Talk:List of mathematical constants

Is there...
any criterion for membership in this collection? kmath (talk) 01:22, 18 January 2014 (UTC)
 * All the constants here seem to have at least 1 secondary sourse that gives a name for each constant; the reference(s) are independent of the name or namesake. I hope this helps. Marvin Ray Burns (talk) 23:31, 17 February 2015 (UTC)

How can the Tetranacci constant be transcendental?
The Tetranacci constant is defined as a particular root of a certain polynomial with integer coefficients. That should make the constant algebraic. Transcendental numbers are precisely those reals, which are not a root of any polynomial with rational coefficients. All the best Slubbert Slamberti (talk) 18:04, 28 January 2015 (UTC)
 * Slubbert, The page doesn't say that the Tetranacci constant is transcendental; it says it has "T" as a symbol. Marvin Ray Burns (talk) 23:41, 17 February 2015 (UTC)

Viswanath constant
There is a small error in the definition of the Viswanath constant, it is said to be a certain limit where an = Fibonacci sequence, but, according to the Wolfram MathWorld entry, it is a certain limit which is obtained from a random Fibonacci-like sequence with probability one. Also, the en:s in the Vardi constant should be explained (they seem to be the Sylvester sequence). K9re11 (talk) 14:17, 12 August 2015 (UTC)

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Smarandache constant bogus reference
The Journal of Smarandache-type notions is a bogus reference. Furthermore the link [19] goes to Eric Weinstein's Fourier Series article, not to that supposed Encyclopedia. See also Florentin Smarandache under the following link:

Any comments? Mdob (talk) 18:47, 21 June 2018 (UTC)

Removal of 'graphics' column
Dear all, I'd like to move that the "graphics" column be removed as it doesn't add much usable information and clutters up the page. Cheers, Jam Jamgoodman (talk) 13:47, 31 March 2019 (UTC)
 * Just an idea to think about: They add a very quick definition of the constant or what the constant is about, Thus one does not have to click a link and read anything to get their fist impression of it. The graphic also serves as a quick way to recognize the constant, that might be easier than remembering the name.Marvin Ray Burns (talk) 04:26, 1 April 2019 (UTC)
 * Thanks for the response, . I suppose you're right that it can be useful for a quick visual interpretation but still, without a legend, many of them are useless. Also, I still think the page is far too cluttered. I think a default-hidden graphic (that users click to expand) and removal of the "web formatted decimal expansion" (which adds no useful information) would adequately tidy up the page.Jamgoodman (talk) 20:54, 11 April 2019 (UTC)


 * PS. I've fixed the poor formatting of the table - it was making it impossible to edit and meant that 4 entries had been hidden inside for years. I've also deleted the 'web format' column as it was adding no useful information and was only restating the first column. The data from this column can easily be recovered from the first column.

How non-trivial must entries be to be included? The criteria seem to make no sense.
The criteria for inclusion is that the the constant must have been used in at least one published source. But what about the area of a circle with radius r=4? or r=7? or r=8? All of these circles have been used countless times in published sources but aren't included. What about arbitrary integers: 194 or 182? Or arbitrary values of common functions: sin(1) and tan(1/2)? These too have been used in many published sources but are missing from the list. Without having a bona fide reason to include or exclude constants, this list makes hardly any sense. I propose the following options:
 * The list should exclude items if they are a trivial multiples, reciprocals or combinations of other elements. Is it really necessary to include $$\frac{1}{\pi}$$ if we have already included $$\pi$$?
 * The list should exclude specific values of functions, such as $$\zeta(2)$$ or $$\log(3)$$. These values can be included on those functions' own pages. To clarify, I mean values that first arose with those functions. I am not suggesting to exclude $$\pi$$ from the list just because it is a (multiple of) a value of $$\arctan(x)$$
 * The number of published sources required for inclusion be raised. If we really include every number that has ever been published, the list would go on for ever.
 * The list be split up into separate articles based on numbers' characteristics. For instance lists of transcendental constants, list of infinite series, etc. Jamgoodman (talk) 21:37, 11 April 2019 (UTC)

