Geodesic
Generalized Rabl Mappings and Apollonius-Type Problems
Journal for geometry and graphics, Tome 11 (2007) no. 1, pp. 27-38 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 51N05, 51N15
Mots-clés : cyclography, Rabl mapping, Maurin projection, Apollonius-type problems 
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     author = {S. Bacso and Z. Szilasi },
     title = {Generalized {Rabl} {Mappings} and {Apollonius-Type} {Problems}},
     journal = {Journal for geometry and graphics},
     pages = {27--38},
     year = {2007},
     volume = {11},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JGG_2007_11_1_JGG_2007_11_1_a2/}
}
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S. Bacso; Z. Szilasi . Generalized Rabl Mappings and Apollonius-Type Problems. Journal for geometry and graphics, Tome 11 (2007) no. 1, pp. 27-38. http://geodesic.mathdoc.fr/item/JGG_2007_11_1_JGG_2007_11_1_a2/