Convex Regions and their 'Fairest' Equipartitioning Fans

A k-fan is a set of k half-lines (rays) all starting from the same point, called the origin of the fan. We discuss the partition of convex 2D regions into n (a positive integer) equal area convex pieces by fans with the following additional requirement: the perimeters of the resultant equal area pieces should be as close to one another as possible. We present some basic properties of such fans, which we call 'fairest equipartitioning fans', and raise further questions.