On trigonometry in Beltrami-Klein model of hyperbolic geometry
type: Item
instance of: scholarly article
title: On trigonometry in Beltrami-Klein model of hyperbolic geometry
zbMATH Open document ID: 1296.51024
author: Mahfouz Rostamzadeh
author: Sayed-Ghahreman Taherian
published in: Results in Mathematics
publication date: 2014-06-18T00:00:00Z
review text: The authors prove a replacement theorem which allows us to win from a certain true statement \(P\) about a triangle \(\Delta\) (inside the unit disc) in the Euclidean plane a true statement \(P'\) about \(\Delta\) in the Beltrami-Klein model of hyperbolic geometry. In detail: the statement \(P\) contains vectors, angles, and trigonometry as known from Euclidean geometry, for \(P'\), \textit{A. A. Ungar} [Comput. Math. Appl. 49, No. 2--3, 187--221 (2005; Zbl 1071.83505)] introduced analogous concepts for the plane hyperbolic geometry.
reviewed by: Rolf Riesinger
Mathematics Subject Classification ID: 51M10
Mathematics Subject Classification ID: 51A25
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 51N25
zbMATH DE Number: 6305237
zbMATH Keywords: trigonometry in hyperbolic geometry
zbMATH Keywords: K-loop
zbMATH Keywords: gyrogroup
zbMATH Keywords: Beltrami-Klein model
zbMATH Keywords: special relativity
MaRDI profile type: Publication
full work available at URL: s00025-013-0350-6
OpenAlex ID: W2044442530
cites work: Q5662517
cites work: Zur Begründung metrischer affiner Ebenen
cites work: On algebraic structures related to Beltrami-Klein model of hyperbolic geometry
cites work: Beyond the Einstein addition law and its gyroscopic Thomas precession. The theory of gyrogroups and gyrovector spaces
cites work: Einstein's special relativity: Unleashing the power of its hyperbolic geometry
DOI: 10.1007/S00025-013-0350-6
description: scientific article; zbMATH DE number 6305237