Harmonic Knots

The harmonic knot $\overset{˝}{(} a, b, c)$ is parametrized as $K(t)= (T_a(t) ,T_b (t), T_c (t)) $w h e r e$ a $,$ b $a n d$ c $a r e p a i r w i s e c o p r i m e i n t e g e r s a n d$ T_n$ is the degree $n$ Chebyshev polynomial of the first kind. We classify the harmonic knots $\overset{˝}{(} a, b, c)$ for $a \leq 4.$ We study the knots $\overset{˝}{(} 2 n - 1, 2 n, 2 n + 1),$ the knots $\overset{˝}{(} 5, n, n + 1),$ and give a table of the simplest harmonic knots.