Abstract
We investigate equitable 3-cuttings of two mass distributions in the plane (partitions of the plane into 3 sectors with a common apex such that each sector contains 1/3 of each mass). We prove the existence of a continuum of equitable 3-cuttings that satisfy some closure property. This permits us to generalize earlier results on both convex and non-convex equitable 3-cuttings with additional constraints.
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Bespamyatnikh, S., Kirkpatrick, D. (2003). Constrained Equitable 3-Cuttings. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_8
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DOI: https://doi.org/10.1007/978-3-540-44400-8_8
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