Decluttering
The table really shouldn't be spilling over. It contains too many entries in both rows and columns. I propose that the table be split into rows by 'year of discovery' and that some of its columns (such as continued fraction and 'wolfram formula') be moved into separate articles or just deleted entirely. If the table contains too much information to actually be navigable, it becomes useless

Suggestions for improvements
I've made a list of improvements that I think can be made to the article and would like to hear other users' thoughts. If I hear no objections by May, I'll be implementing them:


 * Decluttering the tables
 * 1. Turning the OEIS links into inline references and putting them by the decimal expansion of the numbers. This is because the column adds no direct information; it is just a clickable link that would function equally well as a link in another column
 * 2. Removing the Wolfram Alpha code section. This column is essentially just a reiteration of the Formula column.
 * 3. Turning the 'Figure' column into a gallery at the end of each table. Only a sparse few geometry/analytic geometry derived constants will have relevant figures that can be easily interpreted. For the vast majority of entries in the article, it either has no figure or is meaningless without a legend. Any complicated figure will be impossible to interpret without a sufficiently descriptive legend.
 * Removing irrelevant content
 * 1. Turning all constants into footnotes if they're merely trivial modifications. Case in point, 1/pi, 1/e, 1/(2*pi), etc.. These aren't sufficiently different from the original constant to really be of any particular note.
 * 2. Half of the formulae listed in the article are completely overcomplicated ways of expressing the constant. Why is sqrt(5) represented as a sum of complex exponentials? That's utterly ridiculous. Call a spade a spade. Clearly sqrt(5) is the x such that x^2=5.
 * 3. Set up a list of criteria for entries to follow to be included in the article. For instance whether they are (1) given a name, (2) sufficiently notable (3) aren't trivial modifications of other constants, etc.. Without this, any constant that has ever been used in a published paper would be included in the table, which is stupid. The list would be 100,000 entries long. Wikipedia is not a directory, it is a site for articles about notable things. However, I recognise that this 'notability' criterion will - as with all things on Wikipedia - require subjective judgements. Hence, I propose that the constants in the article be vetted for their notability and removed if they're not sufficiently notable.

Jamgoodman (talk) 10:03, 15 April 2019 (UTC)

Constant for number of ordered ways to factor an integer
I am unsure what constants merit inclusion in this article, but there is one that I am fond of that is missing. It is from Einar Hille's 1936 article A problem in "Factorisatio Numerorum". A positive integer can be factored into the product of integers greater than 1 in a number of ways. For instance, 12 can be written in eight distinct ways when the order of the factors matters: 12 = 6 × 2 = 4 × 3 = 3 × 4 = 3 × 2 × 2 = 2 × 6 = 2 × 3 × 2 = 2 × 2 × 3. In some cases a large number n can be written in nρ ways where ρ = ζ−1(2) ≈ 1.72 and ζ−1 is the inverse of the Riemann zeta function. This is the constant that I would like to see. 165.156.39.49 (talk) 14:44, 17 June 2019 (UTC)
 * Hi, 165.156.39.49. This is a good suggestion but the consensus on the article is to only add constants that have articles. This is to curb the possibility of adding thousands of arguably notable constants to the page. So the inverse of the Riemann zeta function at 2 wouldn't yet fit that criterion.


 * In future, it's not a bad idea to be bold with your edits and make any change you think is necessary: WP:BOLD. Pages like this can stagnate if they don't often have edits. Looking through talk-page archives for discussions of changes you'd like to propose and being bold with edits you think are useful can be a great way to promote improvement on the article. Jamgoodman (talk) 15:09, 17 June 2019 (UTC)
 * Have you considered adding it to Particular values of the Riemann zeta function article (which I've just linked to in the See also)? NeilOnWiki (talk) 13:39, 21 March 2021 (UTC)

Omega constant series?
The series given for the omega constant does not converge $$\Omega = \sum_{n=1}^\infty \frac{(-n)^{n-1}}{n!}$$ Is this intentional and/or should it be corrected? Ashorocetus (talk &#124;  contribs) 23:02, 8 May 2020 (UTC)


 * If you think you've spotted an error, be Bold and go for it: make the change you see fit. Without people adding citations or removing unreliable content, the page will stagnate and propagate misinformation. If you can find a citation for that series, add it. If there doesn't seem to be one, feel free to remove it from the page. Jamgoodman (talk) 17:19, 9 June 2020 (UTC)

Article cleanup 2020
First off, I'd like to commend, , and for their help in cleaning up this article. It was a total mess before last year and it took many hours for me to disassemble it and remove fluff. I think for an article like this, it's easy to fill it with unnoteworthy examples since there are too many constants to include in a single article. I've detailed in (a previous section of this talk page) my suggestions for criteria for constants to be sufficiently notable to be included.

The reason I'd sorted the article by a "Year (of discovery)" column was to group the "same" (e.g., pi vs. 2pi) constants together. Sorting the article by the value of the constants means that these two constants would be far apart despite their obvious similarity (which made it harder to remove duplicates like these). Also, there needs to be a way of breaking apart the page and not having a ridiculously long list (e.g., by time-periods). However, the year of discovery of a lot of the constants here cannot be easily found, so I resorted to including the earliest date I could find of their mention (in all these cases, I'd included "Before" with the date). But this isn't an optimal solution since it relies on original research and the earliest date I find may not be anywhere close to the true date of discovery.

So, another way the page could be sorted would be alphabetically by the constant's name. However, this would rely on removing all un-named constants. If people could give their opinions on this decision, or provide alternative solutions, I urge them to contribute to the talk page. Many thanks, Jamgoodman (talk) 19:14, 18 June 2020 (UTC)


 * This looks like an amazing amount of work by everyone. Personally, I like the chronological ordering, which gives a sense of development of ideas and probably acts as a proxy for increasing knowledge-level for a reader. If I need a named value, I can easily do a string search on the page but not automatically search by time period. The tables are (obviously) very wide and I wonder whether it would be worth splitting them into two within each section, where the first is descriptive (name, symbol, formula, year, set? I'm unsure where the set should go) and the second is value based (name, symbol, value, source(s)). A source column (which I suspect we had before) would keep the source with the value and provide single-click access, without a long separated list at the end of the article. I guess it would be worth getting feedback with someone with much much better awareness of accessibility than I have on this, but I hope this is the kind of opinion you were after. NeilOnWiki (talk) 14:28, 21 March 2021 (UTC)


 * I would just like to weigh in; I think it would alleviate a lot of these issues if there were some way to divide up the constants by notability in some way. Ashorocetus (talk&thinsp;&#124;&thinsp;contribs) 18:17, 21 March 2021 (UTC)

I don't like the cleanup of this article and I think it should just be a giant table again sorted by value of the constants. 63.227.221.214 (talk) 19:54, 24 May 2021 (UTC)

Missing items
Supergolden ratio and silver ratio are missing. — Preceding unsigned comment added by Existent human being (talk • contribs) 12:43, 27 June 2021 (UTC)

So called thrembo constant
This thrembo constant business is making me sick over the fact that I ever suggested that untrained hobbyists can make meaningful contributions to mathematics Thermboists haven't come up with an unambiguous definition, and the "formula they give, "1+1+1+1+1+1+Ϫ-6" if set to 0, since that's about all it could possibly mean implies the thrembo constant = Ϫ = the integer constant 0. Otherwise, there is noting defined there. So, mathematically, the way they use thermbo, it does not exist.Marvin Ray Burns (talk) 21:36, 23 January 2022 (UTC)


 * Please don't feed the trolls. - MrOllie (talk) 21:39, 23 January 2022 (UTC)
 * This. So much this. Nutellafrenchtoast (talk) 20:55, 29 March 2022 (UTC)

missing constants
the Embree–Trefethen constant is missingÆæÆœŧ (talk) 13:11, 31 January 2022 (UTC)

Ordering
I doubt organizing constants by discovery date is that useful anymore. — Preceding unsigned comment added by Atavoidturk (talk • contribs) 16:10, 16 March 2022 (UTC)

