A Modern View of Geometry

Description

"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. Content: Pages:1 to 25 Pages:26 to 50 Pages:51 to 75 Pages:76 to 100 Pages:101 to 125 Pages:126 to 150 Pages:151 to 175 Pages:176 to 200 Pages:201 to 209