Special Cases of Hyperbolic Parallelograms on the Lobachevsky Plane

In this paper, we consider particular cases of hyperbolic parallelograms obtained by transferring characteristic properties of rectangles and squares on the Euclidean plane associated with their diagonals to the Lobachevsky plane. The existence of these quadrangles in the Cayley–Klein model in a cir...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 263; no. 3; pp. 387 - 395
Main Authors Maskina, M. S., Kuptsov, M. I.
Format Journal Article
LanguageEnglish
Published New York Springer US 04.05.2022
Springer
Springer Nature B.V
Subjects
Analysis
Euclidean geometry
Flying-machines
Mathematics
Mathematics and Statistics
Parallelograms
Rectangles
hyperbolic parallelogram
51F99
Lobachevsky plane
hyperbolic rhombus
Cayley–Klein model
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Summary:In this paper, we consider particular cases of hyperbolic parallelograms obtained by transferring characteristic properties of rectangles and squares on the Euclidean plane associated with their diagonals to the Lobachevsky plane. The existence of these quadrangles in the Cayley–Klein model in a circle of the Euclidean plane is proved.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05935-4