This work is about sets of points with integer pairwise distances (ideal sets) and Heron sets – ideal sets of points with integer area of its convex hull. It shows that any two-dimensional Heron set has an isometric copy in Z2. The main intermediaries of the proof are Gaussian integers, quadratic residues, and triangulations of planar sets. There are also the properties of the Heron sets and, in particular, construction of non-collinear Heron sets.


Andrei Shvedau

Nikolay Sheshko