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Some Connections between Minkowski and Hyperbolic Planes

Jarosław Kosiorek, Andrzej Matraś (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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.

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