# 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.

# Sinusoidal Fun

Link to some totally rad sinusoidal picture graphs I’ve been working at lately.  The first 3 pictures have movement!

Turns out sinusoidal curves can be amazing for creating really cool animations.

These pictures were part of a nerdy Valentine to my husband.  (Valentine? Yup!  These pictures are Desmosified versions of some of our favorite things!  And, he’s nearly as nerdy as me, so it’s cool.)  I already showed them to him because I was too pumped up on Desmos-ing to wait until the 14th to share them with him.

I hope you enjoy!

Peace out Desmos world!