Elliptical Spirograph Locus
Circle rolling around the outside of an ellipse. What is the locus of points for this version of a Spirograph device?
Notice the jagged locus along with the jump discontinuities. Here a table of values was used for the distances around the ellipse. They end up being approximations which cause the uneven locus. Experiment with this process and see why the arc length integral was not a good choice here.