I’ve always been intrigued by the soccer ball with its hexagons and pentagons, and with the mind-bending artwork of M.C. Escher. The fact that the two were mathematically related totally escaped me until recently. I do OK with basic arithmetic, but quickly get lost when they start mixing non-Roman script with the variables. So I approached the VizMath MOOC with an expectation that I was going to be totally lost. I am lost, but wander in amazement at the genius and the beauty. I am not particularly worried about finding my way.
Daina Taimina’s crocheted creations are a good example. While not even pretending to understand how these might represent (or fail to represent) the shape of the universe, they drew me in, made me believe I might copy them, if never understand them. It wasn’t until she showed us the rough approximations of her work in hexagons though, that I found my inspiration to act – and blog.
In an attempt to share some of the wonder with my ABE math students, I created a sheet of pentagons, hexagons, and heptagons to cut out and tape together. There are enough polygons on one sheet to make a complete circle of both curved and negatively curved (hyperbolic) planes. Extension of the planes, either to a complete sphere or complete insanity will require additional sheets, and probably collaborative effort.
(And yes, I do know there are extra hexagons. I couldn’t bring myself to waste the white space when it’s so easy to crowd them. Just be thankful my childhood training in frugality wasn’t so overpowering that I had to tile them. I was tempted…)