Some Polynomial Curves on the Torus

This Demonstration plots the graphs of the functions on the flat torus on the left and on the non-flat torus with zero center radius on the right. The standard example is (when ), which gives a closed curve if is rational or a nonclosed curve that is dense on the torus when is irrational. The more general case, when , shows some interesting behavior of the curves obtained on both tori. The parameter is a scaling factor.
  • Contributed by: Vignon Oussa
  • (Bridgewater State University)
  • Additional contributions by: James Munden
  • (St. Louis Community College)


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[1] F. B. Fuller, "Notes on Trajectories in a Solid Torus," Annals of Mathematics 56(3), 1952 pp. 438–439. www.jstor.org/stable/1969652.
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