Why is this so mathematical?

On a high level, the drawings produced are special types of mathematical curves, called hypotrochoids and epitrochoids. However, without getting any equations involved, you can ask some interesting questions. How can you predict the kind of pattern you will get based on the number of teeth on the ring and gearwheel and the distance between the pen hole and the center of the gearwheel. Conversely, if you want to make a particular type of pattern, which ring, gearwheel, and pen hole should you use?

After interacting with a bunch of students, I found that a few observations helped to push them along:

1. What would happen if you put your pen in the exact center of the gearwheel? You'd just make a circle because the distance from the pen to the ring would not change.

2. What happens if you use the ring has 96 teeth and the gearwheel has 24 teeth? You make a square, and 96/24 = 4. This leads to thinking about the number of teeth in each ring and gearwheel and keeping track of the results of different combinations.

Kits like this one (amazon affiliate link here) come with spiro-putty to hold down the rings. Since we didn't have spiro-putty with us at the festival, it was a challenge for the kids to keep the rings still (the parents often ended up helping with this). It was also challenging to keep the gearwheel pressed against the ring. This requires slow and controlled movement.

A lot of the parents fondly remembered playing with spirographs as kids, but it seemed to be a novel concept to most of the kids at the festival, even though a few excitedly realized after trying it out that they already had a kit lying around at home unused. I would encourage parents to not just buy one for their kids, but to open it up and start playing around with it themselves. Once you have some artwork to marvel over, offer to show your kids how to do it and stick around until they get the hang of it. Ask them questions like the ones included above, and try to spark their curiosity. Lots of toys and games become mathematical when you start asking questions, making observations and predictions, etc.

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