Symmetry and Pattern in Projective Geometry
Lord, Eric.
Symmetry and Pattern in Projective Geometry [electronic resource] / by Eric Lord. - XI, 184 p. 103 illus., 20 illus. in color. online resource.
Foundations: the Synthetic Approach -- The Analytic Approach -- Linear Figures -- Quadratic Figures -- Cubic Figures -- Quartic Figures -- Finite Geometries.
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. Brief introductions to Plücker coordinates and Grassmann coordinates are also 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 H S M 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 undergraduate students and those wishing to learn more about the subject of geometry. Subject and theorems that are often considered quite complicated are made accessible and presented in an easy-to-read and enjoyable manner. .
9781447146315
10.1007/978-1-4471-4631-5 doi
Mathematics.
Computer science--Mathematics.
Projective geometry.
Mathematics.
Projective Geometry.
Symbolic and Algebraic Manipulation.
Mathematics, general.
QA471
516.5
Symmetry and Pattern in Projective Geometry [electronic resource] / by Eric Lord. - XI, 184 p. 103 illus., 20 illus. in color. online resource.
Foundations: the Synthetic Approach -- The Analytic Approach -- Linear Figures -- Quadratic Figures -- Cubic Figures -- Quartic Figures -- Finite Geometries.
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. Brief introductions to Plücker coordinates and Grassmann coordinates are also 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 H S M 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 undergraduate students and those wishing to learn more about the subject of geometry. Subject and theorems that are often considered quite complicated are made accessible and presented in an easy-to-read and enjoyable manner. .
9781447146315
10.1007/978-1-4471-4631-5 doi
Mathematics.
Computer science--Mathematics.
Projective geometry.
Mathematics.
Projective Geometry.
Symbolic and Algebraic Manipulation.
Mathematics, general.
QA471
516.5