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Geometry From Differentiable Viewpoint

Geometry From Differentiable Viewpoint - 2nd edition

ISBN13: 978-0521133111

Cover of Geometry From Differentiable Viewpoint 2ND 13 (ISBN 978-0521133111)
ISBN13: 978-0521133111
ISBN10: 0521133114
Cover type:
Edition/Copyright: 2ND 13
Publisher: Cambridge University Press
Published: 2013
International: No

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Geometry From Differentiable Viewpoint - 2ND 13 edition

ISBN13: 978-0521133111

John McCleary

ISBN13: 978-0521133111
ISBN10: 0521133114
Cover type:
Edition/Copyright: 2ND 13
Publisher: Cambridge University Press

Published: 2013
International: No
Summary

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 formulation on manifolds such as space-time. The presentation is enlivened by historical diversions such as Hugyens's clock and the mathematics of cartography. The intertwined approaches will help undergraduates understand the role of elementary ideas in the more general, differential setting. This thoroughly revised second edition includes numerous new exercises and a new solution key. New topics include Clairaut's relation for geodesics, Euclid's geometry of space, further properties of cycloids and map projections, and the use of transformations such as the reflections of the Beltrami disk.

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