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: min {BX+CX−AX:X∈ R 2 } . The correct solution for any triangle is provided here.