Orthogonal equipartitions
نویسندگان
چکیده
منابع مشابه
Orthogonal equipartitions
Consider two absolutely continuous probability measures in the plane. A subdivision of the plane into k ≥ 2 regions is equitable if every region has weight 1/k in each measure. We show that, for any two probability measures in the plane and any integer k ≥ 2, there exists an equitable subdivision of the plane into k regions using at most k − 1 horizontal segments and at most k − 1 vertical segm...
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A well-known problem of B. Grünbaum (1960) asks whether for every continuous mass distribution (measure) dμ = f dm on Rn there exist n hyperplanes dividing Rn into 2n parts of equal measure. It is known that the answer is positive in dimension n = 3 (see H. Hadwiger (1966)) and negative for n ≥ 5 (see D. Avis (1984) and E. Ramos (1996)). We give a partial solution to Grünbaum’s problem in the c...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2009
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2008.09.004