The Non-Euclidean Revolution: (With an Introduction by H.S.M Coxeter) by Richard J. Trudeau
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About this book :-
The Non-Euclidean Revolution: (With an Introduction by H.S.M Coxeter) written by
Richard J. Trudeau .
Thisbook proceeds on three levels. On one it's just a geometry book with extra material on history and philosophy. For a while we will talk about Euclidean geometry-the "plane geometry" of high school-then switch to "hyperbolic geometry," another plane geometry invented around 1820. We will compare the two and reflect on what we have done.
On another level this book is about a scientific revolution, every bit as significant as the Copernican revolution in astronomy, the Darwinian revolution in biology, or the Newtonian or 20th-century revolutions in physics, but which is largely unsung because its effects have been more subtle-a revolution brought about by the invention of an alternative to traditional Euclidean geometry. Hyperbolic geometry is as logically consistent as Euclid's, has as much claim to being "true" as Euclid's, and yet extensively contradicts Euclid's. In Euclidean geometry the angles of a triangle add up to 180°; in hyperbolic geometry they add up to less, and the sum varies from triangle to triangle. In Euclidean geometry the Theorem ofPythagoras2 holds; in hyperbolic geometry it does not. The effect of this paradoxical situation on 19th-century mathematicians and scientists was profound. Mathematicians embarked on an agonizing reappraisal of their subject that would last for decades; and scientists found themselves asking whether science wasn't in fact a very different thing than they had always thought.
On the third and most speculative level this book is about the possibility of significant, absolutely certain knowledge about the world. It offers striking evidence-though of course it cannot prove-that such knowledge is impossible.
Book Detail :-
Title: The Non-Euclidean Revolution: (With an Introduction by H.S.M Coxeter)
Edition:
Author(s): Richard J. Trudeau
Publisher: Birkhäuser Basel
Series:
Year: 2001
Pages: 282
Type: PDF
Language: English
ISBN: 978-0-8176-4237-2,978-1-4612-2102-9
Country: US
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About Author :-
The author Richard J. Trudeau is the Prossor of Mathematics, Department of Mathematics, Stonehill College, North Easton, MA 02357, USA
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Book Contents :-
The Non-Euclidean Revolution: (With an Introduction by H.S.M Coxeter) written by
Richard J. Trudeau
cover the following topics.
Introduction (H. S. M. Coxeter)
1. First Things
2. Euclidean Geometry
3. Geometry and the Diamond Theory of Truth
4. The Problem With Postulate
5. The Possibility of Non-Euclidean Geometry
6. Hyperbolic Geometry
7. Consistency
8 Geometry and the Story Theory of Truth
Bibliography
Index
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