翻訳と辞書 Words near each other ・ Spirembolus synopticus ・ Spirembolus tiogensis ・ Spirembolus tortuosus ・ Spirembolus vallicolens ・ Spirembolus venustus ・ Spirembolus whitneyanus ・ Spirendolol ・ Spirent ・ Spires ・ Spires Academy ・ Spires of Naples ・ Spires of Spirit ・ Spires That in the Sunset Rise ・ Spiret Peak ・ Spirgai ・ Spiric section ・ Spiridion Lusi ・ Spiridione Gopcevich ・ Spiridon (disambiguation) ・ Spiridon Brusina ・ Spiridon Drozhzhin ・ Spiridon Gopčević ・ Spiridon Ilo ・ Spiridon Kacarosi ・ Spiridon Mattar ・ Spiridon Peninsula ・ Spiridon Popescu ・ Spiridon Sobol ・ Spiridon Stais ・ Spiridon Zhevakhov Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Spiric section ： ウィキペディア英語版 Spiric section In geometry, a spiric section, sometimes called a spiric of Perseus, is a quartic plane curve defined by equations of the form :$(x^2+y^2)^2=dx^2+ey^2+f.\; \backslash ,$ Equivalently, spiric sections can be defined as bicircular quartic curves that are symmetric with respect to the ''x'' and ''y''-axes. Spiric sections are included in the family of toric sections and include the family of hippopedes and the family of Cassini ovals. The name is from σπειρα meaning torus in ancient Greek. A spiric section is sometimes defined as the curve of intersection of a torus and a plane parallel to its rotational symmetry axis. However, this definition does not include all of the curves given by the previous definition unless imaginary planes are allowed. Spiric sections were first described by the ancient Greek geometer Perseus in roughly 150 BC, and are assumed to be the first toric sections to be described. ==Equations== Start with the usual equation for the torus: :$(x^2+y^2+z^2+b^2-a^2)^2\; =\; 4b^2(x^2+y^2).\; \backslash ,$ Interchanging ''y'' and ''z'' so that the axis of revolution is now on the ''xy''-plane, and setting ''z''=''c'' to find the curve of intersection gives :$(x^2+y^2-a^2+b^2+c^2)^2\; =\; 4b^2(x^2+c^2).\; \backslash ,$ In this formula, the torus is formed by rotating a circle of radius ''a'' with its center following another circle of radius ''b'' (not necessarily larger than ''a'', self-intersection is permitted). The parameter ''c'' is the distance from the intersecting plane to the axis of revolution. There are no spiric sections with ''c'' > ''b'' + ''a'', since there is no intersection; the plane is too far away from the torus to intersect it. Expanding the equation gives the form seen in the definition :$(x^2+y^2)^2=dx^2+ey^2+f\; \backslash ,$ where :$d=2(a^2+b^2-c^2),\backslash \; e=2(a^2-b^2-c^2),\backslash \; f=-(a+b+c)(a+b-c)(a-b+c)(a-b-c).\; \backslash ,$ In polar coordinates this becomes :$(r^2-a^2+b^2+c^2)^2\; =\; 4b^2(r^2\backslash cos^2\backslash theta+c^2)\; \backslash ,$ or :$r^4=dr^2\backslash cos^2\backslash theta+er^2\backslash sin^2\backslash theta+f.\; \backslash ,$ 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「Spiric section」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.