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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 169, Pages 39–47
DOI: https://doi.org/10.36535/0233-6723-2019-169-39-47 (Mi into513) 		 
Special cases of hyperbolic parallelograms on the Lobachevsky plane

M. S. Maskinaa, M. I. kuptsovb

a The Academy of Law Management of the Federal Penal Service of Russia
b Ryazan State Radio Engineering University
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DOI: https://doi.org/10.36535/0233-6723-2019-169-39-47
Abstract: In this paper, we consider particular cases of hyperbolic parallelograms obtained by transferring to the Lobachevsky plane of characteristic properties of rectangles and squares on the Euclidean plane associated with their diagonals. The existence of these quadrangles in the Cayley–Klein model in a circle of the Euclidean plane is proved.
Keywords: Lobachevsky plane, Cayley–Klein model, hyperbolic parallelogram, hyperbolic rhombus.
Document Type: Article
UDC: 514.139
MSC: 51F99
Language: Russian
Citation: M. S. Maskina, M. I. kuptsov, “Special cases of hyperbolic parallelograms on the Lobachevsky plane”, Proceedings   of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 169, VINITI, Moscow, 2019, 39–47
Citation in format AMSBIB
\Bibitem{MasKup19}
\by M.~S.~Maskina, M.~I.~kuptsov
\paper Special cases of hyperbolic parallelograms on the Lobachevsky plane
\inbook Proceedings   of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25--28, 2018. Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 169
\pages 39--47
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into513}
\crossref{https://doi.org/10.36535/0233-6723-2019-169-39-47}
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