Talk:Minkowski's question-mark function: Difference between revisions

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== About the derivatives ==

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::Here's another example: x = 3/5 = [0; 1, 1, 2] = → 0100111... ⇒ ?(3/5) = 0.100111...₂ = 0.101₂ = 5/8.

:[[User:Hugo Spinelli|Hugo Spinelli]] ([[User talk:Hugo Spinelli|talk]]) 10:10, 17 October 2023 (UTC)

::Then why does [3;2,1,2,1,4,5,...] generate 11.001001000011111... rather than 11.01001000011111...? — [[User:Sonata Green|Sonata Green]]^{([[User_talk:Sonata_Green|talk]])} 21:34, 17 October 2023 (UTC)

:::@[[User:Sonata Green|Sonata Green]] The example is wrong. It should be <math>[3; 3, 1, 2, 1, 4, 5, ...]</math>. See [https://www.wolframalpha.com/input?i=minkowski+question+mark+function+%28FromContinuedFraction%5B%7B3%2C+3%2C+1%2C+2%2C+1%2C+4%2C+5%7D%5D%29 WolframAlpha], for instance. One of the references given (Pytheas Fogg, 2002) appears to make the same mistake. The other one (Finch, 2003) is very explicit that the first sequence of zeros is <math>(a_1 - 1)</math>-long. —[[User:Hugo Spinelli|Hugo Spinelli]] <small>([[User talk:Hugo Spinelli|talk]])</small> 17:33, 20 October 2023 (UTC)

== Where do the matrices come from in the "Periodic orbits as continued fractions" section? ==

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. — [[User:Flipdisk|Flipdisk]] ([[User talk:Flipdisk|talk]]) 08:30, 27 March 2024 (UTC)

Actually, now that I read the earlier parts of the article more carefully, this section does seem to make sense in context, so I reverted my changes. But I still don't see where it appears in the source material. [[User:Flipdisk|Flipdisk]] ([[User talk:Flipdisk|talk]]) 08:32, 27 March 2024 (UTC)