A polygon, with all sides and all diagonals of rational length, will be called a rational polygon.

Prof. I. Schoenberg has set a problem whether rational polygons are everywhere dense in the class of all polygons, that is, given an arbitrary polygon whether there exists a rational polygon whose sides and diagonals are of length arbitrarily near to those of the given one. Once set, the problem becomes very interesting both for its simplicity and for its fundamental nature. For obvious reasons the likely answer to the problem is in the negative. In this note I consider two problems simply related to the above problem.