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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 Catalan surface ： ウィキペディア英語版 Catalan surface In geometry, a Catalan surface, named after the Belgian mathematician Eugène Charles Catalan, is a ruled surface all of whose rulings are parallel to a fixed plane. The vector equation of a Catalan surface is given by :''r'' = ''s''(''u'') + ''v'' ''L''(''u''), where ''r'' = ''s''(''u'') is the space curve and ''L''(''u'') is the unit vector of the ruling at ''u'' = ''u''. All the vectors ''L''(''u'') are parallel to the same plane, called the ''directrix plane'' of the surface. This can be characterized by the condition: the mixed product (''L' ''(''u''), ''L" ''(''u'') ) = 0.() The parametric equations of the Catalan surface are () $x=f(u)+vi(u),\backslash quad\; y=g(u)+vj(u),\backslash quad\; z=h(u)+vk(u)\; \backslash ,$ If all the rulings of a Catalan surface intersect a fixed line, then the surface is called a conoid. Catalan proved that the helicoid and the plane were the only ruled minimal surfaces. ==See also== *Ruled surface *Conoid * generalized 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「Catalan surface」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.