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Hyperbolic Geometry with Clifford Algebra

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Abstract

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.

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References

  1. Hestenes, D. and Sobczyk, G.: Clifford Algebra to Geometric Calculus, D. Reidel, Dordrecht, 1984.

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  2. Hestenes, D. and Ziegler, R.: Projective geometry with Clifford algebra, Acta Appl. Math. 23 1991.

  3. Iversen, B.: Hyperbolic Geometry, Cambridge University Press, 1992.

  4. Fenchel, W.: Elementary Geometry in Hyperbolic Space, Walter de Gruyter, 1989.

  5. Greenberg, M. J.: Euclidean and Non-Euclidean Geometries, 2nd edn, W. H. Freeman, 1980.

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Authors and Affiliations

  1. Institute of Systems Science, Academia Sinica, Beijing, 100080, P.R. China

    Hongbo Li

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  1. Hongbo Li
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Li, H. Hyperbolic Geometry with Clifford Algebra. Acta Applicandae Mathematicae 48, 317–358 (1997). https://doi.org/10.1023/A:1005884731270

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  • DOI: https://doi.org/10.1023/A:1005884731270

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