"Knotty Surprises"
featuring Nicole Yamzon

Video (sound is faint, but clear if you turn the volume up)

How much math can you find in a twisted-up paper ring? No matter how much you know, the answer is probably "more than you expect." On April 27, 2014, undergraduate student and longtime SMMG helper Nicole Yamzon showed us that the Möbius band and its siblings have a surprises in store for old friends and new acquaintances alike.

We started by putting a half-twist in a strip of paper and taping the ends together, creating a classic Möbius band: a shape with only one side and one edge. What would happen if we put in two half-twists, or three? We tried it, and found a nice pattern.

Then we started cutting up all our hard work. When we cut our classic Möbius bands down the middle, they refused to fall apart. Instead, they each became a single band with two half-twists. When we cut a third of the way from the edge, the bands did fall into two pieces—but not in the way we expected! Cutting our three-half-twist bands down the middle gave us an even stranger surprise.

Soon, we realized there was no limit to the complexity of the shapes we could make. We tried cutting all sorts of bands in lots of different ways, with intricate and beautiful results. Along the way, we found unexpected connections with the number line, the fourth dimension, and even experimental fusion reactors. No matter how much we'd known about Möbius bands before, we all left knowing more—and knowing there was plenty left for us to discover.

Printable version of the flyer