Radial Perfect Partitions of Convex Sets in the Plane

In this paper we study the following problem: how to divide a cake among the children attending a birthday party such that all the children get the same amount of cake and the same amount of icing. This leads us to the study of the following. A perfect k-partitioning of a convex set S is a partitioning of S into k convex pieces such that each piece has the same area and 1 k of the perimeter of S. We show that for any k, any convex set admits a perfect k-partitioning. Perfect partitionings with additional constraints are also studied.

• Type: Conference
• Year: 1998
• Where: JCDCG
• Authors: Jin Akiyama, Atsushi Kaneko, Mikio Kano, Gisaku Nakamura, Eduardo Rivera-Campo, Shin-ichi Tokunaga, Jorge Urrutia
• Keywords: Birthday Party, Convex Set, Discrete Geometry, JCDCG 1998, Perfect K-partitioning