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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 Crofton formula ： ウィキペディア英語版 Crofton formula In mathematics, the Crofton formula, named after Morgan Crofton (1826–1915), is a classic result of integral geometry relating the length of a curve to the expected number of times a "random" line intersects it. ==Statement== Suppose γ is a rectifiable plane curve. Given an oriented line ''l'', let ''n''γ(''l'') be the number of points at which γ and ''l'' intersect. We can parametrize the general line ''l'' by the direction φ in which it points and its signed distance ''p'' from the origin. The Crofton formula expresses the arc length of the curve γ in terms of an integral over the space of all oriented lines: :$\backslash text\; (\backslash gamma)\; =\; \backslash frac14\backslash iint\; n\_\backslash gamma(\backslash varphi,\; p)\backslash ;\; d\backslash varphi\backslash ;\; dp.$ The differential form :$d\backslash varphi\backslash wedge\; dp$ is invariant under rigid motions, so it is a natural integration measure for speaking of an "average" number of intersections. 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「Crofton formula」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.