  The apparently intractable shape of a fold in a compressed elastic film lying
on a fluid substrate is found to have an exact solution. Such systems buckle at
a nonzero wavevector set by the bending stiffness of the film and the weight of
the substrate fluid. Our solution describes the entire progression from a
weakly displaced sinusoidal buckling to a single large fold that contacts
itself. The pressure decrease is exactly quadratic in the lateral displacement.
We identify a complex wavevector whose magnitude remains invariant with
compression.
