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.
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:
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:
I wrote a review of Big Big Train’s soon-to-be-released album, Grand Tour, and it has been posted at the Spirit of Cecilia site. It’s a terrific set of songs by one of the most talented rock groups working today.
What Hath the Train Wrought, Part I
FracTad's Fractopia 