The aspect ratio of a rectangle is the ratio of its long side to its shorter (or equal) side. If you have a rectangle with a big aspect ratio, meaning it is long and thin, you can twist it around in space and make a Moebius band. If the aspect ratio is small, then you cannot. In 1977, B. Halpern and C. Weaver conjectured that the cutoff is sqrt(3). That is, you can make a Moebius band out of a rectangle if and only if the aspect ratio is greater than sqrt(3). In this talk I will give a complete and self-contained proof of this conjecture.

The talk should be accessible to people who have had a few upper-level university math courses.