Thingiverse
Trefoil Mobius Knot ornament
by mm1440
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Square tube rotating -270 degree around "harmonic" knot curve.
Curve: 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]),
(.45 Sin(t) - .30 Cos[2 t] +1.13 Sin[2 t] - .11 Cos[3 t] + .27 Sin[3 t])
This parameterization is credited to Aaron Trautwein in a paper by Louis Kauffman on "Harmonic Knots".
animation of similar knot: http://vimeo.com/792
Curve: 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]),
(.45 Sin(t) - .30 Cos[2 t] +1.13 Sin[2 t] - .11 Cos[3 t] + .27 Sin[3 t])
This parameterization is credited to Aaron Trautwein in a paper by Louis Kauffman on "Harmonic Knots".
animation of similar knot: http://vimeo.com/792
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