Newsletter #4 : Spirographs!

[This is a back-issue of this website’s newsletter]


How many of us enjoyed playing with Spirographs as kids? I know I did. I didn’t realize at the time that there’s an awful lot of math hidden in those cogs! Now, I’ve made a Spirograph applet, and uploaded it to the website.  If you haven’t heard of the spirograph before, The Spirograph was invented in 1962 by an engineer. He was actually working on something else altogether, but his family noticed that the tools he was using made beautiful spirally patterns! With their encouragement, the tools became a toy – and a very popular one at that.
When the kids of the 1960’s and 1970’s opened their new Spirograph sets, they’d find cogs and wheels of various sizes, as well as pens and paper. One cog would be pinned to the paper (into a cardboard backing). Another cog would be placed against the first. Then, using the pen, the second cog would be rolled around the first. In the process, a pretty spirally pattern would form.
It is still possible to buy Spirograph sets, but the modern ones are not as good as the original. On the other hand, the computer age makes it possible to play with free online Spirograph toys, such as the Spirograph Java Applet I’ve just uploaded to the website.
But what’s all this got to do with math?

The curves produced by a Spirograph are called epicycloids (if the moving circle is outside the fixed one) or hypotrochoids (if it is inside). As you play with a spirograph set or applet, you’ll see that sometimes the curve is very rich and complex, other times it is a very simple symmetric pattern. And this is where the math comes in. You can actually tell how many points a spirograph flower will have, just from the relative sizes of the two circles. I won’t give the formula here. Instead, I’ll recommend you read here about kids’ spirograph math. At that page, I explain the kind of math an elementary school child will pick up from a spirograph, and how you can encourage them in it.
The Spirograph Applet I’ve uploaded allows the child to save and print his or her designs. Normally applets are not allowed to use your hard disk or printer, so when the web page is loaded, you are asked if you want to “trust” the applet. If you say “No”, the Save and Print (and Open) options are disabled, but everything else will work just fine. If you want to save and print, you’ll have to say “Yes”.
Of course, I’d recommend you say “Yes” to trust my applet! On the other hand, it’s generally unwise to trust Applets (or other “interactive content”) from unknown websites.

So, introduce the applet to your kids. Suggest, perhaps, they make a nice birthday card for mom, dad, grandma, grandpa, uncle, aunt, brother or sister. And watch them intuit some spirograph math while they exercise their artistic talents!