The Torricelli-Fermat Point Generalised

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
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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