While creating the pages for graphing parametric equations, I drew some
interesting graphs. One curve reminded me of the elfin writing in Lord of
the Rings and I was inspired to try creating my own “One Ring.” It took some
work to get curves
drawn on the surface of a modified torus to look like I wanted, but eventually it worked and I created
many other curves along the way.
Each curve is drawn using parametric equations in three dimensions
(sample equations below gallery images). Click on
the Sample Ring button below to see a sample of one curve wrapped around the
modified torus. My favorites are in the gallery below.