> "A polygon is said to be *rational* if all its sides and diagonals are rational, and I. J. Schoenberg has posed the difficult question, ‘Can any given polygon be approximated as closely as we like by a rational polygon?’" This is a quote from > D.D. Ang, D.E. Daykin, and T.K. Sheng. "On Schoenberg's rational polygon problem." *Journal of the Australian Mathematical Society* **9**.3-4 (1969): 337-344. ([journal link](http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=4881628&fileId=S1446788700007266).) I seek to understand the current status of this question. I know (from D.E.Daykin, "Rational polygons," ([journal link](http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=6708660))) that Mordell showed that the set of all rational quadrilaterals is dense in the set of all quadrilaterals. I am only finding ~40-yr-old papers, none of which are easily accessed online. <hr /> ![MathWorld][1] <br /> <sup>[MathWorld image of a rational quadrilateral](http://mathworld.wolfram.com/RationalQuadrilateral.html)</sup> <hr /> [1]: https://i.sstatic.net/NKhTE.gif