We introduce the question: Given a positive integer N, can any 2D convex polygonal region be partitioned into N convex pieces such that all pieces have the same area and the same perimeter? The answer to this question is easily ‘yes’ for N = 2. We give an elementary proof that the answer is ‘yes’ for N = 4 and generalize it to higher powers of 2.
R. Nandakumar and N Rao, R., “Fair partitions of polygons: An elementary introduction”, Proceedings-Mathematical Sciences, vol. 122, pp. 459–467, 2012.