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.
Click and drag on any of the images below to rotate them. Press SHIFT while
dragging to zoom in and out. Click, drag, and release to spin an image. Press
HOME to return it to its original position.
Zig Zag
N Monogram
Loops with Stripe
Leaves
Bunched Squiggles
Paper Dolls
Beans
Lightning
LOTR Loops
Skiers
Leaves and Berries
Kites
Sample Equation
These are the parametric equations for the Zig Zag Ring: