Orthogonality on the given hyperbolic planes
Abstract
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.
References
2. F. Karteszi, Introduction to Finite Geometries, Budapest, 1976.
3. K. Menger, Non-euclidean geometry of joining and intersecting, Bull. Amer. Math. Soc. 44 (1938), 821-824.
4. T.G. Ostrom, Ovals and finite Bolyai-Lobachevsky planes, Amer. Math. Monthly 69 (1962), 899-901.
5. L. Włodarski, On differential notions of the interior of a conic, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), 965-967.
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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