On the area of the polygon determined by the short diagonals of a convex polygon

被引：0

作者：

Cho, J. ^{[1
]}

Ismailescu, D. ^{[2
]}

Kim, Y. ^{[3
]}

Lee, A. W. ^{[4
]}

机构：

[1] Phillips Exeter Acad, Exeter, NH 03833 USA

[2] Hofstra Univ, Dept Math, Hempstead, NY 11550 USA

[3] Taft Sch, Watertown, CT 06795 USA

[4] Choate Rosemary Hall, Wallingford, CT 06492 USA

来源：

ACTA MATHEMATICA HUNGARICA | 2020年 / 160卷 / 01期

关键词：

convex polygon; global optimization; nonnegative polynomial;

D O I：

10.1007/s10474-019-00949-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be a convex pentagon in the plane and let K-1 be the pentagon bounded by the diagonals of K. It has been conjectured that the maximum of the ratio between the areas of K-1 and K is reached when K is an affine regular pentagon. In this paper we prove this conjecture. We also show that for polygons with at least six vertices the trivial answers are the best possible.

引用

页码：72 / 87

页数：16

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