Department of Mathematics

Ever since the last ice age, when savages emerged from their frozen caves and made Moebius bands out of paper strips, humans have wondered about the smallest aspect ratio rectangle one can bend into a paper Moebius band  in space– the optimal Moebius band, if you will.  In this talk I will prove that if you can bend a 1xL strip of paper into a smooth embedded Moebius band then L>sqrt(3).  This answers the 1977 Halpern-Weaver Conjecture about this matter.