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Inversion of trefoil knot

  • Trefoil knot - Black curve
  • Inversion - Red curve

GeoGebra script

translateY = Slider(-3, 3, 0.01, 1, 200) # Trefoil knot fx(x) = sin(x) + 2sin(2x) fy(x) = cos(x) - 2cos(2x) + translateY fz(x) = -sin(3x) trefoilKnot = Curve(fx(t), fy(t), fz(t), t, 0, 2pi) # 2-sphere sx(x, y) = cos(x) sin(y) sy(x, y) = sin(x) sin(y) sz(x, y) = cos(y) twoSphere = Surface(sx(u, v), sy(u, v), sz(u, v), u, 0, 2pi, v, 0, pi) # Inversion norm2(x) = (fx(x))^2 + (fy(x))^2 + (fz(x))^2 trefoilKnotInverted = Curve(fx(t) / norm2(t), fy(t) / norm2(t) , fz(t) / norm2(t), t, 0, 2pi)