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 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 \(\frac{1}{k}\) 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.
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References
Akiyama, J., Nakamura, G., Rivera-Campo, E., Urrutia, J.: Perfect division of a cake. In: Proceedings of the Tenth Canadian Conference on Computational Geometry, pp. 114–115
Goodman, J., O’Rourke, J.: Handbook of Discrete and Computational Geometry. CRC Press, Boca Raton (1997)
Kaneko, A., Kano, M.: Perfect n-partitions of convex sets in the plane (submitted)
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© 2000 Springer-Verlag Berlin Heidelberg
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Akiyama, J. et al. (2000). Radial Perfect Partitions of Convex Sets in the Plane. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 1998. Lecture Notes in Computer Science, vol 1763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46515-7_1
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DOI: https://doi.org/10.1007/978-3-540-46515-7_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67181-7
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