A typical performance by dancers Karl Schaffer and Erik Stern begins with a handshake. However, it’s not simple: the two men fail to connect, missing hands and falling past each other, over and over, in a variety of ways. When they do finally grasp hands, they have to face the opposite problem: they’re unable to disconnect, despite turning, spinning, and prying.
That greeting is more than just a vaudevillian routine. The sequence resonates with core ideas in the mathematical field of combinatorics, which is concerned with different ways to combine objects in the same set according to certain rules. In this case, the set includes the two dancers; the rule is to shake hands. With only those parameters, the dance shows a variety of possibilities, symmetries, and structures.
Dance, says Schaffer, “is particularly conducive to mathematics inquiry and thinking.” He should know. Schaffer teaches mathematics at DeAnza College in Cupertino, California. Since their first performance in 1991—Two Guys Dancing About Math—he and Stern, a dance teacher at Weber State University inOgden, Utah, have been choreographing and performing dance pieces based on mathematical ideas.
Image courtesy Hazen Imaging.