Teaching Stones

Let me tell you about a new project I started. After teaching many classes semester after semester, I wanted a way to commemorate and remember former sections, students, and years. This led me to create teaching stones.

At some point during the semester (a test day maximizes attendance), I ask the students for a 3D-coordinate point. The goal is to take the convex hull of these points to create a polyhedron. To ensure the points are in convex position, I ask for two numbers: one between zero and π, and the other between zero and 2π. By interpreting these points as spherical coordinates on a sphere of radius 1, we guarantee that the points are in convex position.

Since students choose their own points, each class will produce a unique polyhedron. Many students select meaningful coordinates, choosing numbers associated with area codes, birthdays, military unit numbers, and more. I then 3D-print the class's stone and allow students to sign it, initial it, or write something on it, depending on the size of the print and the size of the class.

These stones are not only a teaching tool for spherical coordinates, projections, polyhedra, and convexity, but also a keepsake to remember the truly amazing students I have had the privilege to teach, mentor, and get to know over the years. I highly recommend trying this out with your own class! Shown here is the teaching stone from my calculus III class during the summer of 2024.