On a “Complementary Problem” of Courant and Robbins

Abstract

For a given triangle ABC with ∠A>120°, the Simpson variant of Torricelli’s geometrical construction for solving a problem, allegedly first formulated by Fermat in the early 1600s, will identify a point which incorrectly was claimed by Courant and Robbins (Courant, R., Robbins, H., 1941. What is Mathematics? Oxford University Press, Oxford.) to solve the so-called Complementary problem: $\text{min}\text{{BX+CX−AX:X∈}\text{R}{}^2\text{}}$. The correct solution for any triangle is provided here.