The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was merge to List of mathematical constants. There is consensus that this should not exist as a standalone but that some of the content would fit at the aforementioned link Star Mississippi 01:17, 8 March 2022 (UTC)[reply]

Mathematical constants by continued fraction representation[edit]

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Unreferenced, indiscriminate table, with context supported only by links obscured with LaTeX math markup, e.g. ${\frac {1}{M(1,{\sqrt {2)))))$ (Gauss's constant). A user removed all the continued fractions at List of mathematical constants in 2019 because it was causing excessive clutter. Can't find similar tables online, but not 100% confident that it fails WP:LISTN. –LaundryPizza03 (d c̄) 23:52, 20 February 2022 (UTC)[reply]

Note: This discussion has been included in the list of Mathematics-related deletion discussions. –LaundryPizza03 (d c̄) 23:52, 20 February 2022 (UTC)[reply]
Note: This discussion has been included in the list of Lists-related deletion discussions. –LaundryPizza03 (d c̄) 23:52, 20 February 2022 (UTC)[reply]
Keep Valid list article. As it says at the bottom Although some of the symbols in the leftmost column are displayed in black due to math markup peculiarities, all are clickable and link to the respective constant's page. They do link to other pages. This article was created in 2002. This seems quite encyclopedic. Dream Focus 00:03, 21 February 2022 (UTC)[reply]
Comment No one in nearly 20 years has bothered to put the names of these constants into the page? That's the most impressive example of insular mathematics fandom that I have seen all weekend. I'm concerned that there are no discernible criteria for inclusion or exclusion here. I wouldn't object in principle to a list of constants whose continued fraction representations have themselves been noteworthy. For example, there is no algebraic or analytic expression for the Feigenbaum constants, so their continued fractions will just be translations of the known decimal approximations. I'd like to see this list saved (I'm always happier when a page can be Heymanned instead of deleted), but it's definitely got problems, and I can see the case for letting it go. XOR'easter (talk) 02:19, 21 February 2022 (UTC)[reply]
- Why would the names be better than just the Symbols that represent them? If you don't recognize one are you going to recognize the other? Dream Focus 03:27, 21 February 2022 (UTC)[reply]
  - Yes. Very much so. The letter $C$ $C$ by itself has no unique meaning in mathematics, for example. The table itself demonstrates the necessity of names by giving two different meanings of ${\displaystyle C_{2))$ ${\displaystyle C_{2))$ (the Hardy–Littlewood twin prime constant and the base-2 Champernowne constant). It gives meanings for ${\displaystyle B_{2))$ ${\displaystyle B_{2))$ and ${\displaystyle B_{4))$ ${\displaystyle B_{4))$ based on Brun's theorem, but those could also be the second and fourth Bernoulli numbers. XOR'easter (talk) 03:57, 21 February 2022 (UTC)[reply]
    - Alright. I added a names column and half of the names done thus far. Dream Focus 04:24, 21 February 2022 (UTC)[reply]
Delete I haven't been able to find a tabulation of constants sorted by continued-fraction representation in the literature. If one exists, it's pretty darn obscure, and thus not great evidence that we need to devote a whole page to the topic. It just doesn't seem to be anybody's priority, or the way that anybody has thought about the topic (as far as thoughts that survive peer review are concerned). The list assembles things that the academic literature has not. It doesn't advance a new conclusion; it's just an indiscriminate collection. It includes the typical cruft that accumulates in articles on the more recreational side of mathematics, like a constant that has had maybe three papers ever written about it, or an expression plucked out of a MathWorld page on things that can be defined using continued fractions and then granted the name "Continued Fraction Constant". (MathWorld has gathered a lot of fluff over the years.) And there isn't an example to follow for how to build a reasonable list of this kind. I wrote above that I wouldn't object in principle to a list of constants whose continued fraction representations have themselves been noteworthy. Here we have the gulf between principle and practice. Having read more and thought more, I don't think this provides value beyond the examples already given in the main continued fraction article. XOR'easter (talk) 04:49, 21 February 2022 (UTC)[reply]
- Aside from chapter 10 of Annie Cuyt's book, do you mean? ☺ Uncle G (talk) 07:10, 21 February 2022 (UTC)[reply]
  - Handbook of Continued Fractions for Special Functions? It's not really a sorted tabulation, though, is it? It's much more like how the continued fraction article presents the examples included there. That page already has $e$ , $\pi$ , the square and cube roots of 2, the golden ratio, the Euler–Mascheroni constant, and Khinchin's constant. Trim this page down to what that chapter can justify, and it's redundant with the main article. I tend to think that if we can't explain in prose the significance of expanding a particular constant as a continued fraction, we shouldn't bother with it. We're trying to build an encyclopedia, not a replacement for the CRC handbook of old. XOR'easter (talk) 08:54, 21 February 2022 (UTC)[reply]
Delete Topic lacks sources supporting that a fractional representation of these numbers is notable. MrsSnoozyTurtle 09:30, 22 February 2022 (UTC)[reply]
Merge with List of mathematical constants Atavoidturk (talk) 17:20, 23 February 2022 (UTC)[reply]
Merge with List of mathematical constants as the continued fractions would work nicely in the tables on that page. Gusfriend (talk) 11:07, 25 February 2022 (UTC)[reply]
Leaning towards Merge with List of mathematical constants. It's not end-of-the-world bad that one or two entries are unsourced - the decimal expansions of these numbers are available in many places around the Internet, so it might be okay to permit a continued fraction expansion sans source per WP:CALC (although this is kinda pushing it - the simplest way I can think of to calculate a continued fraction expansion would be to write a ~10-line Python program, which is far beyond the current policy of "basic arithmetic"), although citing nothing would be borderline WP:SYNTH/WP:OR.
More importantly: Are there any reliable sources that discuss - or even mention - the continued fraction expansions of these numbers? (I looked up both the Cuyt et al. and Borwein et al. on Google Books and found nothing, though I’d like someone who actually has a physical copy of at least one of these two books to verify, and though I was also able to find a few of these sequences on OEIS.) Just because every real number has a continued fraction expansion doesn't mean that every interesting real number has an interesting continued fraction expansion - and I, for one, find these continued fraction expansions to be positively boring. As an inclusionist(-ish), I tend to be reluctant to get an article deleted, but also merging this with Continued fraction might feel a bit WP:UNDUE. Duckmather (talk) 22:12, 27 February 2022 (UTC)[reply]
- Cuyt chapter 10 not only has the regular continued fraction representations, but even has citations of sources for them in its turn. Chapter 10 has, in order, π, Euler's number, integer powers and roots of π and e, ln(2), sqrt(2), the cube root of 2, Euler's γ, the Golden Ratio, the rabbit constant, Apéry's constant, Catalan's constant, Gompertz' constant, and Khinchin's constant. The regular continued fraction for Apéry's constant is sourced to "[AZ97]", for example, which is arXiv:math/9804121v1. Uncle G (talk) 13:44, 28 February 2022 (UTC)[reply]

