Fermat’s Problem in Banach-Minkowski Spaces

Abstract

The following problem was posed by Fermat early in the 17th century: Given three points in the plane, find a fourth point such that the sum of its distances to the three given points is a minimum. Torricelli solved this problem in 1646. He asserted that the circles that circumscribe the equilateral triangles constructed on the side of and outside of the given triangle intersect in the desired point, called the Torricelli point.