Format:
1 Online-Ressource (xv, 311 Seiten)
Edition:
Second edition
ISBN:
9781139022248
Content:
"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"--
Content:
Machine generated contents note: Part I. Prelude and Themes: Synthetic Methods and Results: 1. Spherical geometry; 2. Euclid; 3. The theory of parallels; 4. Non-Euclidean 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 Gauss-Bonnet Theorem; 12. Constant-curvature surfaces; Part III. Recapitulation and Coda: 13. Abstract surfaces; 14. Modeling the non-Euclidean plane; 15. Epilogue: where from here?
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521116077
Additional Edition:
ISBN 9780521133111
Additional Edition:
Erscheint auch als Druck-Ausgabe McCleary, John, 1952 - Geometry from a differentiable viewpoint Cambridge [u.a.] : Cambridge University Press, 2012 ISBN 9780521116077
Additional Edition:
ISBN 9780521133111
Additional Edition:
Print version ISBN 9780521116077
Language:
English
Subjects:
Mathematics
Keywords:
Differentialgeometrie
;
Differentialgeometrie
DOI:
10.1017/CBO9781139022248
URL:
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