rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Perspectives on Projective Geometry
    sub title: A Guided Tour Through Real and Complex Geometry
  name:
    name part: Richter-Gebert, Jürgen.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2011
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXII, 571 p. 380 illus., 250 illus. in color. online resource.
  abstract: 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.
  table of contents: 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.
  note: by Jürgen Richter-Gebert.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Algorithms
  subject:
    topic: Visualization
  subject:
    topic: Geometry
  subject:
    topic: Convex geometry
  subject:
    topic: Discrete geometry
  subject:
    topic: Mathematics
  subject:
    topic: Geometry
  subject:
    topic: Algebra
  subject:
    topic: Algorithms
  subject:
    topic: General Algebraic Systems
  subject:
    topic: Visualization
  subject:
    topic: Convex and Discrete Geometry
  classification: QA440-699
  classification: 516
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783642172861
  identifier: http://dx.doi.org/10.1007/978-3-642-17286-1
  record info:
    record creation date: 110204
    record change date: 20151204184008.0
    record identifier: 978-3-642-17286-1