Smarandache Theorem in Hyperbolic Geometry
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2014) no. 2, pp. 221-232 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper a hyperbolic version of the Smarandache pedal polygon theorem is considered.
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A. V. Kostin; I. Kh. Sabitov. Smarandache Theorem in Hyperbolic Geometry. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 10 (2014) no. 2, pp. 221-232. http://geodesic.mathdoc.fr/item/JMAG_2014_10_2_a2/

[1] M. Berger, Géométrie. Espaces euclidiens, CEDIC/Fernand Natan, Paris, 1978

[2] F. Smarandache, Problemes avec et Sans ... Problems, Somi-press, Fes, Morocco, 1983, 49 ; 54–60 | MR

[3] A. V. Kostin, “Smarandache Theorem in Spherical Geometry”, Izv. Belinsky Penza State Pedagogical University, 2012, no. 30, 78–83

[4] O. Demirel, E. Soyturk, “The Hyperbolic Carnot Theorem in the Poincare Disc Model of Hyperbolic Geometry”, Novi Sad J. Math., 38 (2008), 33–39 | MR | Zbl

[5] C. Barbu, N. Sönmez, “On the Carnot Theorem in the Poincare Upper Half-Plane Model of Hyperbolic Geometry”, Acta Universitatis Apulensis, 31 (2012), 321–325 | MR

[6] C. Barbu, Contributions to the Study of the Hyperbolic Geometry, PhD thesis Summary, Cluj–Napoca, 2012

[7] C. Barbu, “Smarandache's Pedal Polygon Theorem in the Poincare Disk Model of Hyperbolic Geometry”, Intern. J. Math. Combin., 1 (2010), 99–102 | MR | Zbl

[8] N. Sönmez, C. Barbu, The Hyperbolic Smarandache Theorem in the Poincare Upper Half-Plane Model of Hyperbolic Geometry, http://www.intellectualarchive.com/IAB_Files/Intellectual_Archive_Bulletin_February_2012.pdf

[9] N. Sönmez, Request, Personal Communication to I. Sabitov, 28.08.2011

[10] I. Kh. Sabitov, “Solution of Cyclic Polygons”, Mathematic Prosvetshenie, 14:3 (2010), 83–106

[11] B. A. Rozenfeld, Noeuclidean Geometries, Nauka, M., 1969 (Russian) | MR

[12] N. M. Nestorovich, Geometric Constructions in Lobachevsky Plane, GITTL, M.–L., 1951 (Russian)

[13] G. S. M. Kokseter, S. L. Greitzer, Novye vstrechi s geometriej, Nauka, M., 1978 | MR