Relisted to generate a more thorough discussion and clearer consensus.
Relisting comment: Consensus is against keeping, but are the "delete" people OK with the proposed merger?
Please add new comments below this notice. Thanks, Sandstein 13:15, 28 February 2022 (UTC)[reply]

@LaundryPizza03, Dream Focus, XOR'easter, and MrsSnoozyTurtle: your view about the merger proposed above? Sandstein 13:17, 28 February 2022 (UTC)[reply]
A merge would have to be selective. There are 35 entries in this table that aren't entirely trivial; the only source offered that might give a criterion for inclusion has about half that many (and that list only partially overlaps with this one). XOR'easter (talk) 19:02, 28 February 2022 (UTC)[reply]
Hello Sandstein. Thank you for proposing an WP:ATD. I agree with the approach of XOR'easter for the merger. MrsSnoozyTurtle 21:36, 28 February 2022 (UTC)[reply]
- This sounds reasonable, since many sources about specific constants list their continued fractions, including sources about specific continued fractions. Continued fraction expansions probably pass WP:ROUTINE as well, since they are straghtforward to calculate if enough decimal places are known. –LaundryPizza03 (d c̄) 21:42, 28 February 2022 (UTC)[reply]
- "Only source offered" is a bit weak. I think that no-one has really looked to see what sources there are, to see what criteria for inclusion are supported. After all, it's not hard to turn up Stephen R. Finch's Mathematical Constants (CUP 2003) which has a chapter on well-known constants with their continued fractions. But I'm the first to even mention it. Haakon Waadeland has another book Continued Fractions (Springer 2008) with "mathematical constants" being the first section of Appendix A. If conclusions were based upon actual research, they would be a lot safer. We shouldn't be going by what sources are offered but by what sources we can find. After all, the first source offered for Kinnoull was a bowling club WWW site (c.f. Special:Permalink/207128450). Uncle G (talk) 21:44, 28 February 2022 (UTC)[reply]
  - I did look for sources and found very little. And what I did find suggests to me that a table is the wrong way to present this information. For example, Finch (p. 46) gives three different expansions for $\zeta (3)$ . Lorentzen and Waadeland (p. 267) give five different expansions for $e$ . The right way to reflect the available sources could be to incorporate that information as prose discussions (maybe in continued fraction, maybe elsewhere), but we'd be talking about writing new content, not a merge. XOR'easter (talk) 23:31, 28 February 2022 (UTC)[reply]
Keep Useful and informative list. Article went from being unreferenced to having references and more complete information. Not the article is not what it was when nomiinated for deletion. Can be improved, but there is no valid reason proffered to delete. 7&6=thirteen (☎) 13:17, 2 March 2022 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.