Abstract
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 1/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 of the perimeter of S. We show that for any k, any convex set admits a perfect 1/k-partitioning. Perfect partitionings with additional constraints are also studied.
Cite
CITATION STYLE
Akiyama, J., Ivaneko, A., Ivano, M., Nakamura, G., Rivera-Campo, E., Tokunaga, S., & Urrutia, J. (2000). Radial perfect partitions of convex sets in the plane. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1763, pp. 1–13). Springer Verlag. https://doi.org/10.1007/978-3-540-46515-7_1
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