Regular heptagon's intersections circles

Abstract

The regular heptagon (i.e., the planar regular convex polygon with seven vertices) has not been studied extensively like its cousins the equilateral triangle, the square, the regular pentagon, and the regular hexagon. Perhaps the reason is because this is the regular polygon with the smallest number of vertices that cannot be constructed only with compass and straightedge. The few sporadic known results on regular heptagons were reviewed by Leon Bankoff and Jack Garfunkel 30 years ago in the reference [1].