Foundations of Geometry: Euclidean, Bolyai-Lobachevskian, and Projective Geometry: Euclidean, Bolyai-Lobachevskian, and Projective Geometry (Dover Books on Mathematics)

Book Details:

• Author: Karol Borsuk

• Publisher: Dover

• Edition: Revised

• Binding: Paperback

• Format: Import

• Number of Pages: 448

• ISBN: 9780486828091

• Release Date: 28-12-2018

• Languages: English

• Package Dimensions: 9.0 x 5.9 x 0.9 inches

About the Book:

"Geometry: Euclidean and Non-Euclidean" by Karol Borsuk is a masterfully crafted text that provides a detailed, systematic exploration of both Euclidean and non-Euclidean geometry. The book is recognized for its rigor and accessibility, making it an indispensable resource for anyone interested in the study of geometry, from students to professionals.

The book is divided into two main parts. Part One focuses on Euclidean and Bolyai-Lobachevskian geometry, developed through an axiom system inspired by the work of David Hilbert. Topics include axioms of incidence and order, congruence, the axiom of continuity, models of absolute geometry, and, of course, a comprehensive treatment of Euclidean and Bolyai-Lobachevskian geometry. Part Two explores projective geometry, following a similar development approach and concluding with an investigation into the models of projective geometry.

The text begins with a thorough introduction, which covers background material such as topological space, analytic geometry, and other related topics to build a strong foundation. Rigorous proofs are provided throughout the text, ensuring a deep understanding of the mathematical principles. Whether you are a student delving into advanced geometry or a professional seeking to refresh your knowledge, this book offers valuable insights and in-depth coverage of one of the most fundamental branches of mathematics.