Finding the Fermat point via analysis

2014/04/23 by Ye, Luqing
#49K02(Primary) #53B02(Secondary) #FOS: Mathematics #History and Overview (math.HO)

paper · doi:10.48550/arxiv.1404.5898

Abstract

Let P₁,P₂,P₃ be three given points in R², and P be an arbitrary point in R². The classical Fermat's problem to Torricelli asks for the location of the point P such that |PP₁|+|PP₂|+|PP₃| is a minimum. There exist several elegant geometrical solutions in the literature.In this note, we consider finding the Fermat point by using methods in advanced calculus. The main tools we use are the extreme value theorem,Fermat's theorem, and the intermediate value theorem.

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