A Stained-Glass Fractal

I have been invited to participate in Harpeth Hall’s faculty art show this fall, so I’m planning on spending some time this summer creating three or four pieces that use mathematics in their design.

I just completed the first one, which uses the fractal property of self-similarity: each outer circle is split into two smaller circles. Of course, if it were a true fractal, the process would repeat ad infinitum, but due to the limitations of working with glass I had to stop after four iterations.

Artglass fractal

Creating a “Geometric Eye” Using Desmos

Geometric Eye

Several years ago, I came across some videos by the artist Dearing Wang that showed how to create mandalas and other geometric figures using only a compass and straightedge. One of them was a figure he called a “Geometric Eye“. Drawing one by hand took hours. Using the online Desmos math app, you can create one in minutes! Here’s my screencast explaining how:

Creating Rotated Solids Using GeoGebra 3D

One of the hardest Calculus topics for my students to visualize is rotating areas around an axis to create a solid. Fortunately, you can now create a great 3D representation of rotated solids using GeoGebra’s 3D app. Once you get the hang of it, it is quick and a heck of a lot easier than trying to draw them by hand!

Before I go any further, I want to give credit to Steve Phelps for posting a demo of this technique on his Twitter feed. If you are a math teacher, you really should follow him @MathTechCoach. I have learned more cool tech tricks from him than anyone else online.

Here’s my screencast illustrating how to create your very own rotated solids: