Why Is Pi Less Than Twice Phi?

被引：3

作者：

Morales, Alejandro H. ^{[1
]}

Pak, Igor ^{[2
]}

Panova, Greta ^{[3
,4
]}

机构：

[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 02001 USA

[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[3] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

[4] Inst Adv Study, Olden Lane, Princeton, NJ 08540 USA

来源：

AMERICAN MATHEMATICAL MONTHLY | 2018年 / 125卷 / 08期

关键词：

NUMBERS;

D O I：

10.1080/00029890.2018.1496757

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a proof of the inequality in the title in terms of Fibonacci numbers and Euler numbers via a combinatorial argument and asymptotics for these numbers. The result is motivated by Sidorenko's theorem on the number of linear extensions of a partially ordered set and its complement. We conclude with some open problems. [GRAPHICS]

引用

页码：715 / 723

页数：9

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