翻訳と辞書 Words near each other ・ "O" Is for Outlaw ・ "O"-Jung.Ban.Hap. ・ "Ode-to-Napoleon" hexachord ・ "Oh Yeah!" Live ・ "Our Contemporary" regional art exhibition (Leningrad, 1975) ・ "P" Is for Peril ・ "Pimpernel" Smith ・ "Polish death camp" controversy ・ "Pro knigi" ("About books") ・ "Prosopa" Greek Television Awards ・ "Pussy Cats" Starring the Walkmen ・ "Q" Is for Quarry ・ "R" Is for Ricochet ・ "R" The King (2016 film) ・ "Rags" Ragland ・ ! (album) ・ ! (disambiguation) ・ !! ・ !!! ・ !!! (album) ・ !!Destroy-Oh-Boy!! ・ !Action Pact! ・ !Arriba! La Pachanga ・ !Hero ・ !Hero (album) ・ !Kung language ・ !Oka Tokat ・ !PAUS3 ・ !T.O.O.H.! ・ !Women Art Revolution 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 catenoid ： ウィキペディア英語版 catenoid A catenoid is a surface in 3-dimensional Euclidean space arising by rotating a catenary curve about its directrix. Not counting the plane, it is the first minimal surface to be discovered. It was found and proved to be minimal by Leonhard Euler in 1744. Early work on the subject was published also by Jean Baptiste Meusnier. There are only two minimal surfaces of revolution (surfaces of revolution which are also minimal surfaces): the plane and the catenoid.〔(Catenoid at MathWorld )〕 The catenoid may be defined by the following parametric equations: :$x=c\; \backslash cosh\; \backslash frac\; \backslash cos\; u$ :$y=c\; \backslash cosh\; \backslash frac\; \backslash sin\; u$ :$z=v$ :where u and v are real parameters and c is a non-zero real constant. In cylindrical coordinates: :$\backslash rho\; =c\; \backslash cosh\; \backslash frac$ :Where c is a real constant. A physical model of a catenoid can be formed by dipping two circles into a soap solution and slowly drawing the circles apart. The catenoid may be also defined approximately by the Stretched grid method as a facet 3D model == Helicoid transformation == Because they are members of the same associate family of surfaces, one can bend a catenoid into a portion of a helicoid without stretching. In other words, one can make a (mostly) continuous and isometric deformation of a catenoid to a portion of the helicoid such that every member of the deformation family is minimal (having a mean curvature of zero). A parametrization of such a deformation is given by the system :$x(u,v)\; =\; \backslash cos\; \backslash theta\; \backslash ,\backslash sinh\; v\; \backslash ,\backslash sin\; u\; +\; \backslash sin\; \backslash theta\; \backslash ,\backslash cosh\; v\; \backslash ,\backslash cos\; u$ :$y(u,v)\; =\; -\backslash cos\; \backslash theta\; \backslash ,\backslash sinh\; v\; \backslash ,\backslash cos\; u\; +\; \backslash sin\; \backslash theta\; \backslash ,\backslash cosh\; v\; \backslash ,\backslash sin\; u$ :$z(u,v)\; =\; u\; \backslash cos\; \backslash theta\; +\; v\; \backslash sin\; \backslash theta\; \backslash ,$ :for $(u,v)\; \backslash in\; (-\backslash pi,\; \backslash pi]\; \backslash times\; (-\backslash infty,\; \backslash infty)$, with deformation parameter , where $\backslash theta\; =\; \backslash pi$ corresponds to a right-handed helicoid, $\backslash theta\; =\; \backslash pm\; \backslash pi\; /\; 2$ corresponds to a catenoid, and $\backslash theta\; =\; 0$ corresponds to a left-handed helicoid. 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「catenoid」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.