The Plasticity of Some Fittable Surfaces on a Given Quadruple of Points in the Three-Dimensional Euclidean Space
We construct a two-dimensional sphere in the three-dimensional Euclidean space which intersects a circular cylinder in three given points and the corresponding weighted Fermat-Torricelli point for a geodesic triangle such that these three points and the corresponding weighted Fermat- Torricelli poin...
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| Datum: | 2014 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2014
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| Schriftenreihe: | Журнал математической физики, анализа, геометрии |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/106810 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Plasticity of Some Fittable Surfaces on a Given Quadruple of Points in the Three-Dimensional Euclidean Space / A.N. Zachos // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 4. — С. 485-495. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We construct a two-dimensional sphere in the three-dimensional Euclidean space which intersects a circular cylinder in three given points and the corresponding weighted Fermat-Torricelli point for a geodesic triangle such that these three points and the corresponding weighted Fermat- Torricelli point remain the same on the sphere for a different triad of weights which correspond to the vertices on the surface of the sphere. We derive a circular cone which passes from the same points that a circular cylinder passes. By applying the inverse weighted Fermat-Torricelli problem for different weights, we obtain the plasticity equations which provide the new weights of the weighted Fermat-Torricelli point for fixed geodesic triangles on the surface of a fittable sphere and a fittable circular cone with respect to the given quadruple of points on a circular cylinder, which inherits the curvature of the corresponding fittable surfaces. |
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