Hyperbolic geometry with geometric algebra (Q1369768)

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scientific article; zbMATH DE number 1077089
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English
Hyperbolic geometry with geometric algebra
scientific article; zbMATH DE number 1077089

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    Hyperbolic geometry with geometric algebra (English)
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    20 April 1998
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    Using the definitions in geometric algebra developed by \textit{D. Hestenes} and \textit{G. Sobczyk} [`Clifford algebra to geometric calculus', New York: D. Reidel, Dordrecht (1984; Zbl 0541.53059)], the author announces (without proofs) three results in hyperbolic geometry. In his first theorem he states formulas for the area and the perimeter of a convex polygon in the hyperbolic plane. The second theorem is a generalization of Ptolemy's theorem for hyperbolic \(n\)-space. In the third theorem, criteria are stated for a triangle in the hyperbolic plane to have inscribed and escribed circles.
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    inscribed circles
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    geometric algebra
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    hyperbolic geometry
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    area
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    perimeter
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    convex polygon
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    Ptolemy's theorem
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    triangle
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    hyperbolic plane
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    escribed circles
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