In The Search For Beauty: Unravelling Non-euclidean Geometry

by Voldemar Smilga

Overview

This is a popular book that chronicles the historical attempts to prove the fifth postulate of Euclid on parallel lines that led eventually to the creation of non-Euclidean geometry. To absorb the mathematical content of the book, the reader should be familiar with the foundations of Euclidean geometry at the high school level. But besides the mathematics, the book is also devoted to stories about the people, brilliant mathematicians starting from Pythagoras and Euclid and terminating with Gauss, Lobachevsky and Klein. For two thousand years, mathematicians tried to prove the fifth postulate (whose formulation seemed to them too complicated to be a real postulate and not a theorem, hence the title In the Search for Beauty). But in the 19th century, they realized that such proof was impossible, and this led to a revolution in mathematics and then in physics. The two final chapters are devoted to Einstein and his general relativity which revealed to us that the geometry of the world we live in is not Euclidean.Also included is an historical essay on Omar Khayyam, who was not only a poet, but also a brilliant astronomer and mathematician.

Product Details

ISBN-13:	9789813274358
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	01/09/2019
Pages:	248
Product dimensions:	6.00(w) x 9.00(h) x 0.63(d)

Table of Contents

Foreword v

Acknowledgments ix

1 Before Euclid-Prehistoric Times 1

2 Euclid 13

3 The Fifth Postulate 35

4 The Age of Proofs. The Beginning 53

5 Omar Khayyam 61

6 The Age of Proofs (Continued) 87

7 Non-Euclidean Geometry. The Solution 105

8 Nikolai Ivanovich Lobachevsky 133

9 Non-Euclidean Geometry. Some Illustrations 153

10 New Ideas. Riemann. Noncontradictoriness 165

11 An Unexpected Finale. The General Theory of Relativity 183

12 Einstein 205

Name Index 233