On the equipartition of plane convex bodies and convex polygons
On the equipartition of plane convex bodies and convex polygons
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论平面凸体与凸多边形的均分
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
F. Hurtado
中科院分区：
文献类型：
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作者：
R. Guardia;F. Hurtado
本文考虑用弦将平面紧致凸体划分成等面积部分，即等分问题。我们证明了两个基本结果，但有一些特殊的例外：(A)当弦是两两不相交的时，划分的对偶树一定是一条路，(B)一个凸n边形不允许有一个公共内点的n个以上弦产生的等分划.
Abstract.In this paper we consider the problem of partitioning a plane compact convex body into equal-area parts, i.e., an equipartition, by means of chords. We prove two basic results that hold with some specific exceptions: (a) When chords are pairwise non-crossing, the dual tree of the partition has to be a path, (b) A convex n-gon admits no equipartition produced by more than n chords having a common interior point.