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词汇 Torus knot
分类 英语词汇 英语翻译词典
释义

Torus knot

中文百科

环面纽结

(3,8)环面纽结
由Apple Grapher(Mac OS X v10内附的软件)绘制的3D立体(3,7)环面纽结
三叶结是典型的(3,2)环面纽结

纽结理论中,环面纽结torus knot)是一种特殊的结。它由一对整参数pq决定。

(p,q)-环面纽结可以表示为:

x = \left(2+\cos\left(\frac{q\phi}{p}\right)\right)\cos\phi
y = \left(2+\cos\left(\frac{q\phi}{p}\right)\right)\sin\phi
z = \sin\left(\frac{q\phi}{p}\right)

这个纽结所处的平面为 (r − 2) + z = 1(以圆柱坐标系表示)。

英语百科

Torus knot 环面纽结

A (3,−7)-3D torus knot.
EureleA Award showing a (2,3)-torus knot.
(2,8) torus link
the (2,−3)-torus knot, also known as the left-handed trefoil knot

In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R. Similarly, a torus link is a link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of coprime integers p and q. A torus link arises if p and q are not coprime (in which case the number of components is ***(p, q)). A torus knot is trivial (equivalent to the unknot) if and only if either p or q is equal to 1 or −1. The simplest nontrivial example is the (2,3)-torus knot, also known as the trefoil knot.

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