Manipulate[
Module[{rr = 2},
torus[u_, v_] := {(rr + Cos[2 \[Pi] u]) Cos[
2 \[Pi] v], (rr + Cos[2 \[Pi] u]) Sin[2 \[Pi] v],
Sin[2 \[Pi] u]};
Toro = ParametricPlot3D[torus[u, v], {u, 0, 1}, {v, 0, 1},
Boxed -> False, Axes -> False, MeshStyle -> None];
Knot = ParametricPlot3D[torus[m u, 2 n u], {u, 0, 1},
Boxed -> False, Axes -> False,
PlotStyle -> {Thickness[0.01], Blue}]];
Show[Toro, Knot],
{{m, 3}, 1, 15, 1}, {{n, 4}, 1, 15, 1}]
see https://mathematica.stackexchange.com/questions/66025/plotting-knot-torus
https://mathematica.stackexchange.com/questions/115414/curve-wound-on-torus
http://demonstrations.wolfram.com/ToroidalHelices/
