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: Geometry Revealed
    sub title: A Jacob's Ladder to Modern Higher Geometry
  name:
    name part: Berger, Marcel.
    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: 2010
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 860 p. 666 illus. online resource.
  abstract: Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended... In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is very much alive and at the very heart of the work of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concepts to be created. The book is visually rich and inviting, so that readers may open it at random places and find much pleasure throughout according their own intuitions and inclinations. Marcel Berger is t he author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with an affinity for geometry.
  table of contents: Points and lines in the plane -- Circles and spheres -- The sphere by itself: can we distribute points on it evenly? -- Conics and quadrics -- Plane curves -- Smooth surfaces -- Convexity and convex sets -- Polygons, polyhedra, polytopes -- Lattices, packings and tilings in the plane -- Lattices and packings in higher dimensions -- Geometry and dynamics I: billiards -- Geometry and dynamics II: geodesic flow on a surface.
  note: by Marcel Berger.
  subject:
    topic: Mathematics
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Geometry
  subject:
    topic: Convex geometry
  subject:
    topic: Discrete geometry
  subject:
    topic: Differential geometry
  subject:
    topic: History
  subject:
    topic: Combinatorics
  subject:
    topic: Mathematics
  subject:
    topic: Geometry
  subject:
    topic: History of Mathematical Sciences
  subject:
    topic: Convex and Discrete Geometry
  subject:
    topic: Differential Geometry
  subject:
    topic: Combinatorics
  subject:
    topic: Dynamical Systems and Ergodic Theory
  classification: QA440-699
  classification: 516
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783540709978
  identifier: http://dx.doi.org/10.1007/978-3-540-70997-8
  record info:
    record creation date: 100721
    record change date: 20151204180523.0
    record identifier: 978-3-540-70997-8