Abstract
In this paper, we consider particular cases of hyperbolic parallelograms obtained by transferring characteristic properties of rectangles and squares on the Euclidean plane associated with their diagonals to the Lobachevsky plane. The existence of these quadrangles in the Cayley–Klein model in a circle of the Euclidean plane is proved.
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M. S. Maskina, Teaching proof of mathematically gifted students in elective courses [in Russian], Ph.D. thesis, Saransk (2003).
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 169, Proceedings of the International Conference “Geometric Methods in the Control Theory and Mathematical Physics” Dedicated to the 70th Anniversary of Prof. S. L. Atanasyan, 70th Anniversary of Prof. I. S. Krasil’shchik, 70th Anniversary of Prof. A. V. Samokhin, and 80th Anniversary of Prof. V. T. Fomenko. Ryazan State University named for S. Yesenin, Ryazan, September 25–28, 2018. Part II, 2019.
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Maskina, M.S., Kuptsov, M.I. Special Cases of Hyperbolic Parallelograms on the Lobachevsky Plane. J Math Sci 263, 387–395 (2022). https://doi.org/10.1007/s10958-022-05935-4
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DOI: https://doi.org/10.1007/s10958-022-05935-4