Problem of Rational Distances from a Point to the Vertices of a Unit Square on a Plane and Its Application to Control Theory

Abstract

Among the unsolved problems of mathematics there are those whose hidden meaning turns out to be many times more important and instructive than solutions of these problems themselves. Most likely, this is exactly the case with the problem of rational distances from a point to the vertices of a unit square on a plane, if you approach it not quite from the frontal side.