# 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

## Snapshots

## Details

Reference

[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.

## Permanent Citation

"Some Polynomial Curves on the Torus"

http://demonstrations.wolfram.com/SomePolynomialCurvesOnTheTorus/

Wolfram Demonstrations Project

Published: March 11 2013