Abstract
We show that, given two probability measures in the plane, there exists a 4-fan that simultaneously equipartitions them. In other words, there is a point and four half-lines emanating from it such that each of the four sectors have measure \frac 1 4 in both measures.
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Received June 1, 2001, and in revised form October 4, 2001. Online publication February 28, 2002.
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Bárány, I., Matoušek, J. Equipartition of Two Measures by a 4-Fan. Discrete Comput Geom 27, 293–301 (2002). https://doi.org/10.1007/s00454-001-0071-6
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DOI: https://doi.org/10.1007/s00454-001-0071-6