Timeline for Golden ratio in contemporary mathematics
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 6, 2021 at 13:40 | comment | added | Robert Furber | People often summarize the result in the second paragraph as "$\phi$ is the most irrational real number". However, since Liouville showed that reals that are very well approximated by rationals are transcendental, I say it should really be "$\phi$ is the most rational irrational". | |
| Sep 6, 2021 at 10:49 | comment | added | Oscar Cunningham | @DenisNardin The point is that $\mathrm{gcd}$ is a limit, and if $F$ preserves limits the $AFT$ says it must have a left adjoint $z$ which will then preserve colimits. | |
| Sep 5, 2021 at 18:21 | comment | added | Denis Nardin | @OscarCunningham I am very curious about one would use the adjoint functor theorem to prove this. To me it seems just the (much more elementary) statement that the adjoint of a composite is the composite of the adjoints (in the other direction). | |
| Sep 5, 2021 at 2:43 | comment | added | Tony Huynh | Regarding your first point, there is a nice video on Numberphile that illustrates why the golden mean is so irrational: youtube.com/watch?v=sj8Sg8qnjOg | |
| Sep 4, 2021 at 22:53 | comment | added | Oscar Cunningham | Category theorists might be amused to note that $\mathrm{lcm}(z(n),z(m))=z(\mathrm{lcm}(n,m))$, because of the Adjoint Functor Theorem. | |
| Sep 4, 2021 at 16:04 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Sep 4, 2021 at 15:46 | comment | added | JoshuaZ | @ManfredWeis Fixed. Phrase should not have been repeated. Sorry about that. | |
| Sep 4, 2021 at 15:46 | history | edited | JoshuaZ | CC BY-SA 4.0 |
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| Sep 4, 2021 at 14:53 | history | edited | JoshuaZ | CC BY-SA 4.0 |
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| Sep 4, 2021 at 14:26 | history | answered | JoshuaZ | CC BY-SA 4.0 |