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Geometry from a differentiable viewpoint

Author: John McCleary
Publisher: New York : Cambridge University Press, 2013
Edition/Format:   Print book : English : 2. editionView all editions and formats
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  Read more...
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Document Type: Book
All Authors / Contributors: John McCleary
ISBN: 0521133114 9780521133111
OCLC Number: 915912917
Description: 357 s. : illustrations ; 26 cm
Contents: Part A: Prelude and Themes: Synthetic Methods and Results: 1. Spherical geometry; 2. Euclid; 3. The theory of parallels; 4. Non-Euclidean geometry; Part B. 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 C. Recapitulation and Coda: 13. Abstract surfaces; 14. Modeling the non-Euclidean plane; 15. Epilogue: where from here?

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This text, for a first course in differential or modern geometry, introduces methods within a historical context that is familiar to students from high school. The thoroughly revised second edition  Read more...

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Review of the first edition: '... an unusual and interesting account of two subjects and their close historical interrelation.' The Mathematical Gazette '... the author has succeeded in making Read more...

 
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