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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 Holditch's theorem ： ウィキペディア英語版 Holditch's theorem In plane geometry, Holditch's theorem states that if a chord of fixed length is allowed to rotate inside a convex closed curve, then the locus of a point on the chord a distance ''p'' from one end and a distance ''q'' from the other is a closed curve whose area is less than that of the original curve by $\backslash pi\; pq$. The theorem was published in 1858 by Rev. Hamnet Holditch.〔〔Holditch, Rev. Hamnet, "Geometrical theorem", ''The Quarterly Journal of Pure and Applied Mathematics'' 2, 1858, p. 38.〕 While not mentioned by Holditch, the proof of the theorem requires an assumption that the chord be short enough that the traced locus is a simple closed curve.〔Broman, Arne, ("A fresh look at a long-forgotten theorem" ), ''Mathematics Magazine'' 54(3), May 1981, 99–108.〕 ==Observations== The theorem is included as one of Clifford Pickover's 250 milestones in the history of mathematics. Some peculiarities of the theorem include that the area formula $\backslash pi\; pq$ is independent of both the shape and the size of the original curve, and that the area formula is the same as for that of the area of an ellipse with semi-axes ''p'' and ''q''. The theorem's author was a president of Caius College, Cambridge. 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「Holditch's theorem」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.