Ideas of space : Euclidean, non-Euclidean, and relativistic
著者
書誌事項
Ideas of space : Euclidean, non-Euclidean, and relativistic
Clarendon Press , Oxford University Press, 1989
2nd ed
- : pbk
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注記
Bibliography: p. [235]-239
Includes index
内容説明・目次
内容説明
The parallel postulate of Euclidean geometry occupies a unique position in the history of mathematics. This is an account of the history of the development of Euclidean, non-Euclidean and relativistic ideas of the shape of the universe. The author reviews the failure of classical attempts to prove the postulate, before showing how the work of Gauss, Lobachevskii and Bolyai laid the foundations of modern differential geometry by constructing geometries in which the parallel postulate fails. The material, which has been revised and updated for this edition, includes a chapter on the Arabic contribution to mathematical history.
目次
- Early geometry
- Euclidean geometry and the parallel postulate
- investigations by Islamic mathematicians
- 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
- non-Euclidean mechanics
- the question of absolute space
- space, time and space-time
- paradoxes of special relativity
- gravitation and non-Euclidean geometry
- speculations.
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