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.
Auflage
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Editions-Typ
Illustrationen
153 line drawings, bibliography, index
ISBN-13
978-0-19-853934-6 (9780198539346)
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Schweitzer Klassifikation
Autor*in
Senior Lecturer in MathematicsSenior Lecturer in Mathematics, Open University
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.
