A Convex Polygon of Twist Influenced by Nandakumar and Ramana Rao

Abstract

In this study, the researchers address the conundrum: To divide a 2-dimensional convex polygonal region Q into a specified natural number n of convex pieces, all of which have equal areas although perimeters could be different, such that the total length of cuts used is maximized. With the aid of AutoCAD software, the results show that a convex polygon Q divided into n=2 equal area partitions must have its cut line λ¬ or its area bisector originate in some vertex "v" _"α" of Q with the least measure. We claim that this cut line λ is the maximum possible cut length that divides polygon Q into n=2 equal area partitions. The resulting proof of this conjecture can be used recursively for a convex polygon Q divided into n=2^k equal area partitions, where k∈N