Some of the best math projects double as art projects, and Star Polygons is a beautiful example. The mathematics is fascinating, and with pencil and paper you can stay busy exploring rigorous mathematics by finding patterns, making conjectures, and breaking them when you discover a counterexample.

Then, when you’re ready to do something craftier, the exercise can become a visual delightful.

The video launch below will help you get started with this at home. This exploration can be done for kids K – 12. (At lower grades, focus on drawing the shapes precisely. In high school, try to algebratize and formalize the general solutions.)

The PDF can also get you started, and contains nicely-spaced dot circles. The main thing to remember is that you can change the number of dots, the jump rule, or both. That gives you a lot to explore! The goal is to predict when a jump rule hits all the dots.

The craft part is less my specialty, but happily, the blog Math In Unexpected Places did a beautiful post on Star Polygons a few years ago, and everything you need to turn this into a craft project is there. The title of the blog post is Star-o-Rama (and how to make them). Image from that blog to whet your craft appetite is below!

Enjoy!