Computing Chebyshev knot diagrams

2010/01/28 by Koseleff, Pierre-Vincent, Pecker, Daniel, Rouillier, Fabrice
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1001.5192

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∈ \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.

Related

• Chebyshev Knots
• The first rational Chebyshev knots
• Chebyshev diagrams for rational knots
• Chebyshev diagrams for two-bridge knots
• Curves defined by Chebyshev polynomials