Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 36 (1995), No. 2

D. Ruoff: 
On the Derivation of the Non-Euclidean Angle of Parallelism Function

Abstract
This paper investigates the role that elementary area theory can play in
deriving the formula for the non-Euclidean angle of parallelism function.
It is shown how the pivotal feature of area theory, the connection between
area and angle defect of a polygon, extends to a quantitative relation among
the entities associated with a given angle of parallelism. The sought-after
formula then is easily determined. The whole investigation is carried out
in the framework laid out by Oskar Perron.