Smarandache Theorem in Hyperbolic Geometry
DOI:
https://doi.org/10.15407/mag10.02.221Ключові слова:
гіперболічна геометрія, сферична геометрія, педальний багатокутникАнотація
Подано гіперболічну версію теореми Смарандача про педальний багатокутник.
Mathematics Subject Classification: 51M09.
Посилання
M. Berger, Geometria, V. 1. Mir, Moscow, 1984. (Russian) (Franch transl.: M. Berger, Géométrie. Espaces eulidiens. CEDIC/Fernand Natan, Paris, 1978.)
F. Smarandache, Problemes avec et Sans . . . Problems. pp. 49 & 54-60, Somi-press, Fes, Morocco, 1983.
A.V. Kostin, Smarandache Theorem in Spherical Geometry. — Izv. Belinsky Penza State Pedagogical University (2012), No. 30, 78–83.
O. Demirel and E. Soyturk, The Hyperbolic Carnot Theorem in the Poincare Disc Model of Hyperbolic Geometry. — Novi Sad J. Math. 38 (2008), 33–39.
C. Barbu and N. Sönmez, On the Carnot Theorem in the Poincare Upper HalfPlane Model of Hyperbolic Geometry. — Acta Universitatis Apulensis 31 (2012), 321–325.
C. Barbu, Contributions to the Study of the Hyperbolic Geometry. PhD thesis Summary. Cluj–Napoca, 2012.
C. Barbu, Smarandache’s Pedal Polygon Theorem in the Poincare Disk Model of Hyperbolic Geometry. — Intern. J. Math. Combin. 1 (2010), 99–102.
N. Sönmez and C. Barbu, The Hyperbolic Smarandache Theorem in the Poincare Upper Half-Plane Model of Hyperbolic Geometry. www.IntellectualArchive.com/getfile.phpefile=r1E9bSRUgGH&orig
N. Sönmez, Request. Personal Communication to I. Sabitov, 28.08.2011.
I.Kh. Sabitov, Solution of Cyclic Polygons. — Mathematic Prosvetshenie 14 (2010), No. 3, 83–106.
B.A. Rozenfeld, Noeuclidean Geometries. Nauka, Moscow, 1969. (Russian)
N.M. Nestorovich, Geometric Constructions in Lobachevsky Plane. Moscow–Leningrad, 1951. (Russian)
H.S.M. Coxeter and S.L. Greitzer, Geometry Revisited. Toronto–New York, 1967.(Russ. transl.: G.S.M. Kokseter, S.L. Greitzer, Novye vstrechi s geometriej. Nauka,Moscow, 1978.)
