Torus knots are Fourier-(1,1,2) knots
Geometric Topology
2007-08-28 v1
Abstract
Every torus knot can be represented as a Fourier-(1,1,2) knot which is the simplest possible Fourier representation for such a knot. This answers a question of Kauffman and confirms the conjecture made by Boocher, Daigle, Hoste and Zheng. In particular, the torus knot T(p,q) can be parameterized as x(t)=cos(pt), y(t)=cos(qt+pi/(2p)), and z(t)=cos(pt+pi/2)\cos((q-p)t+pi/(2p)-pi/(4q)).
Keywords
Cite
@article{arxiv.0708.3590,
title = {Torus knots are Fourier-(1,1,2) knots},
author = {Jim Hoste},
journal= {arXiv preprint arXiv:0708.3590},
year = {2007}
}
Comments
5 pages, 1 figure