Hyperbolic geometry with Clifford algebra (Q1370795)

This paper is part of the programme of using Clifford algebras to construct algebraic models for geometry, as formulated in \textit{D. Hestenes} and \textit{G. Sobczyk} [Clifford algebra to geometric calculus (D. Reidel, Dordrecht) (1984; Zbl 0541.53059)] and applied to projective geometry in \textit{D. Hestenes} and \textit{R. Ziegler} [Acta Appl. Math. 23, No. 1, 25-63 (1991; Zbl 0735.51001)]. In the author's opinion this calculus, which is used here for deriving a long list of formulas (among which the author is most proud of a formula for the perimeter and one for the area of a convex polygon) for 2-dimensional hyperbolic geometry (the \(n\)-dimensional case being the subject of a forthcoming paper), is computationally convenient. Agreeing or disagreeing with this opinion will likely depend on one's familiarity with and enthusiasm for the above-mentioned programme.