The Fermat-Torricelli problem on surfaces
In this note a simple proof of the famous Fermat-Torricelli problem is given. For the vertices of a given triangle, Fermat asks for a fourth point such that the sum of its Euclidean distances to the three given points is minimized. Many authors present geometric approaches to the Fermat-Torricelli p...
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| Veröffentlicht in: | Applied Mathematics-A Journal of Chinese Universities 2016-09, Vol.31 (3), p.362-366 |
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| container_title | Applied Mathematics-A Journal of Chinese Universities |
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| creator | Chen, Zhi-guo |
| description | In this note a simple proof of the famous Fermat-Torricelli problem is given. For the vertices of a given triangle, Fermat asks for a fourth point such that the sum of its Euclidean distances to the three given points is minimized. Many authors present geometric approaches to the Fermat-Torricelli problem. We solve the problem by analytic and geometrical method and extend it to the sphere, we also characterize the median point P on the general regular surface. |
| doi_str_mv | 10.1007/s11766-016-2715-6 |
| format | Article |
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| ispartof | Applied Mathematics-A Journal of Chinese Universities, 2016-09, Vol.31 (3), p.362-366 |
| issn | 1005-1031 1993-0445 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals; Alma/SFX Local Collection |
| subjects | Applications of Mathematics Euclidean geometry Mathematics Mathematics and Statistics 三角形 中值点 几何方法 正则曲面 简单证明 表面 解析法 距离和 |
| title | The Fermat-Torricelli problem on surfaces |
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