Synopsis
Explore how geometry broke free from the parallel postulate and opened new worlds of shape and space. This non‑Euclidean journey surveys the ideas, proofs, and key contributors that revealed consistent alternatives to Euclid’s classical geometry, from early debates to modern formulations.
Beginning with the historic question of parallels, the book traces how mathematicians like Bolyai, Lobachevsky, Gauss, and Riemann expanded geometry beyond Euclid. It introduces hyperbolic and elliptic planes, theorems on parallels, trigonometry, and the tools used to measure length and area in these new settings. The work balances historical context with clear explanations of constructions and the logic behind non‑Euclidean systems.
- Foundational ideas about the parallel postulate and its alternatives
- Step-by-step constructions in hyperbolic and elliptic geometries
- Theory and formulas for hyperbolic plane trigonometry and area
- Historical development and the search for consistency and truth in geometry
Ideal for readers interested in the history and foundations of geometry, and for those who want a solid introduction to non‑Euclidean ideas alongside their historical context.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
Autres éditions populaires du même titre
Résultats de recherche pour The Elements of Non-Euclidean Plane Geometry and Trigonometr...
Image fournie par le vendeur
The Elements of Non-Euclidean Plane Geometry and Trigonometry (Classic Reprint)
impression à la demandeVendeur : Forgotten Books, London, Royaume-Uni
Évaluation du vendeur 4 sur 5 étoiles
Paperback. Etat : New. 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. print-on-demand item. N° de réf. du vendeur 9781334014949_0
Acheter neuf
EUR 17,58
Livraison gratuite
Expédition depuis Royaume-Uni vers Etats-Unis
Expédition depuis Royaume-Uni vers Etats-Unis
Quantité disponible : Plus de 20 disponibles
Image d'archives
The Elements of NonEuclidean Plane Geometry and Trigonometry Classic Reprint
Vendeur : PBShop.store US, Wood Dale, IL, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781334014949
Acheter neuf
EUR 24,87
Livraison gratuite
Expédition nationale : Etats-Unis
Expédition nationale : Etats-Unis
Quantité disponible : 15 disponible(s)
Image d'archives
The Elements of NonEuclidean Plane Geometry and Trigonometry Classic Reprint
Vendeur : PBShop.store UK, Fairford, GLOS, Royaume-Uni
Évaluation du vendeur 5 sur 5 étoiles
PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781334014949
Acheter neuf
EUR 22,84
Expédition à EUR 4,81
Expédition depuis Royaume-Uni vers Etats-Unis
Expédition depuis Royaume-Uni vers Etats-Unis
Quantité disponible : 15 disponible(s)