  It has been recently conjectured that scattering amplitudes in planar N=4
super Yang-Mills are given by the volume of the (dual) amplituhedron. In this
paper we show some interesting connections between the tree-level amplituhedron
and a special class of differential equations. In particular we demonstrate how
the amplituhedron volume for NMHV amplitudes is determined by these
differential equations. The new formulation allows for a straightforward
geometric description, without any reference to triangulations. Finally we
discuss possible implications for volumes related to generic N^kMHV amplitudes.
