Recycling Topology

It's hard to miss the triangle of three bent arrows that signifies recycling. It appears in newspapers and magazines and on bottles, envelopes, cardboard cartons, and other containers.

But have you noticed that there are two versions of this ubiquitous symbol? The difference between them lies in the direction of the twist in two of the arrows that make up each figure.

Cliff Long, a math professor at Bowling Green State University, has an eye for such details. In his mathematical studies of surfaces and shapes, he has found it inspiring to carve certain forms out of wood. "The carvings ... have significantly improved [my] understanding of the surfaces É and the mathematics behind them," Long says.

recycling figures

Comments are welcome. Please send messages to Ivars Peterson at ipeterson@maa.org.