翻訳と辞書 Words near each other ・ Ribble Way ・ Ribblehead ・ Ribblehead railway station ・ Ribblehead Viaduct ・ Ribblesdale ・ Ribblesdale High School ・ Ribblesdale Stakes ・ Ribbleton ・ Ribbleton railway station ・ Ribbon ・ Ribbon (award) ・ Ribbon (band) ・ Ribbon (company) ・ Ribbon (computing) ・ Ribbon (disambiguation) ・ Ribbon (mathematics) ・ Ribbon (rhythmic gymnastics) ・ Ribbon cable ・ Ribbon candy ・ Ribbon Cascade (Teton County, Wyoming) ・ Ribbon category ・ Ribbon Creek incident ・ Ribbon development ・ Ribbon diagram ・ Ribbon eel ・ Ribbon Fall ・ Ribbon farm ・ Ribbon Hero ・ Ribbon Hero 2 ・ Ribbon Hopf algebra 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 Ribbon (mathematics) ： ウィキペディア英語版 Ribbon (mathematics) In mathematics (differential geometry) by a ribbon (or strip) $(X,U)$ is meant a smooth space curve $X$ given by a three-dimensional vector $X(s)$, depending continuously on the curve arc-length $s$ ($a\backslash leq\; s\; \backslash leq\; b$), together with a smoothly varying unit vector $U(s)$ perpendicular to $X$ at each point (Blaschke 1950). The ribbon $(X,U)$ is called ''simple'' and ''closed'' if $X$ is simple (i.e. without self-intersections) and closed and if $U$ and all its derivatives agree at $a$ and $b$. For any simple closed ribbon the curves $X+\backslash varepsilon\; U$ given parametrically by $X(s)+\backslash varepsilon\; U(s)$ are, for all sufficiently small positive $\backslash varepsilon$, simple closed curves disjoint from $X$. The ribbon concept plays an important role in the Cǎlugǎreǎnu-White-Fuller formula (Fuller 1971), that states that :$Lk\; =\; Wr\; +\; Tw\; \backslash ;,$ where $Lk$ is the asymptotic (Gauss) linking number (a topological quantity), $Wr$ denotes the total writhing number (or simply writhe) and $Tw$ is the total twist number (or simply twist). Ribbon theory investigates geometric and topological aspects of a mathematical reference ribbon associated with physical and biological properties, such as those arising in topological fluid dynamics, DNA modeling and in material science. ==References== *Blaschke, W. (1950) ''Einführung in die Differentialgeometrie''. Springer-Verlag. ISBN 9783817115495 *Fuller, F.B. (1971) (The writhing number of a space curve ). ''PNAS USA'' 68, 815-819. 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「Ribbon (mathematics)」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.