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OverviewHigh Quality Content by WIKIPEDIA articles! In differential geometry, the Gaussian curvature or Gauss curvature of a point on a surface is the product of the principal curvatures, 1 and 2, of the given point. It is an intrinsic measure of curvature, i.e., its value depends only on how distances are measured on the surface, not on the way it is embedded in space. This result is the content of Gauss's Theorema egregium.We represent the surface by the implicit function theorem as the graph of a function, f, of two variables, and assume the point p is a critical point, i.e., the gradient of f vanishes (this can always be attained by a suitable rigid motion). Then the Gaussian curvature of the surface at p is the determinant of the Hessian matrix of f (being the product of the eigenvalues of the Hessian). (Recall that the Hessian is the 2-by-2 matrix of second derivatives.) This definition allows one immediately to grasp the distinction between cup/cap versus saddle point behavior in terms of second year calculus. Full Product DetailsAuthor: Lambert M. Surhone , Mariam T. Tennoe , Susan F. HenssonowPublisher: VDM Publishing House Imprint: VDM Publishing House Dimensions: Width: 22.90cm , Height: 0.60cm , Length: 15.20cm Weight: 0.162kg ISBN: 9786131241703ISBN 10: 6131241708 Pages: 102 Publication Date: 14 August 2010 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |