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.
I had a small but talented group of students in my Fractals & Chaos mini-course this year. They used Fractal Explorer, Apophysis, Winfeed, and Chaoscope to create their final projects, which are displayed below. Enjoy!
I taught another three-week stained-glass mini-course this year. After my students learn the basic technique of copper-foil stained glass windows, they research a math topic, write a paper on it, and illustrate it with a window of their own design. Topics this year included systems of inequalities, the Fibonacci Sequence, corresponding angles formed by two lines and a transversal, the Four-Color Theorem, and the Pythagorean Theorem among others.
Here’s a gallery of their finished windows:
Orthocenter of a Triangle
Angle-Side-Angle Triangle Congruence
Compound Curve and System of Inequalities
Corresponding Angles formed by a Transversal
The Fibonacci Sequence
The Four-Color Theorem
Linear Inequality Solution on a Number Line
Medians, Circumcenter, and Tangents
A Catalog of Angles: Acute, Right, Obtuse, and Straight
We have a very impressive dance program at Harpeth Hall with amazingly creative choreographers. One of them asked me to create an animation involving equations and fractal animation that will be projected behind some dancers as they perform. The music is a portion of a minimalist piece called “Sextet”, composed by Chris Fitkin, and performed by Piano Circus (available here.)
After four nights of work with Chaoscope and putting my laptop through its paces calculating over 2800 images to create a relatively smooth animation, here is the finished product. I can’t wait to see it all come together on the stage in a couple of months. By the way, pay attention to the last equation, which is possibly the most beautiful in all of mathematics.