Towards an Evolved Lower Bound for the Most Circular Partition of a Square

Claudia Obermaier and Markus Wagner


We examine the problem of partitioning a square into convex polygons 
which are as circular as possible. Circular means that the polygon’s 
aspect ratio is supposed to be near 1. The aspect ration of a convex 
polygon denotes the ratio of the diameters of the smallest 
circumscribing circle to the largest inscribed disk. This problem has 
been solved for the equilateral triangle as well as for regular k-gon 
with k > 4. In the case of a square, the optimal solution is still an 
open problem. We are planning to find a solution which is ”good enough” 
with the help of evolutionary algorithms.