Displaying similar documents to “Minkowski geometry in the mathematical modelling of natural phenomena”

The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry

Oğuzhan Demirel (2009)

Commentationes Mathematicae Universitatis Carolinae

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In [Comput. Math. Appl. 41 (2001), 135--147], A. A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry. This Ungar's work plays a major role in translating some theorems from Euclidean geometry to corresponding theorems in hyperbolic geometry. In this paper we explore the theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry.

The hyperbolic triangle centroid

Abraham A. Ungar (2004)

Commentationes Mathematicae Universitatis Carolinae

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Some gyrocommutative gyrogroups, also known as Bruck loops or K-loops, admit scalar multiplication, turning themselves into gyrovector spaces. The latter, in turn, form the setting for hyperbolic geometry just as vector spaces form the setting for Euclidean geometry. In classical mechanics the centroid of a triangle in velocity space is the velocity of the center of momentum of three massive objects with equal masses located at the triangle vertices. Employing gyrovector space techniques...

Some Connections between Minkowski and Hyperbolic Planes

Jarosław Kosiorek, Andrzej Matraś (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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The model of the Minkowski plane in the projective plane with a fixed conic sheds a new light on the connection between the Minkowski and hyperbolic geometries. The construction of the Minkowski plane in a hyperbolic plane over a Euclidean field is given. It is also proved that the geometry in an orthogonal bundle of circles is hyperbolic in a natural way.