My freshman geometry class has been asking me all year when we would be able to use Desmos (they know how much I love it.) Now is there time. We are doing a whole unit on coordinate geometry, and so we’ve been Desmos-ing it up.

Here’s the activity we did in class: Circles Activity.

One of the slides in the activity allowed the students to make a simple drawing out of circles. I suggested a Mickey Mouse silhouette or the Olympic Rings.

While most students decided to make the Mickey Mouse Silhouette, a couple went a bit further, one even asking how to make an ellipse.

Of course, working with circles got me to thinking about them. In particular, I got to thinking about how to make use of lists to get Desmos to graph some pretty cool sets of circles. Here’s one that I came up with:

…and that led to a quick exploration of cycloids and epicycloids…

…followed by a little project to trace the path made by the center of a circle that rolls over a sine curve. Here’s what I came up with:

I’m pretty sure that my way of making this happen is not the most efficient way. Do you know a better way to do this? Let me know in the comments!

Thoughts for where to go from here: at some point, I’d like to trace a point on a the edge of a circle as it rolls over a sine curve.