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Perspectives on Projective Geometry : A Guided Tour Through Real and Complex Geometry / by Jürgen Richter-Gebert

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2011Description: Online-Ressource (XXII, 571p. 380 illus., 250 illus. in color, digital)ISBN:
  • 9783642172861
Subject(s): Additional physical formats: 9783642172854 | Buchausg. u.d.T.: Perspectives on projective geometry. Berlin : Springer, 2011. XXII, 571 S.DDC classification:
  • 516.5
  • 516
MSC: MSC: *51A05 | 51A25 | 51M05 | 51M10 | 51-01 | 51N15 | 14N15RVK: RVK: SK 380LOC classification:
  • QA440-699
  • QA471
DOI: DOI: 10.1007/978-3-642-17286-1Online resources: Summary: 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.Summary: 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.PPN: PPN: 1650772211Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
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