GOOD: This book is in good condition, showing most of its wear on the corners. The pages are free of writing.
Product Details
From the back cover: "This self-contained textbook presents an exposition of the well-known classical two dimensional geometries, such as Euclidean, spherical, hyperbolic and the locally Euclidean torus, and introduces the basic concepts of Euler numbers for topological triangulations and Riemannian metrics. The careful discussion of these classical examples provides students with an introduction to the more general theory of curved spaces developed later in the book, as represented by embedded surfaces in Euclidean 3-space, and their generalisation [sic] to abstract surfaces equipped with Riemannian metrics. Themes running throughout the book include those of geodesic curves polygonal approximations to triangulations, Gaussian curvature and the link to topology provided by the Gauss-Bonnet theorem.
"Numerous diagrams help bring the key points to life, and helpful examples and exercises are included to aid understanding. Throughout, the emphasis is placed on explicit proofs, making this text ideal for any student with a basic background in analysis and algebra."
NOTE: British spelling.
BRIEF CONTENTS
Euclidean geometry
Spherical geometry
Triangulations and Euler numbers
Riemannian metrics
Hyperbolic geometry
Smooth embedded surfaces
Geodesics
Abstract surfaces and Gauss-Bonnet
The book concludes with Postscript, References ,and Index.
