On trigonometry in Beltrami-Klein model of hyperbolic geometry
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.
scientific article; zbMATH DE number 6305237