The Elements Of Non-Euclidean Geometry - Brossura

Sommerville, Diane Miller; Sommerville, Duncan M'Laren Young

Brossura

ISBN 10: 0486442225 ISBN 13: 9780486442228

Casa editrice: Dover Pubns, 2005

Riassunto

This volume became the standard text in the field almost immediately upon its original publication. Renowned for its lucid yet meticulous exposition, it can be appreciated by anyone familiar with high school algebra and geometry. Its arrangement follows the traditional pattern of plane and solid geometry, in which theorems are deduced from axioms and postulates. In this manner, students can follow the development of non-Euclidean geometry in strictly logical order, from a fundamental analysis of the concept of parallelism to such advanced topics as inversion and transformations.
Topics include elementary hyperbolic geometry; elliptic geometry; analytic non-Euclidean geometry; representations of non-Euclidean geometry in Euclidean space; and space curvature and the philosophical implications of non-Euclidean geometry. Additional subjects encompass the theory of the radical axes, homothetic centers, and systems of circles; inversion, equations of transformation, and groups of motions; and the classification of conics.
Although geared toward undergraduate students, this text treats such important and difficult topics as the relation between parataxy and parallelism, the absolute measure, the pseudosphere, Gauss’ proof of the defect-area theorem, geodesic representation, and other advanced subjects. In addition, its 136 problems offer practice in using the forms and methods developed in the text.

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Contenuti

I. Historical II. Elementary Hyperbolic Geometry III. Elliptic Geometry IV. Analytical Geometry V. Representations of Non-Euclidean Geometry in Euclidean Space VI. “Space-Curvature” and the Philosophical Bearing of Non-Euclidean Geometry VII. Radical Axes, Homothetic Centres, and Systems of Circles VIII. Inversion and Allied Transformations IX. The Conic Index

Product Description

Book by Sommerville D

Dettagli dell?edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2005
• ISBN 10: 0486442225
• ISBN 13: 9780486442228
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 274