Journal for Geometry and Graphics 11 (2007), No. 1, 027--038
Copyright Heldermann Verlag 2007
Generalized Rabl Mappings and Apollonius-Type Problems
Sandor Bacso
Faculty of Informatics, Debrecen University, Debrecen, Hungary
bacsos@inf.unideb.hu
Zoltan Szilasi
Faculty of Informatics, Debrecen University, Debrecen, Hungary
szilasi@math.klte.hu
We introduce the n-dimensional generalization of the point to circle mapping defined and studied by K. Rabl and show that our generalization can be used effectively to solve three-dimensional Apollonius-type problems. To carry out the constructions in practice, we use on the one hand a simple computer algorithm via Maple, on the other hand some tools of projective and descriptive geometry, including Maurin's projection of the four-space. In the two-dimensional case we present a simple direct method of construction based on elementary projective geometry.
Keywords: cyclography, Rabl mapping, Maurin projection, Apollonius-type problems.
MSC: 51N05; 51N15
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