翻訳と辞書 Words near each other ・ Ellipsoid Hill ・ Ellipsoid method ・ Ellipsoidal coordinates ・ Ellipsoidal reflector spotlight ・ Ellipsometry ・ Ellipsoolithus ・ Ellipsoptera ・ Ellipsuella ・ Ellipta ・ Elliptera ・ Ellipteroides ・ Elliptic algebra ・ Elliptic boundary value problem ・ Elliptic cohomology ・ Elliptic complex ・ Elliptic coordinate system ・ Elliptic curve ・ Elliptic curve cryptography ・ Elliptic curve Diffie–Hellman ・ Elliptic Curve Digital Signature Algorithm ・ Elliptic curve only hash ・ Elliptic curve point multiplication ・ Elliptic curve primality ・ Elliptic cylindrical coordinates ・ Elliptic divisibility sequence ・ Elliptic filter ・ Elliptic flow ・ Elliptic function ・ Elliptic gamma function ・ Elliptic Gauss sum 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 Elliptic coordinate system ： ウィキペディア英語版 Elliptic coordinate system In geometry, the elliptic coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae. The two foci $F\_$ and $F\_$ are generally taken to be fixed at $-a$ and $+a$, respectively, on the $x$-axis of the Cartesian coordinate system. ==Basic definition== The most common definition of elliptic coordinates $(\backslash mu,\; \backslash nu)$ is :$$ x = a \ \cosh \mu \ \cos \nu :$$ y = a \ \sinh \mu \ \sin \nu where $\backslash mu$ is a nonnegative real number and $\backslash nu\; \backslash in\; (2\backslash pi).$ On the complex plane, an equivalent relationship is :$$ x + iy = a \ \cosh(\mu + i\nu) These definitions correspond to ellipses and hyperbolae. The trigonometric identity :$$ \frac \cosh^ \mu} + \frac \sinh^ \mu} = \cos^ \nu + \sin^ \nu = 1 shows that curves of constant $\backslash mu$ form ellipses, whereas the hyperbolic trigonometric identity :$$ \frac \cos^ \nu} - \frac \sin^ \nu} = \cosh^ \mu - \sinh^ \mu = 1 shows that curves of constant $\backslash nu$ form hyperbolae. 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「Elliptic coordinate system」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.