The Elements of Non-Euclidean Plane Geometry and Trigonometry (Classic Reprint)

Horatio Scott Carslaw

ISBN 10: 1334014949 / ISBN 13: 9781334014949

Editore: Forgotten Books, 2018

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Print on Demand. This book delves into the fascinating world of Non-Euclidean Geometry, exploring the revolutionary ideas that challenged the long-held assumptions of traditional geometry. The author meticulously traces the historical evolution of these groundbreaking concepts, starting with the ancient Greek mathematician Euclid and his famous Parallel Postulate. Through a careful examination of the work of mathematicians like Saccheri, Legendre, and Gauss, the book reveals the persistent efforts to prove or disprove Euclidââ â ¢s postulate, ultimately leading to the discovery of alternative geometries. The book delves into the groundbreaking work of Bolyai and Lobachevsky, who independently developed the first consistent Non-Euclidean Geometry, known as Hyperbolic Geometry. The author systematically explains the fundamental principles of this geometry, demonstrating how it deviates from Euclidââ â ¢s system. He further explores Elliptic Geometry, another Non-Euclidean system, and provides a detailed analysis of its key features and properties. The author concludes by demonstrating the logical consistency of Non-Euclidean Geometries, proving that they are just as valid as the Euclidean system. He further explores the implications of these discoveries, revealing that the truth of Euclidean Geometry is not absolute and depends on the specific assumptions made about space. This book offers a comprehensive and accessible exploration of Non-Euclidean Geometry, providing invaluable insights into the nature of geometry and the evolution of mathematical thought. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. Codice articolo 9781334014949_0

Dati bibliografici

Titolo: The Elements of Non-Euclidean Plane Geometry...

Casa editrice: Forgotten Books

Data di pubblicazione: 2018

Legatura: Paperback

Condizione: New

Tipologia articolo: print-on-demand item

Descrizione articolo

Riassunto:

Excerpt from The Elements of Non-Euclidean Plane Geometry and Trigonometry

IN this little book I have attempted to treat the Elements of non-euclidean Plane Geometry and Trigonometry in such a way as to prove useful to teachers of Elementary Geometry in schools and colleges. Recent changes in the teaching of Geometry in England and America have made it more than ever necessary that the teachers should have some knowledge of the hypotheses on which Euclidean Geometry is built, and especially of that hypothesis on which Euclid's Theory of Parallels rests. The historical treatment of the Theory of Parallels leads naturally to a discussion of the non-euclidean Geometries and it is only when the logical possibility of these non-euclidean Geometries is properly understood that a teacher is entitled to form an independent Opinion upon the teaching of Elementary Geometry.

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.