DO THE MATH!: Mathematical Mandalas
No TL;DR found
Abstract
N ervous about your next presentation, test, or big homework assignment? Try relaxing to a soothing song (for example, Kate Bush’s “Pi,” in which she sings the digits of to within and coloring a mandala. The word mandala is Sanskrit and, loosely translated, means circle. Mandalas often contain symbolic iconic or geometric objects. In some cultures, they are archetypal objects representing wholeness or peace and are used for meditative purposes. According to mandalaproject.org, “creating a group mandala is a unifying experience in which people can express themselves individually within a unified structure.” Thus, there is clearly much more to a mandala than a systematic, geometric construction. This integration of mathematics and visual arts is how our MAA chapter decided to “do the math.” A local art fair featured the artist Nancy Cleaver (nancycleaver.smugmug.com), who created an eightfoot mandala with the word “peace” hidden in its symmetries. Our MAA chapter wondered if we could incorporate mathematics into the mandala’s geometric construction in a new way. We suggested mathematical terms that might be hidden in the design: symmetry, geometry, proof, logic, complex, real, and the pair of words, real and complex. Cleaver provided us with sketches of each of these, and students chose their favorite. We used the runner-up to advertise the event and provided a hint for finding the hidden word (see figure 1). We chose a beautiful fall day, a protected location, and got the word out. To create the mandala, Cleaver used a self-constructed wooden compass to draw the concentric circles bounding the mandala, and after dividing the disk into sectors with 30-degree angles, she applied a template to each sector. In the end, we had a mandala with rotational symmetry of order 12 (ignoring colors) and a hidden mathematical constant. Mathematical Mandalas