By P. M. H. Wilson
This self-contained 2007 textbook offers an exposition of the well known classical two-dimensional geometries, similar to Euclidean, round, hyperbolic, and the in the community Euclidean torus, and introduces the fundamental ideas of Euler numbers for topological triangulations, and Riemannian metrics. The cautious dialogue of those classical examples presents scholars with an creation to the extra basic idea of curved areas constructed later within the publication, as represented via embedded surfaces in Euclidean 3-space, and their generalization to summary surfaces built with Riemannian metrics. issues operating all through contain these of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the hyperlink to topology supplied through the Gauss-Bonnet theorem. a number of diagrams aid carry the foremost issues to lifestyles and worthwhile examples and workouts are integrated to help knowing. during the emphasis is put on particular proofs, making this article perfect for any pupil with a uncomplicated history in research and algebra.
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