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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 Fary–Milnor theorem ： ウィキペディア英語版 Fary–Milnor theorem In the mathematical theory of knots, the Fary–Milnor theorem, named after István Fáry and John Milnor, states that three-dimensional smooth curves with small total curvature must be unknotted. The theorem was proved independently by Fáry in 1949 and Milnor in 1950. It was later shown to follow from the existence of quadrisecants . ==Statement of the theorem== If ''K'' is any closed curve in Euclidean space that is sufficiently smooth to define the curvature κ at each of its points, and if the total absolute curvature is less than or equal to 4π, then ''K'' is an unknot, i.e.: :$\backslash text\; \backslash ,\; \backslash oint\_K\; \backslash !\; |\backslash kappa(s)|\; \backslash ,\; \backslash operatornames\; \backslash le\; 4\; \backslash pi\; \backslash \; \backslash text\; \backslash \; K\; \backslash \; \backslash text.$ The contrapositive tells us that if ''K'' is not an unknot, i.e. ''K'' is not isotopic to the circle, then the total curvature will be strictly greater than 4π. Notice that having the total curvature less than or equal to 4π is merely a sufficient condition for ''K'' to be an unknot; it is not a necessary condition. In other words, although all knots with total curvature less than or equal to 4π are the unknot, there exist unknots with curvature strictly greater than 4π. 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「Fary–Milnor theorem」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.