# Plot a circle in 3-D with a tangle

I'd like to plot a circle with a small tangle. I tried it but it didn't work. I want to plot it like in the picture below but only in 3-D if it is possible.

What i did so far

  ParametricPlot3D[{{-1.94+2*Cos[t],0.2+2*Sin[t],0},{(2+Cos[3s])*Cos[2s]/20,(2+Cos[3s])*Sin[2s]/20,0}},{t,-0.07,1.95Pi},{s,0,2Pi},PlotStyle -> {Red,Green}]

• "I tried it but it didn't work." What did you try? How did it fail? Nov 25 '17 at 21:26
• KnotData["Trefoil"] is a start. Nov 25 '17 at 21:29
• my approach was to do it with a ParametricPlot using {cos(t)*sin(t), sin(t)*cos(t)} but i can not find the right factors to plot the loop on top of the circle. Thanks for KnotData, i will try it with it maybe it works Nov 26 '17 at 0:05

It becomes too big for a comment, so I put it in the answer.

Here is something I found in Lee Stemkoski's website. Based on that we can make knots in two ways.

Manipulate[
ParametricPlot3D[{Cos[q t] (3 + Sin[p t]),Sin[q t](3 + Cos[p t]), Sin[p t]}, {t, 0, 2 Pi}]
,{q, 1, 5}, {p, 1, 5}]

Manipulate[
ParametricPlot3D[{Cos[p t], Cos[q t + Pi/2/p],
Cos[p t + Pi/2] + Cos[(q - p) t + Pi/2/p - Pi/4/q]}, {t, 0, 2 Pi}]
,{q, 1, 5}, {p, 1, 5}]


Play with the p and q parameter to change the appearance.

• Thank you very much. What i dit so far is ParametricPlot3D[{{-1.94+2*Cos[t],0.2+2*Sin[t],0},{(2+Cos[3s])*Cos[2s]/20,(2+Cos[3s)*Sin[2s]/20,0}},{t,-0.07,1.95Pi},{s,0,2Pi},PlotStyle -> {Red,Green}] so it plot almost what i want, but its not perfect. Nov 26 '17 at 12:15