After the AP Calculus Exam, I gave my students a project for the remainder of the year. We discussed the parametric functions for a cycloid, the traced path of a point on a rolling circle. The students' task was to create a modified cycloid by having a circle roll along a path of their choosing. The students used Desmos to animate their graph and Screencast-O-Matic to record their animation. The assignment was as much an assignment on parametric functions as it is an assignment on baby programming on Desmos. Below are their creations.
Desmos is a fantastic graphing calculator, but it has some limitations when graphing physical situations, because it is not designed as a physics simulator. As the student was perfecting the epicycloid circle-in-a-circle graph, the inner circle was not rotating fast enough, so that it was "slipping" as it moved along the outer circle. This was a very difficult error to catch in a graphing calculator. Perhaps this is an accepted limitation of the medium.
I started this blog to share my transformation from math nerd to math nerd who loves to share math with young people. I teach high school in Hanoi, Vietnam. Your comments are always welcome.