Torus Knot

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Torus Knot
Field: Geometry
Author: 3DXM Consortium
Website: 3DXM Consortium

Torus Knot, by 3DXM Consortium.

In knot theory, a torus knot is a special kind of knot which lies on the surface of an unknotted torus in R3.

Found at 3DXM Consortium
Field: Geometry

Contents


Further Description and Explanations

  • Explanation for Undergraduates
Note: understanding of this explanation requires: *Differential Geometry

These knots lie on the following torus of revolution (having ellipses as meridian curves):

x(t) = (aa + bbcos(u))cos(v)
y(t) = (aa + bbcos(u))sin(v)
z(t) = ccsin(u)
The knots are obtained by putting u = dd t, v = ee t. The parameters dd and ee should be integers, and the result is referred to as a (dd,ee) knot (The program used to make the image rounds dd and ee before using them.)





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