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 |
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| container_title | The American mathematical monthly |
| container_volume | 125 |
| creator | Morales, Alejandro H. Pak, Igor Panova, Greta |
| description | 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. |
| doi_str_mv | 10.1080/00029890.2018.1496757 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 0002-9890 |
| ispartof | The American mathematical monthly, 2018-09, Vol.125 (8), p.715-723 |
| issn | 0002-9890 1930-0972 |
| language | eng |
| recordid | cdi_crossref_primary_10_1080_00029890_2018_1496757 |
| source | JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals; Alma/SFX Local Collection |
| subjects | Asymptotic methods Combinatorial analysis Combinatorics Fibonacci numbers Linear equations Numbers Primary 05A20 Proof theory Secondary 05A05 Set theory |
| title | Why Is Pi Less Than Twice Phi? |
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