By P. M. H. Wilson

ISBN-10: 0521886295

ISBN-13: 9780521886291

This self-contained textbook provides an exposition of the well known classical two-dimensional geometries, resembling Euclidean, round, hyperbolic, and the in the community Euclidean torus, and introduces the fundamental innovations of Euler numbers for topological triangulations, and Riemannian metrics. The cautious dialogue of those classical examples offers scholars with an advent to the extra basic concept of curved areas constructed later within the e-book, as represented by way of embedded surfaces in Euclidean 3-space, and their generalization to summary surfaces built with Riemannian metrics. topics operating all through comprise these of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the hyperlink to topology supplied through the Gauss-Bonnet theorem. various diagrams support carry the foremost issues to existence and important examples and routines are integrated to assist realizing. through the emphasis is put on specific proofs, making this article excellent for any pupil with a easy historical past in research and algebra.