Regular polygon is a Euclidean Ramsey set (source code)

= Regular polygon is a Euclidean Ramsey set

Every <regular polygon> is a <Euclidean Ramsey set>. A <Hales-Jewett theorem> combinatorial line in a Cartesian power of its vertex set is a scaled regular polygon; including finitely many reciprocal square-root scalings makes one such line isometric to the original polygon.