A GENERALIZATION OF WINTERNITZ'S THEOREM AND ITS DISCRETE VERSION

被引：1
|
作者：
Shyntar, Alexandra [1 ]
Yaskin, Vladyslav [2 ]
机构：
[1] Univ Alberta, Edmonton, AB T6G 2G1, Canada
[2] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 07期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Convex body; centroid; lattice set; GRUNBAUMS INEQUALITY; SECTIONS;
D O I：
10.1090/proc/15465
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let K be a convex body in the plane. Cut K by a line passing through its centroid. It is a well-known result, due to Winternitz, that the areas of the resulting two pieces are at least 4/9 times the area of K and at most 5/9 times the area of K. We generalize this inequality to the case when the body is cut by a line not passing through the centroid. As an application we obtain a discrete version of Winternitz's theorem.
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页码：3089 / 3104
页数：16
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