Particular Cases of Quasi-Parallelograms of Type I on the Lobachevsky Plane
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 based on their diagonals. The existence of these quadrangles is proved by us...
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| Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 276; no. 6; pp. 759 - 766 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.11.2023
Springer Springer Nature B.V |
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| Online Access | Get full text |
| ISSN | 1072-3374 1573-8795 |
| DOI | 10.1007/s10958-023-06799-y |
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| 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 based on their diagonals. The existence of these quadrangles is proved by using the Cayley–Klein model in the circle of the Euclidean plane. |
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| AbstractList | 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 based on their diagonals. The existence of these quadrangles is proved by using the Cayley--Klein model in the circle of the Euclidean plane. 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 based on their diagonals. The existence of these quadrangles is proved by using the Cayley--Klein model in the circle of the Euclidean plane. Keywords and phrases: Lobachevsky plane, Cayley--Klein model, quasi-parallelogram, quasi-rhombus. AMS Subject Classification: 51F99 |
| Audience | Academic |
| Author | Maskina, M. S. Zhilnikov, T. A. |
| Author_xml | – sequence: 1 givenname: M. S. surname: Maskina fullname: Maskina, M. S. email: mariaya_maskina@mail.ru organization: Academy of Law Management of the Federal Penal Service of Russia – sequence: 2 givenname: T. A. surname: Zhilnikov fullname: Zhilnikov, T. A. organization: Academy of Law Management of the Federal Penal Service of Russia |
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| References | M. S. Maskina, Teaching proof to mathematically gifted students in elective courses [in Russian], Ph.D. Thesis, Saransk (2003). V. F. Kagan, Foundations of Geometry [in Russian], GITTL, Moscow–Leningrad (1949). AtanasyanLSBazylevVTGeometry1987MoscowProsveshchenie0655.51001[in Russian] M. S. Maskina and M. I. Kuptsov, “Special cases of hyperbolic parallelograms on the Lobachevsky plane,” in: Proc. Int. Conf. “Geometric Methods in Control Theory and Mathematical Physics” [in Russian], Ryazan State Univ., Ryazan (2018), pp. 53–54. AtanasyanLSLobachevsky Geometry2001MoscowProsveshchenie[in Russian] N. I. Lobachevsky, Complete Works. Vol. 3, GITTL, Moscow–Leningrad (1951). 6799_CR6 LS Atanasyan (6799_CR2) 1987 6799_CR5 LS Atanasyan (6799_CR1) 2001 6799_CR4 6799_CR3 |
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| SubjectTerms | Analysis Euclidean geometry Flying-machines Mathematics Mathematics and Statistics Parallelograms Rectangles |
| Title | Particular Cases of Quasi-Parallelograms of Type I on the Lobachevsky Plane |
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