Some features in connections with triangles in the Poincare upper half plane

• Autorzy: Sonmez N.
• Języki publikacji: EN

Abstrakty

EN

In this work, it is shown that the product of lengths that are segments reserved to altitudes of orthocenter is constant in the Poincare triangle. I defined to Carnot theorem Poincare upper half plane.

Słowa kluczowe

EN

Poincare upper half plane; Poincare circle; Poincare triangle

PL

koło Poincare; trójkąt Poincare

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 2
• Strony: 403--409
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Sonmez N.

• Afyon Kocatepe University Faculty of Science and Literatures Department of Mathematics Ans Campus, 03200 - Afyonkarahisar, Turkey,

Bibliografia

• [1] J. W. Anderson, Hyperbolic Geometry, Springer, London, Berlin, Heidelberg, 1999.
• [2] E. F. Krause, Taxicab geometry, Addison-Wesley, Menlo Park, California, 1975.
• [3] R. S. Millman, G. D. Parker, Geometry a metric approach with models, Verlag New York Inc., 1991, p. 367.
• [4] N. Sonmez, On the geometry of Poincare half plane, Ph. D. Thesis, Osmangazi University Institute of Science and Technology, 2006, p. 98.
• [5] S. Stahl, The Poincare half plane a gateway to modern geometry, Jones and Barlett Publishers, Boston, 1993 p. 298.
• [6] S. Stahl, Geometry from Euclid to Knots, Pearson Education, Inc., Upper Saddle Riveri New Jersey, 2002, p. 457.
• [7] J. Stilwell, Sources of hyperbolic geometry, Amer. Math. Soc. (1996) p. 153.
• [8] H. H. Uğurlu, M. Kazaz, A. ve Ozdemir, Stewart, Ceva and Menelaus Theorems for geodesic triangles on the dual hyperbolic unit sphere H2 0 of the dual Lorentzian 3-space D31, III. Geometry Symposium, Eskisehir, 2005.
• [9] A. T. Yakut, Vertex a ngles of simplices in hyperbolic space, Ph. D. Thesis, Gazi University Institute of Science and Tecnology, 2004, p. 142.