Ideas of Space
Euclidean, Non-Euclidean, and Relativistic
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Product details:
- Edition number 2
- Publisher Clarendon Press
- Date of Publication 17 August 1989
- ISBN 9780198539353
- Binding Hardback
- No. of pages254 pages
- Size 241x159x19 mm
- Weight 538 g
- Language English
- Illustrations numerous line drawings 0
Categories
Short description:
Ideas of Space is a lively and readable account of the development of Euclidean, non-Euclidean, and relativistic ideas of the shape of the universe. Jeremy Gray reviews the history of geometry from classical times and shows how it ledto the formulation of Einstein's theories of special and general relativity which today form the basis of our conception of the universe.
In this second edition the author has updated much of the material, and has added a new chapter on the emerging story of the Arabic contribution to this fascinating aspect of the history of mathematics.
Long description:
The history of the development of Euclidean, non-Euclidean, and relativistic ideas of the shape of the universe, is presented in this lively account by Jeremy Gray.
The parallel postulate of Euclidean geometry occupies a unique position in the history of mathematics. In this book, Jeremy Gray reviews the failure of classical attempts to prove the postulate and then proceeds to show how the work of Gauss, Lobachevskii, and Bolyai, laid the foundations of modern differential geometry, by constructing geometries in which the parallel postulate fails. These investigations in turn enabled the formulation of Einstein's theories of special and general relativity, which today form the basis of our conception of the universe.
The author has made every attempt to keep the pre-requisites to a bare minimum. This immensely readable account, contains historical and mathematical material which make it suitable for undergraduate students in the history of science and mathematics.
For the second edition, the author has taken the opportunity to update much of the material, and to add a chapter on the emerging story of the Arabic contribution to this fascinating aspect of the history of mathematics.
Reviews of this edition
'a very readable book that is stimulating and thought provoking.' New Scientist
Table of Contents:
PART I: Early geometry; Euclidean geometry and the parallel postulate; Investigations by Islamic mathematicians. PART II: Saccheri and his Western Predecessors; J H Lambert's work; Legendre's work; Gauss' contribution; Trigonometry; the first new geometries; the discoveries of Lobachevskii and Bolyai; Curves and surfaces; Riemann on the foundations of geometry; Beltrami's ideas; New models and old arguments; Resume. PART III: Non-Euclidean mechanics; The question of absolute space; Space, time and space-time; Paradoxes of special relativity; Gravitation and non-Euclidean geometry; Speculations; Some last thoughts.
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