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Geometry from a Differentiable Viewpoint

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ISBN-10: 0521133114

ISBN-13: 9780521133111

Edition: 2nd 2012 (Revised)

Authors: John McCleary

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The development of geometry from Euclid to Euler to Lobachevsky, Bolyai, Gauss, and Riemann is a story that is often broken into parts – axiomatic geometry, non-Euclidean geometry, and differential geometry. This poses a problem for undergraduates: Which part is geometry? What is the big picture to which these parts belong? In this introduction to differential geometry, the parts are united with all of their interrelations, motivated by the history of the parallel postulate. Beginning with the ancient sources, the author first explores synthetic methods in Euclidean and non-Euclidean geometry and then introduces differential geometry in its classical formulation, leading to the modern…    
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Book details

Edition: 2nd
Copyright year: 2012
Publisher: Cambridge University Press
Publication date: 10/29/2012
Binding: Paperback
Pages: 368
Size: 6.89" wide x 9.96" long x 0.71" tall
Weight: 1.386

Prelude and Themes: Synthetic Methods and Results:
Spherical geometry
The theory of parallels
Non-Euclidean geometry
Development: Differential Geometry:
Curves in the plane
Curves in space
Curvature for surfaces
Metric equivalence of surfaces
The Gauss-Bonnet theorem
Constant-curvature surfaces
Recapitulation and Coda:
Abstract surfaces
Modeling the non-Euclidean plane
Epilogue: where from here?