Acta Applicandae Mathematica

, Volume 48, Issue 3, pp 317–358 | Cite as

Hyperbolic Geometry with Clifford Algebra

  • Hongbo Li


The Clifford algebra in D. Hestenes’ formulation is used to study hyperbolic geometry and some interesting theorems are obtained. The computational power of this formulation is fully revealed by the ease of extending old results and discovering new ones. An important new result is the formulas on the area and perimeter of a convex polygon, based on extending Gauss’ equalities.

hyperbolic geometry Clifford algebra Gauss’ equalities 


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    Hestenes, D. and Sobczyk, G.: Clifford Algebra to Geometric Calculus, D. Reidel, Dordrecht, 1984.Google Scholar
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    Hestenes, D. and Ziegler, R.: Projective geometry with Clifford algebra, Acta Appl. Math. 23 1991.Google Scholar
  3. 3.
    Iversen, B.: Hyperbolic Geometry, Cambridge University Press, 1992.Google Scholar
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    Fenchel, W.: Elementary Geometry in Hyperbolic Space, Walter de Gruyter, 1989.Google Scholar
  5. 5.
    Greenberg, M. J.: Euclidean and Non-Euclidean Geometries, 2nd edn, W. H. Freeman, 1980.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Hongbo Li
    • 1
  1. 1.Institute of Systems ScienceAcademia SinicaBeijingP.R. China

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