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.
