This is an account of the history of the development of Euclidean, non-Euclidean and relativistic ideas of the shape of the universe. The material, which has been revised and updated for this edition, includes a chapter on the Arabic contribution to mathematical history.

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.

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