Orthogonality on the given hyperbolic planes - Fryda, Jan (Annales Mathematicae Silesianae, 1990)
It has been proved, by K. Menger in [3], that all concepts of the Bolyai-Lobachevsky geometry can be defined in terms of the operations “joining” and “intersecting”. In the present paper a similar definition of the orthogonality on hyperbolic plane (being a substitute for the Bolyai-Lobachevsky plane) over a finite field with characteristic different from 2 or over a finite extension of the rational field to a subfield of the real field is given and investigated.