Roever Lecture: The optimal paper Moebius band

Abstract: If you have a rectangular strip of paper with a large aspect ratio, meaning that it is long and thin, you can twist it around in space and tape the ends together to make a paper Moebius band. If the aspect ratio is small, you can't do this. What is the cutoff? In this talk, I will prove that you can make the Moebius band if and only if the aspect ratio is greater that sqrt(3). I'll also explain why the Moebius band looks very much like an equilateral triangle if the aspect ratio is near sqrt(3). These results answer the conjecture of B. Halpern and C. Weaver made in 1977.

Host: Steven Frankel