in (W) if and only if the triangle is an equilateral triangle, i.e. ''a'' = ''b'' = ''c''. The Hadwiger–Finsler inequality is named after , who also published in the same paper the Finsler–Hadwiger theorem on a square derived from two other squares that share a vertex. ==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「Hadwiger–Finsler 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.