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: | 23 Jul 2018 14:41 |
URI: | http://dair.dias.ie/id/eprint/824 |
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