Iterative method to compute the Fermat points and Fermat distances of multiquarks

The multiquark confining potential is proportional to the total distance of the fundamental strings linking the quarks and antiquarks. We address the computation of the total string distance and of the Fermat points where the different strings meet. For a meson the distance is trivially the quark–antiquark distance. For a baryon the problem was solved geometrically from the onset by Fermat and by Torricelli, it can be determined just with a rule and a compass, and we briefly review it. However we also show that for tetraquarks, pentaquarks, hexaquarks, etc., the geometrical solution is much more complicated. Here we provide an iterative method, converging fast to the correct Fermat points and the total distances, relevant for the multiquark potentials.