Symmetry and Pattern in Projective Geometry 2013th Edition by Eric Lord (PDF)

Description

Symmetry and Pattern in Projective Geometry is a self-contained study of projective geometry which compares and contrasts the analytic and axiomatic methods. The analytic approach is based on homogeneous coordinates, and brief introductions to Plücker coordinates and Grassmann coordinates are presented. This book looks carefully at linear, quadratic, cubic and quartic figures in two, three and higher dimensions. It deals at length with the extensions and consequences of basic theorems such as those of Pappus and Desargues. The emphasis throughout is on special configurations that have particularly interesting symmetry properties. The intricate and novel ideas of ‘Donald’ Coxeter, who is considered one of the great geometers of the twentieth century, are also discussed throughout the text. The book concludes with a useful analysis of finite geometries and a description of some of the remarkable configurations discovered by Coxeter. This book will be appreciated by mathematics students and those wishing to learn more about the subject of geometry. It makes accessible subjects and theorems which are often considered quite complicated and presents them in an easy-to-read and enjoyable manner.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This very attractive volume is a goldmine of information and insights, and would make an ideal companion to many standard texts. It is very well placed on my bookshelf alongside Coxeter, Hilbert and Cohn-Vossen, JWHT Hudson, et al. The author, in his preface, states that this is not a textbook: it is “a collection of ideas”; and I would add, a very well developed collection. The language is lucid, the diagrams beautiful.The author claims that the book “should be accessible to anyone with a little knowledge of matrices, determinants and vectors, and perhaps a smattering of group theory”, and this seems about right, although some of the sections require serious mental application.The wide-ranging ambit of the book is immediately apparent from the table of contents. It’s a veritable feast, the climax of which must be cubic figures, and desmic systems leading up to Kummer’s quartic surface.It is a pity that there are quite a few misprints, although they are easily spotted and do not detract from the reader’s enjoyment of this lovely book.

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