The optimal paper Moebius band

In this talk I will explain why a strip of paper that is 1 unit wide must be greater than sqrt(3) units long in order for you to twist it into a Moebius band, and why this bound is sharp. This result is the solution to the Halpern-Weaver Conjecture from 1977. As I will explain, it answers 1 out of infinitely many related kinds of questions, the rest of which are unsolved.