# Circular Thinking

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:

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.

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.

## 2 thoughts on “Circular Thinking”

1. Martin Holtham (@ghsmaths) says:

I replicated the circle rolling on the sine curve – I did it in much the same way, although I made it general so that you can change it to a different curve by editing f(x): https://www.desmos.com/calculator/ggig7sihho

I had a think about tracing a point on a circle as it rolls on the curve, but I don’t think it is feasible algebraically, as it would involve using the arc length of the sinx curve…

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1. Suzanne von Oy says:

I love your graph! I enjoyed playing around with the function f(x).

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