Research Article

Year 2017,
Volume: 10 Issue: 2, 20 - 31, 29.10.2017
### Abstract

### Keywords

### References

hyperbolic plane of positive curvature generalized polygon generalized Möbius polygon regular polygon equiangular polygon

- [1] Asmus, Im., Duality between hyperbolic and de Sitter geometry. J. Geom. 96 (2009), no. 1-2, 11-40.
- [2] Böhm, J. and Hof, H. C. I., Flächeninhalt verallgemeinerter hyperbolischer Dreiecke. Geom. Dedicata 42 (1992), no. 2, 223-233.
- [3] Cho, Y.-H., Trigonometry in extended hyperbolic space and extended de Sitter space. Bull. Korean Math. Soc. 46 (2009), no. 6, 1099-1133.
- [4] Coxeter, H. S. M., A Geometrical Background for De Sitter’s World. Amer. Math. Mon. 50 (1943), no. 4, 217-228.
- [5] Klein, F., Vorlesungen Über Nicht-Euclidische Geometrie. Verlag Von Julius Springer, Berlin, 1928.
- [6] Klychkova, V. N., Trirectangle of the hyperbolic plane of positive curvature. Coll. of articles of the Int. sci. and pract. conf. "Modern view on the future of science", Tomsk, May 25, 2016. Aeterna. (2016), 14-17. (In Russian)
- [7] Milnor, J. W., Hyperbolic geometry: The first 150 years. Amer. Math. Soc. (N.S.). 6 (1982), no. 1, 9-24.
- [8] Romakina, L. N., Geometry of the hyperbolic plane of positive curvature. P. 1: Trigonometry. Publishing House of the Saratov University, Saratov, 2013. (In Russian)
- [9] Romakina, L. N., Geometry of the hyperbolic plane of positive curvature. P. 2: Transformations and Simple Partitions. Publishing House of the Saratov University, Saratov, 2013. (In Russian)
- [10] Romakina, L. N., The area of a generalized polygon without parabolic edges of a hyperbolic plane of positive curvature. Asian J. Math. Comp. Research. 10 (2016), no. 4, 293-310.
- [11] Romakina, L. N., On the area of a trihedral on a hyperbolic plane of positive curvature. Mat. Tr. 17 (2014), no. 2, 184-206. (In Russian). Translated in Sib. Adv. Math. 25 (2015), no. 2, 138-153.
- [12] Romakina, L. N., The areas of the regular polygons, inscribed in a hypercycle of a hyperbolic plane of positive curvature. Int. Sci. J. «Innovative science». 6 (2016), 20-22. (In Russian)
- [13] Romakina, L. N., Analogs of a formula of Lobachevsky for angle of parallelism on the hyperbolic plane of positive curvature. Sib. Elektron. Mat. Izv. 10 (2013), 393-407. (In Russian)
- [14] Romakina, L. N., Oval lines of a hyperbolic plane of positive curvature. Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform. 12 (2012), no. 3, 37-44. (In Russian)
- [15] Romakina, L. N., Cycles of the hyperbolic plane of positive curvature. Zap. Nauchn. Sem. POMI. 415 (2013), 137-162. (In Russian). Translated in J. Math. Sci. 212 (2016), no. 5, 605-621.
- [16] Romakina, L. N., The theorem of the area of a rectangular trihedral of the hyperbolic plane of positive curvature. Dal’nevost. Mat. Zh. 13 (2013), no. 1, 127-147. (In Russian)
- [17] Romakina, L. N., To the theory of the areas of a hyperbolic plane of positive curvature. Publications de l’Institut Mathematique. 99 (2016), no. 113, 139-154. (In Russian).
- [18] Romakina, L. N., Finite closed 3(4)-loops of extended hyperbolic plane. Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform. 10 (2010), no. 3, 14-26. (In Russian)
- [19] Romakina, L. N., The chord length of a hypercycle in a hyperbolic plane of positive curvature. Sibirsk. Mat. Zh. 54 (2013), no. 5, 1115-1127. (In Russian). Translated in Sib. Math. J. 54 (2013), no. 5, 894-904.
- [20] Romakina, L. N., Partitions of a hyperbolic plane of positive curvature generated by a regular n-contour. Relativity theory, gravity and geometry, Proc. of the Petrov 2010 Anniversary Symposium on General Relativity and Gravitation (Kazan’ 2010), Kazan’ State University, Kazan’ (2010). 227-232. (In Russian)
- [21] Romakina, L. N., Simple partitions of a hyperbolic plane of positive curvature. Mat. Sb. 203 (2012), no. 9, 83-116. (In Russian). Translated in Sbornik: Mathematics. 203 (2012), no. 9, 1310-1341.
- [22] Rosenfel’d, B. A., Zamakhovskii, M. P., Geometry of Lie groups. Symmetric, parabolic and periodic spaces. Moscow centre for Countinuous Mathematical Education, Moscow, 2003. (In Russian)
- [23] Rosenfel’d, B. A., Noneuclidean spaces. Nauka, Moscow, 1969. (In Russian)
- [24] De Sitter,W., On the Relativity of Inertia. Remarks Concerning Einstein’s Latest Hypothesis. Proc. Royal Acad. Amsterdam. 19 (1917), no. 2, 1217-1225.

