  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.
