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 inJournal of mathematical sciences (New York, N.Y.) Vol. 276; no. 6; pp. 759 - 766
Main Authors Maskina, M. S., Zhilnikov, T. A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.11.2023
Springer
Springer Nature B.V
Subjects
Analysis
Euclidean geometry
Flying-machines
Mathematics
Mathematics and Statistics
Parallelograms
Rectangles
51F99
quasi-rhombus
Lobachevsky plane
quasi-parallelogram
Cayley–Klein model
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-023-06799-y

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Summary: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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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06799-y