The Classical Geometries: A Modern Perspective

This book presents some of the most beautiful mathematics from antiquity, the Renaissance, and the 19th century. It starts with ordinary (Euclidean) geometry, moving from basic to advanced results. It goes on to cover projective, hyperbolic (non-Euclidean), and spherical geometry. It has hundreds of illustrations: classic diagrams, tilings of the plane, the Archimedean and Catalan solids, and non-Euclidean tilings that inspired artists like M. C. Escher. The book offers a multitude of ways to visualize the geometry.At the same time, the book takes a modern perspective. It introduces advanced topics like geodesics and curvature, preparing the student for later courses in differential geometry and Lie groups. Facts from abstract algebra (groups and fields) are introduced as needed. There are hundreds of exercises, many with hints.The book will appeal to advanced undergraduates and beginning grad students in mathematics. Younger students and general readers will enjoy the earlier chapters and the pictures.The author, Nicholas McConnell, has always been fascinated by mathematics. Since his school years, he has read widely in algebra, geometry, and logic, and he has programmed computers to draw beautiful pictures. He received his B.A. from Rutgers University with top honors in mathematics. He is currently a graduate student at the University of Maryland, specializing in algebraic geometry. Read more