A New Proof Of Menelaus's Theorem Of Hyperbolic Quadrilaterals In The Poincare Model Of Hyperbolic Geometry

Florentin Smarandache
Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA.
E-MAIL: marand@unm.edu

Catalin Barbu
Vasile Alecsandri College - Bacu, str. Vasile Alecsandri, nr. 37, cod 600011, Romania.
E-MAIL: kafka_mate@yahoo.com

Abstract: 

In this study, we present a proof of the Menelaus theorem for quadrilaterals in hyperbolic geometry, and a proof for the transversal theorem for triangles.

2000 Mathematics Subject Classification: 51K05, 51M10

Keywords: 
hyperbolic geometry, hyperbolic quadrilateral, menelaus theorem, the transversal theorem, gyrovector
Volume: 
1
Issue: 
1
Discipline: 
Mathematics
Subject: 
graph theory