Fun with circles and teeth

A friend handed me one of these the other day and said “Like Spirographs, remember?”

I didn’t remember, but if I ever used one I’m sure I loved it (and apparently it’s possible to find similar products now but Hasbro doesn’t make the original anymore; if I’m wrong please let me know!). This thing is great fun if you like shapes or patterns or color or the unexpected.

And it’s one of those things that the mathematicians like to play with and calculate about that blurs the boundaries between math and art. I’m pretty sure this is the kind of thing Paul Lockhart is talking about all the time; the math that tickles, and wrinkles the brow with amazement.

I mentioned a talk by Conrad Wolfram a while ago, which I remembered in the midst of playing with the hypotrochoid set because I went looking to find out how the thing works and found this animation on his MathWorld of a point rolling around inside a circle in a fixed way which is what goes on with hypotrochoids.  No numbers required in the marveling at it…