Some Polynomial Curves on the Torus

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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 (March 2013)
(Bridgewater State University)
Additional contributions by: James Munden
(St. Louis Community College)
Open content licensed under CC BY-NC-SA




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

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