翻訳と辞書 Words near each other ・ Treherne, Manitoba ・ Treherneville, Virginia ・ Trehowell Halt railway station ・ Trehunist ・ Trehörningen ・ Trehörningen (Sjödalen) ・ Trehörningen, Hanveden ・ Trehörningen, Tyresta ・ Trehøje Mols ・ Trehøje Municipality ・ Trefoil factor 1 ・ Trefoil factor 2 ・ Trefoil factor 3 ・ Trefoil horseshoe bat ・ Trefoil Island ・ Trefoil knot ・ Trefoil knot fold ・ Trefoil-toothed giant rat ・ Trefonen ・ Trefonen F.C. ・ Trefor ・ Trefor Davies ・ Trefor Evans ・ Trefor Goronwy ・ Trefor Jenkins ・ Trefor Proud ・ Trefor Pugh ・ Trefor Puw ・ Trefor Quarry railway ・ Trefor Richard Morgan 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 Trefoil knot ： ウィキペディア英語版 Trefoil knot In topology, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining together the two loose ends of a common overhand knot, resulting in a knotted loop. As the simplest knot, the trefoil is fundamental to the study of mathematical knot theory, which has diverse applications in topology, geometry, physics, chemistry and magic. The trefoil knot is named after the three-leaf clover (or trefoil) plant. == Descriptions == The trefoil knot can be defined as the curve obtained from the following parametric equations: :$x\; =\; \backslash sin\; t\; +\; 2\; \backslash sin\; 2t$ :$\backslash qquad\; y=\backslash cos\; t\; -\; 2\; \backslash cos\; 2t$ :$\backslash qquad\; z=-\backslash sin\; 3t$ The (2,3)-torus knot is also a trefoil knot. The following parametric equations give a (2,3)-torus knot lying on torus $(r-2)^2+z^2\; =\; 1$: :$x\; =\; (2+\backslash cos\; 3t)\backslash cos\; 2t$ :$\backslash qquad\; y=(2+\backslash cos\; 3t\; )\backslash sin\; 2t$ :$\backslash qquad\; z=\backslash sin\; 3t$ Any continuous deformation of the curve above is also considered a trefoil knot. Specifically, any curve isotopic to a trefoil knot is also considered to be a trefoil. In addition, the mirror image of a trefoil knot is also considered to be a trefoil. In topology and knot theory, the trefoil is usually defined using a knot diagram instead of an explicit parametric equation. In algebraic geometry, the trefoil can also be obtained as the intersection in C2 of the unit 3-sphere ''S''3 with the complex plane curve of zeroes of the complex polynomial ''z''2 + ''w''3 (a cuspidal cubic). If one end of a tape or belt is turned over three times and then pasted to the other, a trefoil knot results.〔Shaw, George Russell (). ''Knots: Useful & Ornamental'', p.11. ISBN 978-0-517-46000-9.〕 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「Trefoil knot」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.