The rational distance problem asks to find a geometric configuration satisfying given properties such that all distances along specific edges are rational numbers. (This is equivalent to having all edge lengths be integers, since the denominators of rational numbers can be cleared by multiplication.) A cuboid whose edges and face diagonals are integers is called an Euler brick. It is not known if there exists a point in a unit square all of whose distances from the corners are rational, although J. H. Conway and M.

Euler brick | N-cluster | no-three-in-a-line-problem | rational distances