Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Romakina L. N. Hyperbolic Parallelograms of the Plane b H. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 3, pp. 43-52. DOI: 10.18500/1816-9791-2013-13-3-43-52

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
27.08.2013
Full text:
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Language: 
Russian
Heading: 
Mathematics
UDC: 
514.133
DOI: 
10.18500/1816-9791-2013-13-3-43-52

Hyperbolic Parallelograms of the Plane b H

Autors: 
Romakina Lyudmila Nikolaevna, Saratov State University
Abstract: 

Hyperbolic parallelograms on a Hyperbolic Plane b H of the positive curvature in the Cayley – Klein model are investigated. We conducted their classification, obtained the metric correlations between the measure of angles and the expressions of lengths of the edges through a measure of included angles.

Key words: 
hyperbolic plane b H of positive curvature
parallelogram
hyperbolic parallelogram
References: 
  1. Rozenfeld B. A. Neevklidovy prostranstva [Non-Euclidean spaces]. Moscow, Nauka, 1969, 548 p. (in Russian).
  2. Romakina L. N. Simple partitions of a hyperbolic plane of positive curvature. Sb. Math., 2012, vol. 203, iss. 9. pp. 1310–1341.
  3. Romakina L. N. Oval Lines of the Hyperbolic Plane of Positive Curvature. Izv. Sarat. Univ. N.S. Ser. Math. Mech. Inform., 2012, vol. 12, iss. 3, pp. 37–44 (in Russian).
  4. Romakina L. N. Analogs of a formula of Lobachevsky for angle of parallelism on the hyperbolic plane of positive curvature. Siberian Electronic Mathematical Reports, 2013, vol. 10, pp. 393–407 (in Russian).
  5. Romakina L. N. The theorem of the area of a rectangular trihedral of the hyperbolic plane of positive curvature. Far Eastern Mathematical Journal, 2013, vol. 13, № 1, pp. 127–147 (in Russian).
  6. Romakina L. N. Finite Closed 3(4)-Loops of Extended Hyperbolic Plane. Izv. Sarat. Univ. N.S. Ser. Math. Mech. Inform., 2010, vol. 10, iss. 3, pp. 14–26 (in Russian).
  7. Romakina L. N. Finite Closed 5-Loops of Extended Hyperbolic Plane. Izv. Sarat. Univ. N.S. Ser. Math. Mech. Inform., 2011, vol. 11, iss. 1, pp. 38–49 (in Russian).
Received: 
19.02.2013
Accepted: 
24.07.2013
Published: 
30.08.2013
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