Revolutions of Geometry - O'Leary, Michael L

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Résumé :
Based on the premise that in order to write proofs, one needs to read finished proofs as well as study both their logic and grammar, Revolutions in Geometry depicts how to write basic proofs in various fields of geometry. This accessible text for junior and senior undergraduates explains the general development of geometry throughout time, discusses the involvement of its major contributors, and places the proofs into the context of geometry's history to illustrate how crucial proof writing is to the job of a mathematician.

Sommaire:

Preface xi

Acknowledgements xiii

Part I Foundations

1 The First Geometers 3

2 Thales 27

3 Plato and Aristotle 53

Part II The Golden Age

4 Pythagoras 87

5 Euclid 123

6 Archimedes 173

Part III Enlightenment

7 Fran?ois Vi?te 227

8 Ren? Descartes 267

9 G?rard Desargues 293

Part IV A Strange New World

10 Giovanni Saccheri 323

11 Johann Lambert 353

12 Nicolai Lobachevski and J?nos Bolyai 393

Part V New Directions

13 Bernhard Riemann 443

14 Jean-Victor Poncelet 483

15 Felix Klein 519

References 565

Index 573