The Elements of Non-Euclidean Geometry (Classic Reprint) - Couverture souple

Duncan M''laren Young Sommerville

Couverture souple

ISBN 10 : 1440066582 ISBN 13 : 9781440066580

Editeur : Forgotten Books, 2018

Synopsis

Explore non-Euclidean geometry from history to modern thought, with rigorous exercises for deep understanding.

This book surveys how geometry broadens beyond Euclid’s framework. It moves from historical origins to modern developments, blending mathematical detail with philosophical context. The edition emphasizes disciplined reasoning and aims to support private study, college work, and advanced teaching.

- Learn the ideas of hyperbolic and elliptic geometry, and how they relate to each other.
- See how projective methods and metric concepts interact in non-Euclidean settings.
- Work through exercises designed to reinforce key theorems and definitions.
- Understand the broader history and the philosophical implications of curved space.

Ideal for readers of advanced geometry, math history, and curriculum-focused study.

A propos du livre

Présentation de l'éditeur

Excerpt from The Elements of Non-Euclidean Geometry

The present work is an extension and elaboration of a course of lectures on Non-Euclidean Geometry which I delivered at the Colloquium held under the auspices of the Edinburgh Mathematical Society in August, 1913.

Non-euclidean geometry is now a well-recognised branch of mathematics. It is the general type of geometry of homogeneous and continuous space, of which euclidean geometry is a special form. The creation or discovery of such types has destroyed the unique character of euclidean geometry and given it a setting amongst geometrical systems. There has arisen, so to speak, a science of Comparative Geometry.

Special care has, therefore, been taken throughout this book to show the bearing of non-euclidean upon euclidean geometry; and by exhibiting euclidean geometry as a really degenerate form - in the sense in which a pair of straight lines is a degenerate conic - to explain the apparent want of symmetry and the occasional failure of the principle of duality, which only a study of non-euclidean geometry can fully elucidate.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

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.

Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2018
• Langue: anglais
• ISBN 10: 1440066582
• ISBN 13: 9781440066580
• Reliure: Broché
• Nombre de pages: 292
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