Category Archives: Spirograph math
Wheel-Within-a-Wheel Exploration with Wild Gears
Exploring the wheel-within-a-wheel patterns gives insight into how these complex patterns form.
Continue reading →Video: Loopy Wheel-Within-a-Wheel Design
I keep trying new combinations of Wild Gears to make “wheel-within-a-wheel” designs. Here is a lacey, loopy one, shown on video and also available as a colouring page.
Continue reading →Video: Drawing on the outside of the ring
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 … Continue reading →
Intro to the Bar Wheel
The bar is the oddest “wheel” that comes with Spirograph sets. This video is just an introduction to it, demonstrating hole 1 in both rings. With ring 144/96, the bar produces a 12-pointed pattern. With ring 150/105 it makes 21 points. So using … Continue reading →
Super Spirograph by the Numbers
How to know in advance how many points a given wheel will make in any Super Spirograph layout.
Continue reading →Deriving the mathematical formula for the pattern made by a Spirograph gear
Math teacher and YouTube user School of Fish shows us how to derive the formula for the path made by a pen as it traces a hypotrochoid pattern. TRIGGER WARNING: If you were severely traumatized by math in high school, … Continue reading →
Spirograph Pattern Guide
In case you’ve lost the cover of your old Spirograph set, or the booklet showing the patterns, or maybe you’ll just find this handy, I’ve re-created the pattern guide showing the patterns created by Hole #1 of each of the … Continue reading →
Calculating the Number of Points in a Spirograph Pattern
Ever since I was a kid, I wanted to know: How can you predict how many points (or “petals”) a spirograph pattern will have? There IS a formula. You need to know the number of teeth on the wheel and the … Continue reading →
What is the radial distance between the holes in Spirograph wheels?
A reader asked whether the hole numbers on the Spirograph wheels correspond to the distance from the edge in millimeters. The answer is “not quite”. They are very regular, however, which is one of the reasons that the designs are so … Continue reading →