Geometry from a differentiable viewpoint
 Author/Creator
 McCleary, John, 1952
 Language
 English.
 Edition
 2nd ed.
 Imprint
 Cambridge, UK ; New York : Cambridge University Press, 2013.
 Physical description
 xv, 357 p. : ill., maps ; 27 cm.
Access
Available online

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QA641 .M38 2013

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QA641 .M38 2013
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 341349) and indexes.
 Contents

 Part I. Prelude and Themes: Synthetic Methods and Results: 1. Spherical geometry 2. Euclid 3. The theory of parallels 4. NonEuclidean geometry Part II. Development: Differential Geometry: 5. Curves in the plane 6. Curves in space 7. Surfaces 8. Curvature for surfaces 9. Metric equivalence of surfaces 10. Geodesics 11. The GaussBonnet theorem 12. Constantcurvature surfaces Part III. Recapitulation and Coda: 13. Abstract surfaces 14. Modeling the nonEuclidean plane 15. Epilogue: where from here?
 (source: Nielsen Book Data)
 Publisher's 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, nonEuclidean 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 nonEuclidean geometry and then introduces differential geometry in its classical formulation, leading to the modern formulation on manifolds such as spacetime. The presentation is enlivened by historical diversions such as Huygens'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 and the use of transformations such as the reflections of the Beltrami disk.
(source: Nielsen Book Data)
Subjects
 Subject
 Geometry, Differential.
Bibliographic information
 Publication date
 2013
 Responsibility
 John McCleary.
 ISBN
 9780521116077
 0521116074
 9780521133111
 0521133114