Synopses & Reviews
This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.
Review
This book is an outstanding undergraduate text presenting a collection of topics in modern geometry. It is easily accessible to a student who has studied calculus and has a modicum of maturity. The text is organized into five chapters, each focusing on one topic: Euclidean geometry, spherical geometry, conics, projective geometry and special relativity. Each topic is beautifully motivated by applications, and filled with creative, engaging problems. MATHEMATICAL REVIEWS
Synopsis
This book is an introduction to the theory and applications of "modern geometry" roughly speaking, geometry that was developed after Euclid. It covers three major areas of non-Euclidean geometry and their applica tions: spherical geometry (used in navigation and astronomy), projective geometry (used in art), and spacetime geometry (used in the Special The ory of Relativity). In addition it treats some of the more useful topics from Euclidean geometry, focusing on the use of Euclidean motions, and includes a chapter on conics and the orbits of planets. My aim in writing this book was to balance theory with applications. It seems to me that students of geometry, especially prospective mathe matics teachers, need to be aware of how geometry is used as well as how it is derived. Every topic in the book is motivated by an application and many additional applications are given in the exercises. This emphasis on applications is responsible for a somewhat nontraditional choice of top ics: I left out hyperbolic geometry, a traditional topic with practically no applications that are intelligible to undergraduates, and replaced it with the spacetime geometry of Special Relativity, a thoroughly non-Euclidean geometry with striking implications for our own physical universe. The book contains enough material for a one semester course in geometry at the sophomore-to-senior level, as well as many exercises, mostly of a non routine nature (the instructor may want to supplement them with routine exercises of his/her own)."
Synopsis
This is a thorough analysis of the fundamentals of plane geometry. The reader is provided with an abundance of geometric facts such as results of Euclidean and spherical geometry, conic sections, projective geometry, and Minkowski geometry to name a few. The book covers unusual material and provides fresh examples and interesting exercises.
Table of Contents
Foreword.- Euclidean Geometry.- Spherical Geometry.- Conics.- Projective Geometry.- Special Relativity.- References.- Index.