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In geometry, a quadrisecant or quadrisecant line of a curve is a line that passes through four points of the curve. ==In knot theory== In three-dimensional Euclidean space, every non-trivial tame knot or link has a quadrisecant. Originally established in the case of knotted polygons and smooth knots by Erika Pannwitz,〔 this result was extended to knots in suitably general position and links with nonzero linking number,〔 and later to all nontrivial tame knots and links.〔 Pannwitz proved more strongly that the number of distinct quadrisecants is lower bounded by a function of the minimum number of boundary singularities in a locally-flat open disk bounded by the knot.〔〔 conjectured that the number of distinct quadrisecants of a given knot is always at least ''n''(''n'' − 1)/2, where ''n'' is the crossing number of the knot.〔〔 However, counterexamples to this conjecture have since been discovered.〔 Two-component links have quadrisecants in which the points on the quadrisecant appear in alternating order between the two components,〔 and nontrivial knots have quadrisecants in which the four points, ordered cyclically as ''a'',''b'',''c'',''d'' on the knot, appear in order ''a'',''c'',''b'',''d'' along the quadrisecant.〔 The existence of these alternating quadrisecants can be used to derive the Fary–Milnor theorem, a lower bound on the total curvature of a nontrivial knot.〔 Quadrisecants have also been used to find lower bounds on the ropelength of knots.〔 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「Quadrisecant」の詳細全文を読む スポンサード リンク
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