Geometry from a Differentiable Viewpoint

Name: Geometry from a Differentiable Viewpoint
Price: 50.49 USD
Availability: InStock
ISBN: 9780521133111

ISBN-10: 0521133114

ISBN-13: 9780521133111

Edition: 2nd 2012 (Revised)

Authors: John McCleary

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Description:

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…

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



Euclid



The theory of parallels



Non-Euclidean geometry



Development: Differential Geometry:



Curves in the plane



Curves in space



Surfaces



Curvature for surfaces



Metric equivalence of surfaces



Geodesics



The Gauss-Bonnet theorem



Constant-curvature surfaces



Recapitulation and Coda:



Abstract surfaces



Modeling the non-Euclidean plane



Epilogue: where from here?