BTW this trig identity approach also works nicely for “Lissajous figure” knots like 7_4 : https://en.wikipedia.org/wiki/Knot_theory <https://en.wikipedia.org/wiki/Knot_theory> and https://en.wikipedia.org/wiki/Lissajous_knot <https://en.wikipedia.org/wiki/Lissajous_knot> . We just need to vary z[t] to get the overpasses and underpasses we want. - Cris