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Title of Journal: Results Math

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Abbravation: Results in Mathematics

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SP Birkhäuser Verlag Basel

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10.1016/0166-218x(86)90050-8

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1420-9012

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Defect and Area in Beltrami–Klein Model of Hyperbo

Authors: Mahfouz Rostamzadeh SayedGhahreman Taherian
Publish Date: 2011/08/12
Volume: 63, Issue: 1-2, Pages: 229-239
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Abstract

Ungar Beyond the Einstein addition law and its gyroscopic Thomas Precession The Theory of Gyrogroups and Gyrouector Spaces 2001 Comput Math Appl 49187–221 2005 Comput Math Appl 53 2007 introduced into hyperbolic geometry the concept of defect based on relativity addition of A Einstein Another approach is from Karzel Resultate Math 47305–326 2005 for the relation between the Kloop and the defect of an absolute plane in the sense Karzel in Einführung in die Geometrie 1973 Our main concern is to introduce a systematical exact definition for defect and area in the Beltrami–Klein model of hyperbolic geometry Combining the ideas and methods of Karzel and Ungar give an elegant concept for defect and area in this model In particular we give a rigorous and elementary proof for the defect formula stated Ungar in Comput Math Appl 53 2007 Furthermore we give a formulary for area of circle in the Beltrami–Klein model of hyperbolic geometry

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