Hyperbolic geometry with geometric algebra
type: Item
instance of: scholarly article
title: Hyperbolic geometry with geometric algebra
zbMATH Open document ID: 0886.51006
DOI: 10.1007/BF02882454
published in: Chinese Science Bulletin
publication date: 1998-04-20T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 51M10
Mathematics Subject Classification ID: 52A55
zbMATH DE Number: 1077089
zbMATH Keywords: inscribed circles
zbMATH Keywords: geometric algebra
zbMATH Keywords: hyperbolic geometry
zbMATH Keywords: area
zbMATH Keywords: perimeter
zbMATH Keywords: convex polygon
zbMATH Keywords: Ptolemy's theorem
zbMATH Keywords: triangle
zbMATH Keywords: hyperbolic plane
zbMATH Keywords: escribed circles
author: Hongbo Li
MaRDI profile type: Publication
cites work: Clifford algebra to geometric calculus. A unified language for mathematics and physics
cites work: Projective geometry with Clifford algebra
full work available at URL: https://doi.org/10.1007/bf02882454
OpenAlex ID: W2018941203
description: scientific article; zbMATH DE number 1077089