Ideas of Space Euclidean, Non-Euclidean, and Relativistic [Hardcover]

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.

PART I
1. Early Geometry
2. Euclidean Geometry and the Parallel Postulate
3. Investigations by Islamic Mathematicians
PART II
4. Saccheri and his Western Predecessors
5. J.H. Lambert's Work
6. Legendre's Work
7. Gauss' Contribution
8. Trigonometry
9. The First New Geometries
10. The Discoveries of Lobachevskii and Bolyai
11. Curves and Surfaces
12. Riemann on the Foundations of Geometry
13. Beltrami's Ideas
14. New Models and Old Arguments
15. Resume
PART III
16. Non-Euclidean Mechanics
17. The Question of Absolute Space
18. Space, Time, and Space-Time
19. Paradoxes of Special Relativity
20. Gravitation and Non-Euclidean Geometry
21. Speculations
22. Some Last Thoughts

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 frolƒÁ