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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 Quadrifolium ： ウィキペディア英語版 Quadrifolium The quadrifolium (also known as four-leaved clover〔 C G Gibson, ''Elementary Geometry of Algebraic Curves, An Undergraduate Introduction'', Cambridge University Press, Cambridge, 2001, ISBN 978-0-521-64641-3. Pages 92 and 93 〕) is a type of rose curve with n=2. It has polar equation: :$r\; =\; \backslash cos(2\backslash theta),\; \backslash ,$ with corresponding algebraic equation :$(x^2+y^2)^3\; =\; (x^2-y^2)^2.\; \backslash ,$ Rotated by 45°, this becomes :$r\; =\; \backslash sin(2\backslash theta)\; \backslash ,$ with corresponding algebraic equation :$(x^2+y^2)^3\; =\; 4x^2y^2.\; \backslash ,$ In either form, it is a plane algebraic curve of genus zero. The dual curve to the quadrifolium is :$(x^2-y^2)^4\; +\; 837(x^2+y^2)^2\; +\; 108x^2y^2\; =\; 16(x^2+7y^2)(y^2+7x^2)(x^2+y^2)+729(x^2+y^2).\; \backslash ,$ The area inside the curve is $\backslash tfrac\; 12\; \backslash pi$, which is exactly half of the area of the circumcircle of the quadrifolium. The length of the curve is ca. 9.6884.〔(Quadrifolium - from Wolfram MathWorld )〕 ==Notes== 〔 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「Quadrifolium」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.