  Surfaces of constant negative curvature in Euclidean space can be described
by either the sine-Gordon equation for the angle between asymptotic directions,
or a Monge-Ampere equation for the graph of the surface. We present the
explicit form of the correspondence between these two integrable non-linear
partial differential equations using their well-known properties in
differential geometry. We find that the cotangent of the angle between
asymptotic directions is directly related to the mean curvature of the surface.
This is a Backlund-type transformation between the sine-Gordon and Monge-Ampere
equations.
