Resumen de Mínimo de la suma de distancias a cuatro puntos del plano euclídeo

Francisco J. Baena

• This article is intended to be complementary of the one published in number 97 of this same Newsletter under the title "On the Theorem of Viviani, the Principle of Reflection and other milestones along the way to Fermat's point" in which there were two proofs of the existence and uniqueness of Fermat's point of a triangle, that is, the only point of the Euclidean plane that minimizes the sum of the distances to the three vertices of a triangle. We deal here with the problem of determining the minimum of the sum of the distances starting from a point of the Euclidean plane to four given points of the above mentioned plane which depends on the relative position of such four points.