# College Math Teaching

## January 6, 2015

### Quick Diversion: a rotating circle of dots within a circle..

Filed under: calculus — Tags: , — collegemathteaching @ 3:37 am

Since grading final exams, I’ve been travelling a bit. I am doing some admin duties but should have some time to do some research prior to….SEARCH COMMITTEE. That is such a time suck.

But here is a bit of fun:

Check out this video

Now here is a challenge (that I will take; feel free to beat me to it): find a set of equations that describes the motion of the centers of these disks.

My idea: I might start with a helix (of the type $x = cos(t), y = sin(t), z = t$ and then have this helix change its center as it “moves up”; perhaps something like $x = 4sos(t) - cos(t), y =4sin(t) - sin(t), z = t$. Then intersect this with planes of the following type: (cylindrical coordinates: $r = \theta$ and then, perhaps the points might described by the intersection of the helix with these planes? I’ll have to check it out.