Perspectives on Projective Geometry

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Sprache: Englisch

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Beschreibung

Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. 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. In particular, it 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 interplay between 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 author¿s experience in implementing geometric software and includes hundreds of high-quality illustrations.

Über den Autor

Full Professor for Geometry and Visualization at Technical University Munich. Research in combinatorial, computational and dynamic geometry, automated geometric theorem proving and visualization. Author of the dynamic geometry program
Cinderella
and of the interactive visualization portal
Mathe-Vital
. Cinderella was awarded the Multimedia Innovation Award, the European Academic Software Award and the Deutsche Bildungssoftwarepreis. Mathe-Vital won the renowned MedidaPrix in 2008.

Zusammenfassung

A comprehensive modern language introduction into the classical topic of projective geometry

Very accessible writing and numerous high quality illustrations

Includes many concrete recipes for implementation of geometric operations

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2016
Fachbereich:	Geometrie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xxii 571 S.
ISBN-13:	9783662519585
ISBN-10:	3662519585
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Richter-Gebert, Jürgen
Auflage:	Softcover reprint of the original 1st ed. 2011
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg
Maße:	235 x 155 x 32 mm
Von/Mit:	Jürgen Richter-Gebert
Erscheinungsdatum:	23.08.2016
Gewicht:	0,89 kg

Artikel-ID: 109583734