Is there a point at rational distances from the vertices of a unit square? This unsolved question is known as the rational distance problem [1, 2].
This Demonstration gives 2877 canonical triples, which are points at rational distances from the vertices , , and . These triples were collected by analyzing primitive Heronian triangles  (triangles with rational sides and areas). If is a triple, so are and the inverse , so each triple gives three others.
A triple has rational coordinates. Consider the squares of the distances: , , and All of these need to be rational, so the differences and are also rational.