Equipartitioning by a convex 3-fan
نویسندگان
چکیده
We show that for a given planar convex set K of positive area there exist three pairwise internally disjoint convex sets whose union is K such that they have equal area and equal perimeter. © 2009 Elsevier Inc. All rights reserved.
منابع مشابه
Functions, Measures, and Equipartitioning Convex k-Fans
A k-fan in the plane is a point x ∈R2 and k halflines starting from x. There are k angular sectors σ1, . . . , σk between consecutive halflines. The k-fan is convex if every sector is convex. A (nice) probability measure μ is equipartitioned by the k-fan if μ(σi) = 1/k for every sector. One of our results: Given a nice probability measure μ and a continuous function f defined on sectors, there ...
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