Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 181, Pages 66–73
DOI: https://doi.org/10.36535/0233-6723-2020-181-66-73 (Mi into659) 		 
Particular cases of first-kind quasi-parallelograms of the Lobachevsky plane

M. S. Maskina, T. A. Zhilnikov

The Academy of Law Management of the Federal Penal Service of Russia
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DOI: https://doi.org/10.36535/0233-6723-2020-181-66-73
Abstract: In this paper, we consider particular cases of quasi-parallelograms, which are obtained by transferring to the Lobachevsky plane various characteristic properties of rhombuses, rectangles, and squares of the Euclidean plane related with their diagonals. The existence of these quadrangles is proved by using the Cayley–Klein model in the circle of the Euclidean plane.
Keywords: Lobachevsky plane, Cayley–Klein model, quasi-parallelogram, quasi-rhombus.
Bibliographic databases:
Document Type: Article
UDC: 514.139
MSC: 51F99
Language: Russian
Citation: M. S. Maskina, T. A. Zhilnikov, “Particular cases of first-kind quasi-parallelograms of the Lobachevsky plane”, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 181, VINITI, Moscow, 2020, 66–73
Citation in format AMSBIB
\Bibitem{MasZhi20}
\by M.~S.~Maskina, T.~A.~Zhilnikov
\paper Particular cases of first-kind quasi-parallelograms of the Lobachevsky plane
\inbook Proceedings of the International Conference "Classical and Modern Geometry"
Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev.
Moscow, April 22-25, 2019. Part 3
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 181
\pages 66--73
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into659}
\crossref{https://doi.org/10.36535/0233-6723-2020-181-66-73}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4208370}
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