A Modern View of Geometry

By Leonard M. Blumenthal

Book Overview

"On the required reading list for all thoughtful students who wish to see mathematics from the 'higher standpoint.' " -- American Mathematical Monthly
Elegant and original, this exposition explores the foundations and development of both Euclidean and non-Euclidean geometry, particularly the postulational geometry of planes. Emphasis is placed upon the coordination of affine and projective planes as well as the basic unity of algebra and geometry.
Geared toward undergraduate and graduate students, the treatment begins with a brief but engaging sketch of the historical background of Euclidean geometry and an elementary summary of set theory and propositional calculus. Subsequent chapters explore coordinates in an affine plane, including those with Desargues and Pappus properties, and coordinatizing projective planes. The final two chapters contain detailed developments of simple sets of postulates for the Euclidean and non-Euclidean planes.

• Format: Paperback
• Language: English
• ISBN: 0486639622
• ISBN13: 9780486639628
• Release Date: April 2017
• Publisher: Dover Publications
• Length: 208 Pages
• Weight: 0.55 lbs.
• Dimensions: 0.4" x 5.6" x 8.2"

Customer Reviews

Great intro

This book provides a great intro to non-standard geometries by creating different axiomatic systems and finding models of them. It then constructs and analyzes operators (addition, multiplication, and the like) on the plane. It devotes a good section to discussing the Desargues and Pappus properties and their fundamentality in most geometries. A good treatise of projective geometry follows, and the book ends with a quick skim of metric geometries and non-euclidean geometries. This is not a good book if you are planning to study Hyperbolic, Spherical or Elliptical geometry, nor does it do a fair treatment of the effects of a metric on a geometry, but it does provide a short, comprehensive intro to axiomatic coordinate geometry.