A non-converging LaTeX document
Today, I wrote this LaTeΧ document. It only uses default LaTeΧ functionality, and uses no packages.
If you compile it (twice so that cross references are not ??s), you will get a four page document (pages numbered i to iv), that repeatedly says: "This document ends on page v."
If you then recompile it, you will get a five page document (pages numbered i to v), that repeatedly says: "This document ends on page iv."
Repeatedly compiling it will alternately give these two results, and so the process of compiling this LaTeX document does not converge.
A surprising fact about quadrilaterals
Comments in green were written by me. Comments in blue were not written by me.