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.

引用

页码：3089 / 3104

页数：16

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