Irrational Distances from a Set of Points - 1990 Putnam Mathematics Competition Problem A4

Watch a detailed mathematical video solution that tackles Problem A4 from the 1990 William Lowell Putnam Mathematical Competition, focusing on proving the existence of irrational distances from a set of points. Learn step-by-step how to approach this challenging proof involving geometric concepts and number theory, with clear explanations of the mathematical reasoning and techniques used to demonstrate that for any three non-collinear points in a plane, there must exist a fourth point that has at least one irrational distance to the original three points.