Ideas of space : Euclidean, non-Euclidean, and relativistic

Author(s)

Bibliographic Information

Ideas of space : Euclidean, non-Euclidean, and relativistic

Jeremy Gray

Clarendon Press , Oxford University Press, 1989

2nd ed

  • : pbk

Available at  / 27 libraries

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Note

Bibliography: p. [235]-239

Includes index

Description and Table of Contents

Description

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.

Table of Contents

  • 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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