Spirograph Math

Figure out the math in the spirograph!


This page explains some of the math that an elementary school child might learn from doing spirograph patterns. Now a kid doesn't play with spirographs in order to learn complex polar-coordinate formulas - nor do they care that the proper names for spirograph curves are epicycloids and hypotrochoids.

A kid plays with spirographs because it's fun.

  • It's fun to make beautiful pictures with a spirograph toy, or spirograph program.
  • It gives a kid a buzz when mom or dad or grandma or grandpa says Wow! You did that all by yourself??
  • It makes a kid proud to see his or her spirograph design displayed on the classroom wall or fridge door.
In the meantime, though, the kid is actually picking up some math. Amazing, but true.

This page has a free spirograph applet for your kids to try. Or, if you plan to buy one, please read this first.

For those not familiar with spirographs, I've made a short movie illustrating the concept. Or, you can skip straight to the math.