Why Is Pi Less Than Twice Phi?

Why Is Pi Less Than Twice Phi?

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 conc...

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Veröffentlicht in:The American mathematical monthly 2018-09, Vol.125 (8), p.715-723
Hauptverfasser: Morales, Alejandro H., Pak, Igor, Panova, Greta
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic methods
Combinatorial analysis
Combinatorics
Fibonacci numbers
Linear equations
Numbers
Primary 05A20
Proof theory
Secondary 05A05
Set theory
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Beschreibung
Zusammenfassung: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.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2018.1496757