The Weighted Fermat Triangle Problem

Yujin Shen and Juan Tolosa

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-16

Abstract:

We completely solve the generalized Fermat problem : given a triangle 𠑃 1 , 𠑃 2 , 𠑃 3 and three positive numbers 𠜆 1 , 𠜆 2 , 𠜆 3 , find a point 𠑃 for which the sum 𠜆 1 𠑃 1 𠑃 + 𠜆 2 𠑃 2 𠑃 + 𠜆 3 𠑃 3 𠑃 is minimal. We show that the point always exists and is unique, and indicate necessary and sufficient conditions for the point to lie inside the triangle. We provide geometric interpretations of the conditions and briefly indicate a connection with dynamical systems.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:283846

DOI: 10.1155/2008/283846

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