Harmonic Knots

Abstract

The harmonic knot $\H(a,b,c)$ is parametrized as $K(t)= (T_a(t) ,T_b (t), T_c (t))$ where $a$, $b$ and $c$ are pairwise coprime integers and $T_n$ is the degree $n$ Chebyshev polynomial of the first kind. We classify the harmonic knots $\H(a,b,c)$ for $ a \le 4. $ We study the knots $\H (2n-1, 2n, 2n+1),$ the knots $\H(5,n,n+1),$ and give a table of the simplest harmonic knots.