Some Polynomial Curves on the Torus
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.
y(t)=ms+b
n
t
y=mt+b
s=n=1
m
m
n>1
s=1orπ