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Field name	Details
Dewey Class	516
Title	Perspectives on Projective Geometry (EB) : A Guided Tour Through Real and Complex Geometry / by Jürgen Richter-Gebert.
Author	Richter-Gebert, Jürgen , 1963-
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2011.
Physical Details	XXII, 571p. 380 illus., 250 illus. in color. : online resource.
ISBN	9783642172861
Summary Note	Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry.Â It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications.Â In particular, itÂ explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplayÂ betweenÂ geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the authorâs experience in implementing geometric software and includes hundreds ofÂ high-qualityÂ illustrations.:
Contents note	1 Pappos's Theorem: Nine Proofs and Three Variations -- 2 Projective Planes -- 3 Homogeneous Coordinates -- 4 Lines and Cross-Ratios -- 5 Calculating with Points on Lines -- 6 Determinants -- 7 More on Bracket Algebra -- 8 Quadrilateral Sets and Liftings -- 9 Conics and Their Duals -- 10 Conics and Perspectivity -- 11 Calculating with Conics -- 12 Projective $d$-space -- 13 Diagram Techniques -- 14 Working with diagrams -- 15 Configurations, Theorems, and Bracket Expressions -- 16 Complex Numbers: A Primer -- 17 The Complex Projective Line -- 18 Euclidean Geometry -- 19 Euclidean Structures from a Projective Perspective -- 20 Cayley-Klein Geometries -- 21 Measurements and Transformations -- 22 Cayley-Klein Geometries at Work -- 23 Circles and Cycles -- 24 Non-Euclidean Geometry: A Historical Interlude -- 25 Hyperbolic Geometry -- 26 Selected Topics in Hyperbolic Geometry -- 27 What We Did Not Touch -- References -- Index.
System details note	Online access to this digital book is restricted to subscription institutions and access available only through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-642-17286-1
Links to Related Works	Subject References: Algebra . Algorithms . Convex and Discrete Geometry . Discrete groups . General Algebraic Systems . Geometry . Mathematics . Visualization . Authors: Richter-Gebert, Jürgen 1963- . RICHTERGEBERT JUERGEN 1963 . Corporate Authors: SpringerLink (Online service) . Classification: 516 .

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Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry

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