Copyright © 2012 Ezzat G. Bakhoum. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The computation of the Gaussian curvature of a surface is a requirement in many propagation problems in physics and engineering. A formula is developed for the calculation of the Gaussian curvature by knowledge of two close geodesics on the surface, or alternatively from the projection (i.e., image) of such geodesics. The formula will be very useful for problems in general relativity, civil engineering, and robotic navigation.