We explore optimal circular nonconvex partitions of regular k-gons. The
circularity of a polygon is measured by its aspect ratio: the ratio of the
radii of the smallest circumscribing circle to the largest inscribed disk. An
optimal circular partition minimizes the maximum ratio over all pieces in the
partition. We show that the equilateral triangle has an optimal 4-piece
nonconvex partition, the square an optimal 13-piece nonconvex partition, and
the pentagon has an optimal nonconvex partition with more than 20 thousand
pieces. For hexagons and beyond, we provide a general algorithm that approaches
optimality, but does not achieve it.Comment: 13 pages, 11 figure
