  We show that every rational knot $K$ of crossing number $N$ admits a
polynomial parametrization $x=T_a(t), y = T_b(t), z = C(t)$ where $T_k(t)$ are
the Chebyshev polynomials, $a=3$ and $b+ \deg C = 3N.$ We show that every
rational knot also admits a polynomial parametrization with $a=4$. If $C (t)=
T_c(t)$ is a Chebyshev polynomial, we call such a knot a harmonic knot. We give
the classification of harmonic knots for $a \le 4.$

Geometric Topology