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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 Astroid ： ウィキペディア英語版 Astroid An astroid is a particular mathematical curve: a hypocycloid with four cusps. Specifically, it is the locus of a point on a circle as it rolls inside a fixed circle with four times the radius.〔Yates〕 By double generation, it is also the locus of a point on a circle as it rolls inside a fixed circle with 4/3 times the radius. It can also be defined as the envelope of a line segment with an end point on each of the axes. It is therefore the envelope of the moving bar in the Trammel of Archimedes. Its modern name comes from the Greek word for "star". The curve had a variety of names, including tetracuspid (still used), cubocycloid, and paracycle. It is nearly identical in form to the evolute of an ellipse. ==Equations== If the radius of the fixed circle is ''a'' then the equation is given by〔Yates, for section〕 :$x^\; +\; y^\; =\; a^.\; \backslash ,$ This implies that an astroid is also a superellipse. Parametric equations are :$x=a\backslash cos^3\; t\; =\; (\; 3\backslash cos\; t\; +\; \backslash cos\; 3t),$ :$y=a\backslash sin^3\; t\; =\; (\; 3\backslash sin\; t\; -\; \backslash sin\; 3t).$ The pedal equation with respect to the origin is :$r^2\; =\; a^2\; -\; 3p^2,$ the Whewell equation is :$s\; =\; \backslash cos\; 2\backslash varphi,$ and the Cesàro equation is :$R^2\; +\; 4s^2\; =\; \backslash frac.$ The polar equation is〔Mathworld〕 :$r=\backslash frac\backslash theta)^\}.$ The astroid is a real locus of a plane algebraic curve of genus zero. It has the equation :$(x^2+y^2-a^2)^3+27a^2x^2y^2=0.\; \backslash ,$ The astroid is therefore a real algebraic curve of degree six. 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「Astroid」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.