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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 Huygens lemniscate ： ウィキペディア英語版 Lemniscate of Gerono In algebraic geometry, the lemniscate of Gerono, or lemniscate of Huygens, or figure-eight curve, is a plane algebraic curve of degree four and genus zero and is a lemniscate curve shaped like an $\backslash infty$ symbol, or figure eight. It has equation :$x^4-x^2+y^2\; =\; 0.$ It was studied by Camille-Christophe Gerono. Because the curve is of genus zero, it can be parametrized by rational functions; one means of doing that is :$x\; =\; \backslash frac,\backslash \; y\; =\; \backslash frac.$ Another representation is :$x\; =\; \backslash cos\; \backslash varphi,\backslash \; y\; =\; \backslash sin\backslash varphi\backslash ,\backslash cos\backslash varphi\; =\; \backslash sin(2\backslash varphi)/2$ which reveals that this lemniscate is a special case of a lissajous figure. The dual curve (see Plücker formula), pictured below, has therefore a somewhat different character. Its equation is :$(x^2-y^2)^3\; +\; 8y^4+20x^2y^2-x^4-16y^2=0.$ ==References== * 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「Lemniscate of Gerono」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.