Hyperbolic trigonometry and its application in the Poincaré ball model of hyperbolic geometry
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چکیده
منابع مشابه
Hyperbolic Trigonometry and its Application in the Poincaré Ball Model of Hyperbolic Geometry
Hyperbolic trigonometry is developed and illustrated in this article along lines parallel to Euclidean trigonometry by exposing the hyperbolic trigonometric law of cosines and of sines in the Poincaré ball model of n-dimensional hyperbolic geometry, as well as their application. The Poincaré ball model of 3-dimensional hyperbolic geometry is becoming increasingly important in the construction o...
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In this paper, we prove that every metric line in the Poincare ball model of hyperbolic geometry is exactly a classical line of itself. We also proved nonexistence of periodic lines in the Poincare ball model of hyperbolic geometry.
متن کاملUniversal Hyperbolic Geometry I: Trigonometry
Hyperbolic geometry is developed in a purely algebraic fashion from first principles, without a prior development of differential geometry. The natural connection with the geometry of Lorentz, Einstein and Minkowski comes from a projective point of view, with trigonometric laws that extend to ‘points at infinity’, here called ‘null points’, and beyond to ‘ideal points’ associated to a hyperbolo...
متن کاملmetric and periodic lines in the poincare ball model of hyperbolic geometry
in this paper, we prove that every metric line in the poincare ball model of hyperbolic geometry is exactly a classical line of itself. we also proved nonexistence of periodic lines in the poincare ball model of hyperbolic geometry.
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This is a collection of some standard formulae from Euclidean, spherical and hyperbolic trigonometry, including some standard models of the hyperbolic plane. Proofs are not given.
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2001
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(01)85012-4