Ideas of Space 'Euclidean, Non-Euclidean and Realativistic' 2/Ed.

2. Auflage 1989
ISBN: 978-0-19-853935-3
Verlag: OUP Oxford

Buch, Englisch, 254 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 552 g

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.

Autoren/Hrsg.

Gray, Jeremy

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Human- und Sozialwissenschaften
• Geisteswissenschaften Geschichtswissenschaft Geschichtliche Themen Wissenschafts- und Universitätsgeschichte
• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie

Inhaltsverzeichnis

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.