Work

Computing Chebyshev knot diagrams

Year: 2010

Type: preprint

Abstract: A Chebyshev curve C(a,b,c,ϕ) has a parametrization of the form x(t)=Ta(t); y(t)=T_b(t) ; z(t)= Tc(t + ϕ), where a,b,c are integers, Tn(t) is the Chebyshev polynomial of degree n and ϕ\in \RR. When C(a,b,c,ϕ) has no double points, it defines a polynomial knot. We determine all possible knots when a, b and c are given.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1001.5192

Authors: Koseleff, Pierre-Vincent, Pecker, Daniel, Rouillier, Fabrice

Institutions: Institut national de recherche en sciences et technologies du numérique, LIP6, Université Pierre-et-Marie-Curie

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4299302276

Cites:

Cited by:

Related to: 10