Synge, J. L.
(1987)
*The Torricelli-Fermat Point Generalised.*
(Preprint)

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## Abstract

The Torricelli-Fermat point (TF-point) of a triangle is that point which minimises the sum of its distances from the vertices. I generalise this definition, replacing the triangle by a set of M+1 points in E^N. Using the theory of convex functions, I show that the TF-point is unique and find explicit conditions to to determine whether it coincides with any of the given points. If it does not, it may be found by solving a set of ordinary differential equations.

Item Type: | Article |
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Divisions: | School of Theoretical Physics > Preprints |

Date Deposited: | 20 Jun 2018 11:13 |

Last Modified: | 14 Dec 2022 20:38 |

URI: | https://dair.dias.ie/id/eprint/824 |

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