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Gyrotriangle Gyrocenters

  • A. A. Ungar
Part of the Fundamental Theories of Physics book series (FTPH, volume 166)

Abstract

Interest in triangle centers has long history, the classical ones being the triangle centroid, orthocenter, incenter and circumcenter. A list of more than 3000 triangle centers is found in Kimberling (Clark Kimberling’s Encyclopedia of Triangle Centers—ETC, 2010). Hyperbolic triangles and their centers are of interest as well (Bottema in Can. J. Math. 10:502–506, 1958; Vermeer in Topol. Appl. 152(3):226–242, 2005; Demirel and Soyturk in Novi Sad J. Math. 38(2):33–39, 2008; Sonmez in Algebras Groups Geom. 26(1):75–79, 2009). The special relativistic approach of this book enables hyperbolic triangle centers to be determined along with relationships between them.

The hyperbolic triangle circumcenter, incenter and orthocenter are called, in gyrolanguage, the gyrotriangle circumgyrocenter, ingyrocenter and orthogyrocenter, respectively. These gyrocenters are determined in this chapter in terms of their gyrobarycentric coordinate representations with respect to the vertices of their reference gyrotriangles.

Keywords

Scalar Equation Euclidean Geometry Tangent Point Hyperbolic Geometry Line Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Dept. Mathematics 2750North Dakota State UniversityFargoUSA

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