Trefoil Mobius Knot ornament

thingiverse

In the animation, a square tube rotates 270 degrees around a "harmonic" knot curve. The curve is defined by the equation r(t) = (.41 Cos(t) - .18 Sin(t) - .83 Cos[2 t] - .83 Sin[2 t] - .11 Cos[3 t] + .27 Sin[3 t]), (.36 Cos(t) + .27 Sin(t) - 1.13 Cos[2 t] + .30 Sin[2 t] + .11 Cos[3 t] - .27 Sin[3 t]), and (.45 Sin(t) - .30 Cos[2 t] + 1.13 Sin[2 t] - .11 Cos[3 t] + .27 Sin[3 t]). This parameterization was credited to Aaron Trautwein in a paper by Louis Kauffman on "Harmonic Knots". A similar knot animation can be viewed at http://vimeo.com/79214087.