1. (Scherk's minimal surface) M : e- cos x = cosy. Let R be the region in the ry-plane on which cos x cos y > 0. R is a checkerboard pattern of open squares, with vertices (r/2 + mt, T/2 + nT). Show that:
(a) M is a surface.
b) For each point (u,u) in R there is exactly one point (u,v,w) in M. The only other points of M are entire vertical lines over each of the vertices of R