# Tracing Parametrics, Chains of Events, and Constructing a Pentagon

Last week I attended a PD session by Suzanne Gaskell, an art teacher at the high school where I teach.  She presented on a work of art she has created and calls

This work of art is a wooden box that tells the story of ancient geometry and its relation to various sacred traditions.  After her presentation, she instructed us on how to perform some interesting constructions, including one I had never done before, the regular pentagon.

It inspired me to create an illustration of the construction for a regular polygon using Desmos.  Here’s what I came up with:

TWO GREAT SKILLS I LEARNED

First skill: how to trace a parametric curve.  Prior to creating this, I didn’t know how to make a parametric curve trace itself out.  Here’s how to do it: (link to graph)

1. Set up a parametric curve and define the domain.
2. Make a slider for a parameter (I used p) that slides between the exact values of the domain for t.
3. Inside the parametric equations, place the restrictions on t as I’ve shown here:

Second skill: how to set up a chain of events.  (Hint: use only a single slider and make each stage appear for a different range of the values.)  Try making something like the graph below.

(how I did it.)

Both of these skills are certainly things I’ll use in the classroom, and in particular, the skill of tracing parametric equations when we get to that topic in Pre-Calculus this spring.