Inversion And Problem of Tangent Spheres

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F10%3A10099253" target="_blank" >RIV/00216208:11320/10:10099253 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Inversion And Problem of Tangent Spheres
Original language 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
AM - Pedagogy and education
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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