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Mathematical Problems in Engineering
Volume 2012, Article ID 371890, 10 pages
http://dx.doi.org/10.1155/2012/371890
Research Article

Gaussian Curvature in Propagation Problems in Physics and Engineering

Department of Electrical and Computer Engineering, University of West Florida, 11000 University Parkway, Pensacola, FL 32514, USA

Received 1 September 2011; Accepted 9 October 2011

Academic Editor: Cristian Toma

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.