Abstract
A k-fan is a point in the plane and k semilines emanating from it. Motivated by a neat question of Kaneko and Kano, we study equipartitions by k-fans of two or more probability measures in the plane, as well as partitions in other prescribed ratios. One of our results is: for any two measures there is a 4-fan such that one of its sectors contains two-fifths of both measures, and each of the the remaining three sectors contains one-fifth of both measures.
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The first author was supported by Hungarian National Foundation Grants T029255, T016391, and T020914 and the second author was supported by Charles University Grants 158/99 and 159/99.
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Bárány, I., Matousek, J. Simultaneous partitions of measures by K-fans. Discrete Comput Geom 25, 317–334 (2001). https://doi.org/10.1007/s00454-001-0003-5
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DOI: https://doi.org/10.1007/s00454-001-0003-5