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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 Bonnesen's inequality ： ウィキペディア英語版 Bonnesen's inequality Bonnesen's inequality is an inequality relating the length, the area, the radius of the incircle and the radius of the circumcircle of a Jordan curve. It is a strengthening of the classical isoperimetric inequality. More precisely, consider a planar simple closed curve of length $L$ bounding a domain of area $A$. Let $r$ and $R$ denote the radii of the incircle and the circumcircle. Bonnesen proved the inequality :$\backslash pi^2\; (R-r)^2\; \backslash leq\; L^2-4\backslash pi\; A.\; \backslash ,$ The term $\backslash pi^2\; (R-r)^2$ in the left hand side is known as the isoperimetric defect. Loewner's torus inequality with isosystolic defect is a systolic analogue of Bonnesen's inequality. ==References== * Bonnesen, T.: "Sur une amélioration de l'inégalité isopérimetrique du cercle et la démonstration d'une inégalité de Minkowski," ''C. R. Acad. Sci. Paris'' 172 (1921), 1087–1089. * Yu. D. Burago and V. A. Zalgaller, ''Geometric inequalities''. Translated from the Russian by A. B. Sosinskiĭ. Springer-Verlag, Berlin, 1988. ISBN 3-540-13615-0. 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「Bonnesen'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.