I feel that organizing constants by discovery date is incredibly useful, and was one of my favourite parts about this page due to how extremely useful and educational that part of it was. I feel that the page is now lesser due to making it no longer share that information. I greatly dislike how it is now, given how little information it now communicates; only taking away and not adding; and how it now contradicts with the description of the page found in the introduction paragraph. I request that it at least have the dates of discovery added back in, don't want to have to search through the history tab to find the better version and get that information every time I need to look at it. comment from RandomAccount000. Not sure how to sign, just made this account because I feel it is important enough to warrant making one. I apologize for being disrespectful, I just don't see the purpose behind this massive change. — Preceding unsigned comment added by RandomAccount000 (talk • contribs) 00:07, 22 March 2022 (UTC)


 * honestly we need more input Atavoidturk (talk) 13:34, 24 March 2022 (UTC)

My proposed solution is to just combine everything into one giant table. This way we can avoid all issues regarding sorting. According to WP:TABDD, we shouldn't really be splitting up sortable tables. Combining everything into a single table will allow the user to use sorting feature, so they can freely sort the entire table according to how they want it to be, whether alphabetically, chronologically, by decimal value, or by set. — lightbulbMEOW&#33;&#33;&#33;  (meow) 13:01, 11 April 2022 (UTC)

Merging the two tables
I think that the cont frac representation should be in the main table. Atavoidturk (talk) 11:37, 13 April 2022 (UTC)


 * I don't think they should. They used to be merged with the main table, but it was decided that continued fractions be put in a separate table instead because of how cluttered it looked. We already have a lot of columns, and all of them are important properties of each constant; we can't really add any new column at this point. Since continued fraction representation is a less important property anyways (and you can already derive it from the decimal expansion so it adds no new info), I think they deserve to be separate from the main table. —  lightbulbMEOW&#33;&#33;&#33;  (meow) 12:30, 13 April 2022 (UTC)
 * Also I'm not sure about the notability of most of the continued fraction representations listed here. Like take for example, Bernstein's constant, or Meissel–Mertens constant. They both have their continued fraction listed in the table, but I can't find any sources where it would be of any actual use. I think we should only be including the continued fraction of constants where there have been studies about them, and remove the ones which don't. — lightbulbMEOW&#33;&#33;&#33;  (meow) 13:05, 13 April 2022 (UTC)
 * made a page (User:Atavoidturk/constants) showing what the table would look like. Atavoidturk (talk) 00:06, 14 April 2022 (UTC)

Fixing wrong dates
Hi, I noticed that a lot of the constants listed here actually have their dates wrong. I found sources for them that date back before the year listed in the table. I tried to correct all the ones I could find by using the sources listed on OEIS and MathWorld. This will also change the ordering of those constants on the table since they're sorted by year, so the table might look significantly changed. — lightbulbMEOW&#33;&#33;&#33;  (meow) 12:44, 14 April 2022 (UTC)

Images
Didn't the old page for this, back before the cleanup started and it was just a big list, have images? Such as the lemniscate constant having an image depicting it and the paper folding constant having a gif of paper folding? For an example just pick any revision from 2016-2017. Edit: I'm also sure the constants had their continued fraction representation next to their value. 77551enpassant (talk) 17:45, 26 May 2022 (UTC)
 * See Removal of 'graphics' column section.Marvin Ray Burns (talk) 05:05, 27 May 2022 (UTC)

OEIS is an .org domain, not .com
Shouldn't the heading of that section read oeis.org instead of .com? — Preceding unsigned comment added by 2003:D2:2F0A:E600:468A:5BFF:FEA1:E695 (talk) 11:31, 1 June 2022 (UTC)


 * Correct, and in the future you should be WP:BOLD Atavoidturk (talk) 15:09, 1 June 2022 (UTC)

Inclusion of tau
User:178.160.242.245 and i have gotten in a debate over the inclusion of tau Atavoidturk (talk) 17:09, 12 May 2023 (UTC)

Article fails to load
Whenever I try to read this article, I get the error message "The maximum request time of 60 NaN secondss was exceeded. [25573698-b423-40c2-bb44-5c2269687f78] 2023-08-01 15:45:39: Fatal exception of type "Wikimedia\RequestTimeout\RequestTimeoutException"" Lophotrochozoa (talk) 15:48, 1 August 2023 (UTC)
 * Presumably this is T341666; you can follow there for updates. 35.139.154.158 (talk) 18:41, 1 August 2023 (UTC)