By P. M. H. Wilson
This self-contained 2007 textbook offers an exposition of the well known classical two-dimensional geometries, resembling Euclidean, round, hyperbolic, and the in the neighborhood Euclidean torus, and introduces the elemental ideas of Euler numbers for topological triangulations, and Riemannian metrics. The cautious dialogue of those classical examples presents scholars with an advent to the extra normal idea of curved areas constructed later within the publication, as represented through embedded surfaces in Euclidean 3-space, and their generalization to summary surfaces outfitted with Riemannian metrics. topics working all through contain these of geodesic curves, polygonal approximations to triangulations, Gaussian curvature, and the hyperlink to topology supplied through the Gauss-Bonnet theorem. various diagrams aid carry the major issues to existence and worthwhile examples and workouts are incorporated to assist realizing. during the emphasis is put on particular proofs, making this article perfect for any pupil with a simple history in research and algebra.
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