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