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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 Trisectrix of Maclaurin ： ウィキペディア英語版 Trisectrix of Maclaurin In geometry, the trisectrix of Maclaurin is a cubic plane curve notable for its trisectrix property, meaning it can be used to trisect an angle. It can be defined as locus of the point of intersection of two lines, each rotating at a uniform rate about separate points, so that the ratio of the rates of rotation is 1:3 and the lines initially coincide with the line between the two points. A generalization of this construction is called a sectrix of Maclaurin. The curve is named after Colin Maclaurin who investigated the curve in 1742. ==Equations== Let two lines rotate about the points $P\; =\; (0,0)$ and $P\_1\; =\; (a,\; 0)$ so that when the line rotating about $P$ has angle $\backslash theta$ with the ''x'' axis, the rotating about $P\_1$ has angle $3\backslash theta$. Let $Q$ be the point of intersection, then the angle formed by the lines at $Q$ is $2\backslash theta$. By the law of sines, :$=\; \backslash !$ so the equation in polar coordinates is (up to translation and rotation) :$r=\; a\; \backslash frac\; =\; \backslash frac\; =\; (4\; \backslash cos\; \backslash theta\; -\; \backslash sec\; \backslash theta)\backslash !$. The curve is therefore a member of the Conchoid of de Sluze family. In Cartesian coordinates the equation of this curve is :$2x(x^2+y^2)=a(3x^2-y^2)\backslash !$. If the origin is moved to (''a'', 0) then a derivation similar to that given above shows that the equation of the curve in polar coordinates becomes :$r\; =\; \backslash frac\{2\; \backslash cos\{\backslash theta\; \backslash over\; 3\}\}\backslash !$ making it an example of an epispiral. 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「Trisectrix of Maclaurin」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.