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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 Ono's inequality ： ウィキペディア英語版 Ono's inequality In mathematics, Ono's inequality is a theorem about triangles in the Euclidean plane. In its original form, as conjectured by T. Ono in 1914, the inequality is actually false; however, the statement is true for acute triangles and right triangles, as shown by Balitrand in 1916. ==Statement of the inequality== Consider an acute or right triangle in the Euclidean plane with side lengths ''a'', ''b'' and ''c'' and area ''A''. Then :$27\; (b^2\; +\; c^2\; -\; a^2)^2\; (c^2\; +\; a^2\; -\; b^2)^2\; (a^2\; +\; b^2\; -\; c^2)^2\; \backslash leq\; (4\; A)^6.$ This inequality fails for general triangles (to which Ono's original conjecture applied), as shown by the counterexample $a=2,\; \backslash ,\; \backslash ,\; b=3,\; \backslash ,\; \backslash ,\; c=4,\; \backslash ,\; \backslash ,\; A=3\backslash sqrt/4.$ The inequality holds with equality in the case of an equilateral triangle, in which up to similarity we have sides $1,1,1$ and area $\backslash sqrt/4.$ 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「Ono'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.