Ideas of Space: Euclidean, Non-Euclidean, and Relativistic / Edition 2

by Jeremy Gray

Overview

Now in a revised and expanded new edition, this volume chronologically traces the evolution of Euclidean, non-Euclidean, and relativistic theories regarding the shape of the universe. A unique, highly readable, and entertaining account, the book assumes no special mathematical knowledge. It reviews the failed classical attempts to prove the parallel postulate and provides coverage of the role of Gauss, Lobachevskii, and Bolyai in setting the foundations of modern differential geometry, which laid the groundwork for Einstein's theories of special and general relativity. This updated account includes a new chapter on Islamic contributions to this area, as well as additional information on gravitation, the nature of space and black holes.

Product Details

ISBN-13:	9780198539353
Publisher:	Oxford University Press
Publication date:	09/21/1989
Edition description:	REV
Pages:	254
Product dimensions:	9.53(w) x 6.40(h) x 0.77(d)

About the Author

Open University

Table of Contents

PART I1. Early Geometry2. Euclidean Geometry and the Parallel Postulate3. Investigations by Islamic MathematiciansPART II4. Saccheri and his Western Predecessors5. J.H. Lambert's Work6. Legendre's Work7. Gauss' Contribution8. Trigonometry9. The First New Geometries10. The Discoveries of Lobachevskii and Bolyai11. Curves and Surfaces12. Riemann on the Foundations of Geometry13. Beltrami's Ideas14. New Models and Old Arguments15. ResumePART III16. Non-Euclidean Mechanics17. The Question of Absolute Space18. Space, Time, and Space-Time19. Paradoxes of Special Relativity20. Gravitation and Non-Euclidean Geometry21. Speculations22. Some Last Thoughts

Editorial Reviews

From reviews of the first edition: "Jeremy Gray has provided a superb exposition which tells a good story." —Mathematics Teaching

"Promises to become a classic text for those interested in considering changing mathematical perceptions of space. Gray's book is a pleasure to read." —Historia Mathematica

"An admirable exposition for well-educated laymen of the evolution of geometrical thought from before Euclid to black holes." —American Mathematical Monthly

From the Publisher