  We study the linearized Fopl - von Karman theory of a long, thin rectangular
elastic membrane that is bent through an angle $2 \alpha$. We prove rigorous
bounds for the minimum energy of this configuration in terms of the plate
thickness $\sigma$ and the bending angle. We show that the minimum energy
scales as $\sigma^{5/3} \alpha^{7/3}$. This scaling is in sharp contrast with
previously obtained results for the linearized theory of thin sheets with
isotropic compression boundary conditions, where the energy scales as $\sigma$.
