The Non-Euclidean Revolution

ISBN-13: 9780817647827 / Angielski / Miękka / 2008 / 270 str.

Richard J. Trudeau

Opis

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

Recenzje

From the reviews:

"Trudeau meets the challenge of reaching a broad audience in clever ways...(The book) is a good addition to our literature on non-Euclidean geometry and it is recommended for the undergraduate library."--Choice, February 1988

"...the author, in this remarkable book, describes in an incomparable way the fascinating path taken by the geometry of the plane in its historical evolution from antiquity up to the discovery of non-Euclidean geometry. This 'non-Euclidean revolution', in all its aspects, is described very strikingly here...Many illustrations and some amusing sketches complement the very vividly written text."--Mathematical Reviews

"In The Non-Euclidean Revolution, we have a mathematically rigorous explanation of ... sea change in mathematics which is at the same time suitable for any educated reader. ... I have found that this book achieves my goal of bringing some serious mathematics into our honors program and Trudeau's goal of bringing his readers through the 19^th century revolution brought about by an alternative to Euclid's geometry. ... Trudeau's book shines as a guide to that revolution." (Mark Bollman, MathDL, May, 2008)

Spis treści

Preface.- Introduction.- First Things.- Euclidean Geometry.- Geometry and the Diamond Theory of Truth.- The Problem with Postulate 5.- The Possibility of Non-Euclidean Geometry.- Hyperbolic Geometry.- Consistency.- Geometry and the Story Theory of Truth.- Bibliography.- Index.

Blurb

How unique and definitive is Euclidean geometry in describing the "real" space in which we live?

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.

"Trudeau meets the challenge of reaching a broad audience in clever ways...(The book) is a good addition to our literature on non-Euclidean geometry and it is recommended for the undergraduate library."--Choice (review of 1st edition)

"...the author, in this remarkable book, describes in an incomparable way the fascinating path taken by the geometry of the plane in its historical evolution from antiquity up to the discovery of non-Euclidean geometry. This 'non-Euclidean revolution', in all its aspects, is described very strikingly here...Many illustrations and some amusing sketches complement the very vividly written text."--Mathematical Reviews