Description

Book Synopsis
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.

Table of Contents


Preface.

Acknowledgments.

PART I FOUNDATIONS.

1 The First Geometers.

2 Thales.

3 Plato and Aristotle.

PART II THE GOLDEN AGE.

4 Pythagoras.

5 Euclid.

6 Archimedes.

PART III ENLIGHTENMENT.

7 François Viète.

8 René Descartes.

9 Gérard Desargues.

PART IV A STRANGE NEW WORLD.

10 Giovanni Saccheri.

11 Johann Lambert.

12 Nicolai Lobachevski and János Bolyai.

PART V NEW DIRECTIONS.

13 Bernhard Riemann.

14 Jean-Victor Poncelet.

15 Felix Klein.

References.

Index.

Revolutions of Geometry Solutions Manual to Accompany Revolutions in Geometry

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    A Paperback by Michael L. O'Leary

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      Publisher: Wiley
      Publication Date: 9/21/2010 12:00:00 AM
      ISBN13: 9780470167564, 978-0470167564
      ISBN10: 0470167564
      Also in:
      Mathematics History of science

      Description

      Book Synopsis
      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.

      Table of Contents


      Preface.

      Acknowledgments.

      PART I FOUNDATIONS.

      1 The First Geometers.

      2 Thales.

      3 Plato and Aristotle.

      PART II THE GOLDEN AGE.

      4 Pythagoras.

      5 Euclid.

      6 Archimedes.

      PART III ENLIGHTENMENT.

      7 François Viète.

      8 René Descartes.

      9 Gérard Desargues.

      PART IV A STRANGE NEW WORLD.

      10 Giovanni Saccheri.

      11 Johann Lambert.

      12 Nicolai Lobachevski and János Bolyai.

      PART V NEW DIRECTIONS.

      13 Bernhard Riemann.

      14 Jean-Victor Poncelet.

      15 Felix Klein.

      References.

      Index.

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