Have you ever drawn designs on the outside of a Spirograph ring? They’re called epitrochoids, as opposed to hypotrochoids which are drawn inside the rings. Epitrochoids have their points on the inside and big arching swoops on the outside. You can fill a letter-size paper if you use a large wheel, as I did in the video below.
How many points will you get? It depends on the same mathematical formula that determines the number of points of a hypotrochoid. You don’t have to do the math, though. Just use this Table of Spirograph Points in the reference section of this website.
Once you’ve drawn your epitrochoid, try drawing a design inside the ring to match it before you take the ring off the paper, as I did in the video.
Here’s another idea: use it as a picture frame or greeting card with a photo or message on the inside!
You can also draw an epitrochoid around another wheel, rather than a ring. Try it.
Drawing around a Spirograph rack, or around open shapes made with Super Spirograph parts, also creates epitrochoids, but that’s a subject for another video.