Geometries and Groups (Universitext)
Contributors: M. Reid (Translator)
Edition: 1st ed. 1987. 2nd printing edition
Publisher: Springer
Published: June 21, 2002
Language: eng
Format: Paperback
Number of pages: 251
ISBN-13: 9783540152811
Subjects: Geometry; Geometry - General; Science; General; Mathematics / Geometry / General
First sentence: Many of the most outstanding achievements of geometry are based on the surprising circumstance that geometrical intuition, formed in some areas, turns out to be applicable in other, sometimes quite dissimilar, areas.
Description: This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's non-Euclidean geometry. Each section is carefully motivated by discussion of the physical and general scientific implications of the mathematical argument, and its place in the history of mathematics and philosophy. The book is expected to find a place alongside classics such as Hilbert and Cohn-Vossen's "Geometry and the imagination" and Weyl's "Symmetry".