It would be awesome with a demo script that calculates the constant in
Gerver's solution to the moving sofa problem with high precision: http://mathworld.wolfram.com/MovingSofaProblem.html The main missing component is a solver for the 4x4 nonlinear problem
(Vinzent, how far off is this?).

Then there are just some double integrals that should be possible to
calculate already, although adaptive quadrature might be necessary due to
their piecewise nature.

Original issue for #96: http://code.google.com/p/mpmath/issues/detail?id=56

Original author: https://code.google.com/u/111502149103757882156/