Critical Points and Curvature for Embedded Polyhedral Surfaces
by Thomas F. Banchoff

Many theorems in global geometry exploit the connection between critical point theory and total curvature. This paper uses the same approcah to prove the critical point theorem and uses it to prove the Gauss-Bonnet theorem. In the case of polyhedra, a new interpretation of Gauss's Theorem Egregium which relates the extrinsic and intrinsic curvature on a surface is given.