Timeline for Gauss-Kuzmin Theorem (continued fractions) - why is important?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 4, 2021 at 11:35 | answer | added | Bim Binsella | timeline score: 0 | |
| Jan 13, 2012 at 12:04 | answer | added | Alexey Ustinov | timeline score: 4 | |
| Nov 21, 2011 at 21:41 | comment | added | Yemon Choi | Important to whom? Interesting in what sense? | |
| Nov 21, 2011 at 18:11 | comment | added | David E Speyer | The standard application is to compute the expected running time of the Euclidean algorithm. See Knuth, Art of Computer Programming, Volume 2. | |
| Nov 21, 2011 at 17:02 | comment | added | KConrad | This kind of theorem is important for understanding the statistical properties of the entries in (regular) continued fractions, which are quite different from the properties of decimal digits. The point is that the Gauss map, which is essentially a shift map on entries in continued fraction expansions, does not have Lebesgue measure as a measure-preserving transformation, but the measure (1/log 2)dx/(1+x) is a m.p.t. for the Gauss map. If you care about understanding patterns in continued fraction expansions then this theorem is important to you; if you don't care then forget about it. | |
| Nov 21, 2011 at 16:50 | answer | added | Alan Haynes | timeline score: 9 | |
| Nov 21, 2011 at 13:33 | history | asked | Dan L | CC BY-SA 3.0 |