Talk:Minkowski's question-mark function

message: Is this function really absolutely continuous?
:The Denjoy's article says it's purely singular. (See also mathworld) --a_dergachev (talk) 03:50, 8 May 2009 (UTC)
thread_title:  question 

message: Is the interwiki link to Russian correct? --Meldor 00:10, 8 November 2007 (UTC)
thread_title:  iw 

message: Some time ago, I wrote a program to compute ?(x) and made a graph of it (much like the one in the article) before I even knew what the function was called.  I just wanted to see what this function looked like whose derivative was zero at all the rationals.  Since this function is continuous, defining it at the rationals is sufficient to define it for all the reals.  An algorithm to compute the function (or more precisely, to approximate it to any desired degree of accuracy) would be nice in the article, and would also serve as an alternative definition.  Something on the order of:
a := floor(x)
b := a + 1
d := 1
y := a
while (d > tolerance)
: c := mediant(a,b)
: d := d / 2
: if (x >= c) then
:: y := y + d
:: a := c
: else
:: b := c
output y
Of course a, b, and c have to be implemented as pairs of integers, and I like them to be proper fractions in practice. 198.145.196.71 (talk) 10:02, 2 March 2008 (UTC)
thread_title:  Algorithm to compute ?(x) 

message: Since this function is periodic, I'm very curious what the fourier series of it would look like. Anyone know? Timeroot (talk) 19:33, 19 January 2010 (UTC)
thread_title:  Fourier Transform 

message: I think the connection given with $SL(2,Z)$ in the opening paragraph of "Recursive definition for rational arguments" is somewhat badly written, for reasons as below.
If $p/q<r/s$ are two rational numbers the $rq-ps>0$ and so if the determinant is $\pm 1$, then in fact $rq-ps=1$.
If $\begin{pmatrix} r & p \\ s & q\end{pmatrix}$ is a matrix with positive integer entries such that $rq-ps=1$, then we can use the Euclid division algorithm to show that it can be uniquely written in the form $A^{a_1}B^{b_1}A^{a_2}B^{b_2}\dots A^{a_k}B^{b_k}$ where $a_i$ and $b_i$ are non-negative integers and all except possibly $a_1$ and $b_k$ are non-zero as well. This is what gives the connection of such matrices with continued fractions.  — Preceding unsigned comment added by 210.212.36.65 (talk) 09:00, 30 March 2012 (UTC)
thread_title:  Connection with SL(2,Z) 

message: In case anyone looks for a short Mathematica one-liner implementing ?(x) for numerical values (I guess that would mean: for rationals) :
qm[x_] := Abs@Fold[#2 - #1 &, Floor@x, 2*2^-Accumulate@Rest@ContinuedFraction@x]
Summsumm2 (talk) 16:08, 4 February 2013 (UTC)
thread_title:  Mathematica implementation/hack 

message: The  Conway box function  section says See also: Sawtooth wave, but neither mentions the other one. What is the connection? How reading about Sawtooth wave allows better or deeper understanding of a boxed question mark function? --CiaPan (talk) 10:22, 22 April 2015 (UTC)
replies: text: I also did not see the link. I suggest this link be deleted. Also, reading the book of Conway it looks like his function is actually Minkowski's question mark, and not its inverse bijection (figure 8, page 84 there). Saros (talk) 22:26, 3 December 2017 (UTC)
thread_title:  Conway box function and Sawtooth wave question 

message: I could not find a single LaTeX command for a box to surround a given expression, however I discovered a quite simple way to make a box with an array:
:: \begin{array}{|c|} \hline EXPR \\ \hline \end{array}
Result:
:: \begin{array}{|c|} \hline EXPR \\ \hline \end{array}
The {|c|} part declares a single column in the array with centered contents and vertical lines on both sides. Commands \hline add horizontal lines above and below the (single) row. Command \\ terminates the row so that the bottom line can be drawn.  Happy editing, everybody! :) CiaPan (talk) 10:50, 22 April 2015 (UTC)
replies: text: Minor language mistakes fixed, thanks to the notice by  at my talk page. --CiaPan (talk) 15:23, 19 July 2019 (UTC)
thread_title:  A box 

message: There were two solutions posted on Salem's problem during Jan 2015.  One was a special case of an earlier result by Jordan and Sahlsten (arXiv:1312.3619), that was submitted to arXiv on December 12, 2013 and accepted to the journal Mathematische Annalen on February, 2015, according to the arXiv version from February 2015. The earlier version of the paper by Jordan and Sahlsten did not mention Salem's problem and the application was pointed out by Persson (arXiv:1501.00876) in a note from January 5, 2015. Yakubovitch's answer (arXiv:1501.00141) was submitted to arXiv on December 31, 2014, and the corrected revision of that article was posted to arXiv on April 15, 2015.  — Preceding unsigned comment added by 79.176.37.159 (talk) 06:45, 13 May 2015 (UTC)
thread_title:  Salem's problem 

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thread_title:  External links modified 

message: I have a copy On Numbers and Games, and the box function is clearly the Minkowski question mark function itself, not its inverse. I suggest removing the whole "Inverse" section from the article. Reyk YO! 07:05, 11 September 2020 (UTC)
thread_title:  Conway box function 

message: I tried implementing this myself and ran into problems with the matrices given.  Deriving them on my own, I got different matrices, and I updated the article with the ones I derived.  I can't actually find where they appear in the cited reference, though. — Flipdisk (talk) 08:30, 27 March 2024 (UTC)
thread_title:  Where do the matrices come from in the "Periodic orbits as continued fractions" section?