Revolutions of Geometry, Solutions Manual to Accompany Revolutions in Geometry

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.

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.

Michael L. O'Leary, PhD, is Associate Professor of Mathematics at the College of DuPage in Glenn Ellyn, Illinois.?He is a Member of the American Mathematical Society, the Canadian Society for the History and Philosophy of Mathematics, and the Mathematical Society of America.?He received his PhD in Mathematics from the University of California, Irvine in 1994.