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  3. Minkowski Geometry
  • Cited by 180
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2013
      June 1996
      ISBN:
      9781107325845
      9780521404723
      DOI:
      https://doi.org/10.1017/CBO9781107325845
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.718kg, 368 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Geometry and Topology
      Series:
      Encyclopedia of Mathematics and its Applications (63)
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    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology
    Series:
    Encyclopedia of Mathematics and its Applications (63)
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    Book description

    Minkowski geometry is a type of non-Euclidean geometry in a finite number of dimensions in which distance is not 'uniform' in all directions. This book presents the first comprehensive treatment of Minkowski geometry since the 1940s. The author begins by describing the fundamental metric properties and the topological properties of existence of Minkowski space. This is followed by a treatment of two-dimensional spaces and characterisations of Euclidean space among normed spaces. The central three chapters present the theory of area and volume in normed spaces, a fascinating geometrical interplay among the various roles of the ball in Euclidean space. Later chapters deal with trigonometry and differential geometry in Minkowski spaces. The book ends with a brief look at J. J. Schaffer's ideas on the intrinsic geometry of the unit sphere. Minkowski Geometry will appeal to students and researchers interested in geometry, convexity theory and functional analysis.

    Reviews

    ‘ … volume, isoperimetry, integral geometry and trigonometry … all are admirably treated here by an expert in the field.’

    Source: Mathematika

    ‘This is a comprehensive monograph that will serve well both as an introduction and as a reference work.’

    Source: Monatshefte für Mathematik

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