Synopses & Reviews
A fascinating tour through parts of geometry students are unlikely to see in the rest of their studies while, at the same time, anchoring their excursions to the well known parallel postulate of Euclid. The author shows how alternatives to Euclids fifth postulate lead to interesting and different patterns and symmetries, and, in the process of examining geometric objects, the author incorporates the algebra of complex and hypercomplex numbers, some graph theory, and some topology. Interesting problems are scattered throughout the text. Nevertheless, the book merely assumes a course in Euclidean geometry at high school level. While many concepts introduced are advanced, the mathematical techniques are not. Singers lively exposition and off-beat approach will greatly appeal both to students and mathematicians, and the contents of the book can be covered in a one-semester course, perhaps as a sequel to a Euclidean geometry course.
Synopsis
This book offers readers a fascinating tour through parts of geometry they are unlikely to see in the rest of their studies. The author shows how alternatives to Euclid's Fifth postulate lead to interesting and different patterns and symmetries. Singer's lively exposition and off-beat approach will appeal both to students and mathematicians. Interesting problems are nicely scattered throughout the book.
Table of Contents
I: Euclid and Non-Euclid. II: Tiling the plane with regular polygons. III: Geometry of the hyperbolic plane. IV: Geometry of the sphere V: More geometry of the sphere. VI: Geometry of Space.