About: Inversion And Problem of Tangent Spheres

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Description	The locus of centers of circles tangent to two given circles in plane is known to be a pair of conic sections. The foci of these conic sections are the centers of the circles given. As a generalization we get the Apollonius task with one missing element. In a spatial generalization of the problem mentioned we are to find a locus of centers of spheres tangent to three given elements (spheres, planes, or incident points). This locus consists of the intersections of pairs of quadric surfaces of revolution, their foci being the centers of spheres given. These intersections are known to be composed of conics. Some special configurations of elements given result in a task clear and easy even for high-school students. Sphere inversion helps to find the loci of points of tangency of the spheres of a parametric system to be found with elements given, whilst the locus of centers must be constructed using some other methods. The locus of centers of circles tangent to two given circles in plane is known to be a pair of conic sections. The foci of these conic sections are the centers of the circles given. As a generalization we get the Apollonius task with one missing element. In a spatial generalization of the problem mentioned we are to find a locus of centers of spheres tangent to three given elements (spheres, planes, or incident points). This locus consists of the intersections of pairs of quadric surfaces of revolution, their foci being the centers of spheres given. These intersections are known to be composed of conics. Some special configurations of elements given result in a task clear and easy even for high-school students. Sphere inversion helps to find the loci of points of tangency of the spheres of a parametric system to be found with elements given, whilst the locus of centers must be constructed using some other methods. (en)
Title	Inversion And Problem of Tangent Spheres Inversion And Problem of Tangent Spheres (en)
skos:prefLabel	Inversion And Problem of Tangent Spheres Inversion And Problem of Tangent Spheres (en)
skos:notation	RIV/00216208:11320/10:10099253!RIV12-MSM-11320___
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Gergelitsová, Šárka
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	264783
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/10:10099253
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	spheres; tangent; problem; Inversioin (en)
http://linked.open.../riv/klicoveSlovo	Inversioin spheres tangent problem
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[CFFC626FD1B5]
http://linked.open...i/riv/nazevZdroje	South Bohemia Mathematical Letters
http://linked.open...in/vavai/riv/obor	AM
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	18
http://linked.open...iv/tvurceVysledku	Gergelitsová, Šárka
issn	1804-1450
number of pages	8 (xsd:int)
http://localhost/t...ganizacniJednotka	11320
is http://linked.open...avai/riv/vysledek of	Inversion And Problem of Tangent Spheres Inversion And Problem of Tangent Spheres

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