The Non-Euclidean Revolution: With an Introduction by H.S.M Coxeter

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Springer Science & Business Media, Dec 1, 2013 - Mathematics - 270 pages
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Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world.

Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world.

A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America.

 

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Contents

Euclidean Geometry
22
Geometry and the Diamond Theory of Truth
106
The Problem With Postulate 5 1 18
118
The Possibility of NonEuclidean Geometry
154
Hyperbolic Geometry
173
Consistency
232
Geometry and the Story Theory of Truth
248
Bibliography
261
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