Year 2017,
Volume: 10 Issue: 2, 20 - 31, 29.10.2017
### Abstract

### References

- [1] Asmus, Im., Duality between hyperbolic and de Sitter geometry. J. Geom. 96 (2009), no. 1-2, 11-40.
- [2] Böhm, J. and Hof, H. C. I., Flächeninhalt verallgemeinerter hyperbolischer Dreiecke. Geom. Dedicata 42 (1992), no. 2, 223-233.
- [3] Cho, Y.-H., Trigonometry in extended hyperbolic space and extended de Sitter space. Bull. Korean Math. Soc. 46 (2009), no. 6, 1099-1133.
- [4] Coxeter, H. S. M., A Geometrical Background for De Sitter’s World. Amer. Math. Mon. 50 (1943), no. 4, 217-228.
- [5] Klein, F., Vorlesungen Über Nicht-Euclidische Geometrie. Verlag Von Julius Springer, Berlin, 1928.
- [6] Klychkova, V. N., Trirectangle of the hyperbolic plane of positive curvature. Coll. of articles of the Int. sci. and pract. conf. "Modern view on the future of science", Tomsk, May 25, 2016. Aeterna. (2016), 14-17. (In Russian)
- [7] Milnor, J. W., Hyperbolic geometry: The first 150 years. Amer. Math. Soc. (N.S.). 6 (1982), no. 1, 9-24.
- [8] Romakina, L. N., Geometry of the hyperbolic plane of positive curvature. P. 1: Trigonometry. Publishing House of the Saratov University, Saratov, 2013. (In Russian)
- [9] Romakina, L. N., Geometry of the hyperbolic plane of positive curvature. P. 2: Transformations and Simple Partitions. Publishing House of the Saratov University, Saratov, 2013. (In Russian)
- [10] Romakina, L. N., The area of a generalized polygon without parabolic edges of a hyperbolic plane of positive curvature. Asian J. Math. Comp. Research. 10 (2016), no. 4, 293-310.
- [11] Romakina, L. N., On the area of a trihedral on a hyperbolic plane of positive curvature. Mat. Tr. 17 (2014), no. 2, 184-206. (In Russian). Translated in Sib. Adv. Math. 25 (2015), no. 2, 138-153.
- [12] Romakina, L. N., The areas of the regular polygons, inscribed in a hypercycle of a hyperbolic plane of positive curvature. Int. Sci. J. «Innovative science». 6 (2016), 20-22. (In Russian)
- [13] Romakina, L. N., Analogs of a formula of Lobachevsky for angle of parallelism on the hyperbolic plane of positive curvature. Sib. Elektron. Mat. Izv. 10 (2013), 393-407. (In Russian)
- [14] Romakina, L. N., Oval lines of a hyperbolic plane of positive curvature. Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform. 12 (2012), no. 3, 37-44. (In Russian)
- [15] Romakina, L. N., Cycles of the hyperbolic plane of positive curvature. Zap. Nauchn. Sem. POMI. 415 (2013), 137-162. (In Russian). Translated in J. Math. Sci. 212 (2016), no. 5, 605-621.
- [16] Romakina, L. N., The theorem of the area of a rectangular trihedral of the hyperbolic plane of positive curvature. Dal’nevost. Mat. Zh. 13 (2013), no. 1, 127-147. (In Russian)
- [17] Romakina, L. N., To the theory of the areas of a hyperbolic plane of positive curvature. Publications de l’Institut Mathematique. 99 (2016), no. 113, 139-154. (In Russian).
- [18] Romakina, L. N., Finite closed 3(4)-loops of extended hyperbolic plane. Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform. 10 (2010), no. 3, 14-26. (In Russian)
- [19] Romakina, L. N., The chord length of a hypercycle in a hyperbolic plane of positive curvature. Sibirsk. Mat. Zh. 54 (2013), no. 5, 1115-1127. (In Russian). Translated in Sib. Math. J. 54 (2013), no. 5, 894-904.
- [20] Romakina, L. N., Partitions of a hyperbolic plane of positive curvature generated by a regular n-contour. Relativity theory, gravity and geometry, Proc. of the Petrov 2010 Anniversary Symposium on General Relativity and Gravitation (Kazan’ 2010), Kazan’ State University, Kazan’ (2010). 227-232. (In Russian)
- [21] Romakina, L. N., Simple partitions of a hyperbolic plane of positive curvature. Mat. Sb. 203 (2012), no. 9, 83-116. (In Russian). Translated in Sbornik: Mathematics. 203 (2012), no. 9, 1310-1341.
- [22] Rosenfel’d, B. A., Zamakhovskii, M. P., Geometry of Lie groups. Symmetric, parabolic and periodic spaces. Moscow centre for Countinuous Mathematical Education, Moscow, 2003. (In Russian)
- [23] Rosenfel’d, B. A., Noneuclidean spaces. Nauka, Moscow, 1969. (In Russian)
- [24] De Sitter,W., On the Relativity of Inertia. Remarks Concerning Einstein’s Latest Hypothesis. Proc. Royal Acad. Amsterdam. 19 (1917), no. 2, 1217-1225.

There are 24 citations in total.

Primary Language | English |
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Journal Section | Research Article |

Authors | |

Publication Date | October 29, 2017 |

Published in Issue | Year 2017 Volume: 10 Issue: 2 |