Geodesic
Special cases of hyperbolic parallelograms on the Lobachevsky plane
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 169 (2019), pp. 39-47.

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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. 
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M. S. Maskina; M. I. kuptsov. Special cases of hyperbolic parallelograms on the Lobachevsky plane. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 169 (2019), pp. 39-47. http://geodesic.mathdoc.fr/item/INTO_2019_169_a5/

[2] Atanasyan L. S., Geometriya Lobachevskogo, Prosveschenie, M., 2001

[3] Atanasyan L. S., Bazylev V. T., Geometriya, Prosveschenie, M., 1987

[4] Kagan V. F., Osnovaniya geometrii, GITTL, M.-L., 1949

[5] Lobachevskii N. I., Polnoe sobranie sochinenii v 3 tomakh, GITTL, M.-L., 1951 | MR

[6] Maskina M. S., Obuchenie dokazatelstvu matematicheski odarennykh uchaschikhsya na fakultativnykh kursakh, Diss. na soisk. uch. step. kand. ped. nauk, Mordov. gos. ped. in-t im. M. E. Evseveva, Saransk, 2003