  Let $A=\sqrt 3$. There are two main conjectures about paper Moebius bands.
First, a smooth embedded paper Moebius band must have aspect ratio at least A.
Second, any sequence of smooth embedded paper Moebius bands having aspect ratio
converging to A converges, in the Hausdorff topology and up to isometries, to
an equilateral triangle of semiperimeter A. We will reduce these conjectures to
10 statements about the positivity of certain explicit piecewise algebraic
expressions.
