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Budowa instalacji teletechnicznych w budynkach wielorodzinnych : podstawowe błędy

Kosiorek J.

Inżynier Budownictwa

2018

nr 4

72-75

The double tangency symmetries in Laguerre planes

Kosiorek J., Matraś A.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 2

123-137

The group generated by double tangency symmetries in a Laguerre plane is investigated. The geometric classification of involutions of a symmetric Laguerre plane is given. We introduce the notion of projective automorphisms using the double tangency and parallel perspectivities. We give the description of the groups of projective automorphisms and automorphisms generated by double tangency symmetries as subgroups of the group M(F, R) of automorphisms of a chain geometry Σ(Y, R) following Benz.

Some connections between Minkowski and hyperbolic planes

Kosiorek J., Matraś A.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 2

133-139

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.