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Foundations of Physics

, Volume 23, Issue 10, pp 1357–1374 | Cite as

Distance geometry and geometric algebra

  • Andreas W. M. Dress
  • Timothy F. Havel
Part II. Invited Papers Dedicated To David Hestenes

Abstract

As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)

Keywords

Euclidean Distance Distance Function Linear Algebra Simple Representation Euclidean Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • Andreas W. M. Dress
    • 1
  • Timothy F. Havel
    • 2
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeld 1Germany
  2. 2.Biological Chemistry and Molecular PharmacologyHarvard Medical SchoolBoston

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