Timeline for Numbers characterized by extremal properties
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 12, 2013 at 4:11 | review | Suggested edits | |||
| Dec 12, 2013 at 9:36 | |||||
| Jul 3, 2010 at 13:55 | vote | accept | Mariano Suárez-Álvarez | ||
| Apr 26, 2010 at 14:27 | comment | added | Allen Knutson | Incidentally, in Manfred Schroeder's "Number theory in science and communication" he explains why audio speakers should have dimensions 1 by phi by phi^2, in that they should be as far as possible from resonances. | |
| Apr 26, 2010 at 9:46 | comment | added | Kevin Buzzard | Qiaochu is right. The next number after sqrt(5) is sqrt(8) and the one after is sqrt(221)/5, and in general you get an infinite sequence, tending to 3. This sequence (or rather its reciprocal) goes by the rather unfortunate name of "the Markoff chain" (see Cassels Ann Math 1949); see for example section 6.3 of Baker's "Concise introduction to the theory of numbers". | |
| Apr 26, 2010 at 4:34 | comment | added | Qiaochu Yuan | Oh. Well, in that case, doesn't the theorem stated count as a quantification of the statement about the golden ratio? (I think there is a strengthening of the statement as follows: if x is an irrational number which is not one of the numbers (a + b phi)/(c + d phi), then the constant in the theorem can be improved from sqrt{5} to some other constant. I remember seeing this on another Wikipedia page, but can't find it.) | |
| Apr 26, 2010 at 2:57 | answer | added | Will Jagy | timeline score: 13 | |
| Apr 26, 2010 at 2:42 | comment | added | Mariano Suárez-Álvarez | Qiaochu, that's precisely the link I gave! :) | |
| Apr 26, 2010 at 2:32 | comment | added | Qiaochu Yuan | en.wikipedia.org/wiki/… | |
| Apr 26, 2010 at 2:30 | history | edited | Mariano Suárez-Álvarez | CC BY-SA 2.5 |
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| Apr 26, 2010 at 2:24 | history | asked | Mariano Suárez-Álvarez | CC BY-SA 2.5 |