Timeline for Why are smooth numbers called "smooth"?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 26, 2014 at 6:40 | answer | added | Joe Bebel | timeline score: 4 | |
| May 8, 2014 at 1:22 | vote | accept | Joseph O'Rourke | ||
| May 7, 2014 at 20:08 | answer | added | Timothy Chow | timeline score: 24 | |
| May 7, 2014 at 1:47 | comment | added | Will Jagy | @KConrad, great, Of Mice and Men. These days there are plenty of books for the math-phobic, but no book called The Fear of All Sums....I asked. However, there are blog posts and newspaper articles with that name. | |
| May 7, 2014 at 1:33 | comment | added | KConrad | @WillJagy: an MO page discussing the etymology of mice is mathoverflow.net/questions/879/… | |
| May 7, 2014 at 1:20 | comment | added | Lucia | I'm not sure about whether this is the reason for the name, but one important property of a $y$-smooth number $n$ is that it can be factored as $n=ab$ where $a$ and $b$ are of any given size. Precisely, we can find such a factorization with $A\le a\le Ay$ for any $A\le n$. Such flexible decompositions are often very useful, and one could say that the divisors of $n$ are in this sense smoothly distributed rather than clustering around a few possible sizes. Anyway, this is why I think of them as being smooth. | |
| May 7, 2014 at 0:49 | answer | added | Terry Tao | timeline score: 19 | |
| May 7, 2014 at 0:41 | comment | added | Yuri Bakhtin | There is a vague analogy with Fourier series. The more weight is carried by high frequencies in a Fourier series, the less smooth the function is. From this point of view, the most smooth functions are composed of finitely many harmonics. | |
| May 7, 2014 at 0:05 | comment | added | Will Jagy | @TobiasFritz, thank you. That makes sense, I had an office-mate in graduate school who did set theory. | |
| May 7, 2014 at 0:02 | comment | added | Tobias Fritz | @WillJagy: en.wikipedia.org/wiki/Mouse_%28set_theory%29 | |
| May 6, 2014 at 23:56 | comment | added | Joseph O'Rourke |
@WillJagy: There is a mice() function in R: Multivariate Imputation by Chained Equations. :-)
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| May 6, 2014 at 23:52 | comment | added | Will Jagy | I think it's time to admit all the good names are taken. I'm pretty sure something important was called "mice" some decades ago. Can't seem to find it, but the principle is correct. | |
| May 6, 2014 at 23:21 | comment | added | Gerry Myerson | I think it's a variation on "round" numbers, which have a lot of twos and fives in their factorization. | |
| May 6, 2014 at 23:21 | comment | added | The Masked Avenger | Probably because naive trial factorization goes so smoothly for such numbers. | |
| May 6, 2014 at 23:18 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |