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| {{oldafdfull|page=Constant|date=7 March 2008|result='''merge''' content to [[Mathematical constant]], then '''redirect''' page to [[Constant (disambiguation)]]}}
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| ==Note==
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| This talk page used to be at the title "Talk:Constant", before it was moved to make way for [[Talk:Constant|the current contents of that page]]. The article text that is referred to in the messages below can be found in the history of [[Talk:Constant/Old history]]. '''[[User:Graham87|Graham]]'''<font color="green">[[User talk:Graham87|87]]</font> 12:03, 6 October 2010 (UTC)
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| == Chatty and unstructured ==
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| This article has expanded tremendously, but it is chatty and unstructured. The version of a month ago looked like [http://en.wikipedia.org/w/index.php?title=Constant&oldid=171745438 this], with clear links to [[physical constant]] and [[mathematical constant]]. I would prefer to revert to that version. /[[User:Pieter Kuiper|Pieter Kuiper]] ([[User talk:Pieter Kuiper|talk]]) 23:33, 10 December 2007 (UTC)
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| I must agree but please be more specific. Also, there are clear links to [[physical constant]] and [[mathematical constant]]. [[User:Randomblue|Randomblue]] ([[User talk:Randomblue|talk]]) 23:42, 10 December 2007 (UTC)
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| :I have not really thought about it, but it might be best to have a disambiguation page here instead of an essay "constant" about concepts that are not really that related to eachother. Some constants are defined, others are mathematics, others are measured, etcetera. /[[User:Pieter Kuiper|Pieter Kuiper]] ([[User talk:Pieter Kuiper|talk]]) 23:53, 10 December 2007 (UTC)
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| ::There is a page [[Constant (disambiguation)]]. I also refer to what I wrote [[User talk:Randomblue#Constant|here]], including this: ''I am actually not convinced that it is worth having a separate article like this next to [[Constant (disambiguation)]] and the specific articles'' (i.e., [[Mathematical constant]] and [[Physical constant]]) and again: ''I remain unconvinced it has a reason to exist''. --[[User talk:Lambiam|Lambiam]] 01:39, 11 December 2007 (UTC)
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| :::I agree with Lambian (although the "rock"-example is a bit of an exaggeration). Users are probably served best by moving [[Constant (disambiguation)]] here. /[[User:Pieter Kuiper|Pieter Kuiper]] ([[User talk:Pieter Kuiper|talk]]) 08:21, 11 December 2007 (UTC)
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| Here are reasons why I think the article should stay:
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| * I don't know about Lambiam but I see that Pieter Kuiper is a "solid state physicist". Perhaps you don't appreciate enough the fact that the concept of a constant is a scientific one, and not solely a mathematical or physical concept. Chemists, biologists, cosmologists, economists, sociologists and maybe even computer scientists work with constants as well.
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| * Many authors (even with just a little research I found two quotes) suggest that constants have a fascinating, intriguing or beautiful aspect to them and this observation is a common observation for at the least mathematical and physical constants.
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| * Constants have quite a remarkable history, related in part to their notation. Also, mathematical constants and physical constants have a common history: Newton was both a mathematician and physicist, Kepler was both a mathematician and an astronomer,...
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| * It turns out that some constants are not discovered in a strictly orthodox way (mathematical constants while doing maths, physical constant while doing physics, etc...) Indeed, some mathematical constants (like the Feigenbaum constants that arised from studying fluids for example) are discovered not when doing mathematics and physical constants are sometimes discovered (or at least predicted) by abstract mathematical means.
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| * Some constants (as I've tried to suggest it) don't really fit in the classification of mathematical and physical constants because they are much more universal: we encounter them in both mathematics and physics.
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| * One cannot really claim that unspecified constants are of a mathematical type, of a physical type, or of any specific type. They are 'tools' that scientists use when doing modeling for example.
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| I must apologize if the article doesn't look pleasant. This is really my first article, I'm no kind of constant expert, and, I've only been working (from scratch) on this article for weeks. I'm ready to completely rewrite the article and apportion various parts to more specific articles. However, I really do think that the scientific concept of a constant can be dealt with as a whole before diving in the depth of the more specialized type. [[User:Randomblue|Randomblue]] ([[User talk:Randomblue|talk]]) 10:53, 11 December 2007 (UTC)
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| :[[User:Randomblue]] does not present his credentials, so it cannot be ruled out that he has a much greater overview over general science than I do. The important point though is whether his essay is what a reader would expect to find in an encyclopedia. The word 'constant' does not mean very much, but it is important to note that it is often used as a contrast to 'variable'. The article [[constant (disambiguation)]] does so at the outset, while this essay never gets to such a central point.
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| :I believe that this essay includes too much original research (which includes [[WP:SYN|synthesis]] and joining together things in creative ways) and that it is too personal for an encyclopedia. /[[User:Pieter Kuiper|Pieter Kuiper]] ([[User talk:Pieter Kuiper|talk]]) 12:27, 11 December 2007 (UTC)
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| :"I really do think that the scientific concept of a constant can be dealt with as a whole". Here we clearly disagree; I think the various notions that are called "constant" are too diverse and disparate to be amenable to a meaningful joint treatment. --[[User talk:Lambiam|Lambiam]] 13:12, 11 December 2007 (UTC)
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| [[User:Pieter Kuiper]], if you want my credentials here they are: I'm a first year undergraduate at the University of Cambridge, studying maths. Hence, you surely have much more experience than I do. However, I am ready to do research to build a very decent article.
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| Contrasting constant with variable seems to be more of a "dictionary" or "thesaurus" point of view. Most people 'know' that constant contrasts with variable. However, it is the entity itself that is of interest here. What is a constant (these real numbers)? How do we define them? What role do they play in science? Why should <math>\pi</math> be more important than 3.65?
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| I agree that this is an "essay" more than a proper encyclopedic article yet, but this is just the kind of work I am used to, and I wish to achieve something appropriate. I suggest you cite sentences that you find too personal (or even delete a few!) so that I can work on them.
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| [[User:Lambiam]], let me rephrase my idea: "Within the scope of the definition of constant ''a real number with significant importance'' it is possible to deal with it as a whole. Indeed, with this definition we exclude the [[constant (computer science)|computer science term]], [[constant function]]s, [[logical constant]]s, etc."
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| [[User:Randomblue|Randomblue]] ([[User talk:Randomblue|talk]]) 15:27, 11 December 2007 (UTC)
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| Also, as I see it, the [[mathematical constant]] article is hardly more than a dry list. I find that discussion always helps grasp a concept. [[User:Randomblue|Randomblue]] ([[User talk:Randomblue|talk]]) 15:49, 11 December 2007 (UTC)
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| :As a Cambridge math student, Randomblue probably knows more about mathematical constants than I do, and he certainly has a greater interest in them. I think most of this article is about mathematics. A large part of the material here could be moved to a general article about mathematical constants. /[[User:Pieter Kuiper|Pieter Kuiper]] ([[User talk:Pieter Kuiper|talk]]) 18:20, 11 December 2007 (UTC)
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| :Apart from a few [[dimensionless physical constant]]s, [[physical constants]] are ''not'' real numbers, and treating them together with the mathematical constants is purely artificial. The numerical values when such constants are expressed in specific units of measurement depend on decisions in defining these units that are completely irrelevant from the viewpoint of physics (such as using not-really-constant geophysical properties of the planet Earth as the basis for choosing the lengths of the second and the meter), and are therefore utterly devoid of any particular significance. And how does importance enter the concept of "mathematical constant"? Can you cite some reliable source that backs that up? Not all mathematical constants are important, as their number is without end (the largest root of ''x''<sup>7</sup>−20''x''<sup>4</sup>+4, Σ ''n''/(''n''<sup>3</sup>+1), √(π+1), and so on). Even many ''named'' mathematical constants have no clear significance, and it is mostly accidental that they were named at all. --[[User talk:Lambiam|Lambiam]] 20:49, 11 December 2007 (UTC)
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| :Well, it is perhaps possible to interpret Steven Finch's (the author of "mathematical constants") quote that "all constant's are not created equal" as "all constant's aren't all as important one another". I guess that examples of important constants include the truly ubiquitous and universal, those who translate nice facts (Conway's constant) and those who link different branches of mathematics (Euler-Mascheroni). Anyway, thanks for the input. I might get working on [[mathematical constant]] or some other article I'm keen about. [[User:Randomblue|Randomblue]] ([[User talk:Randomblue|talk]]) 22:12, 11 December 2007 (UTC)
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| == Idea of the page is wrong, under this name ==
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| Constants don't have to be interesting; they just have to be constant. The reference for the definition is the notoriously unreliable MathWorld. I came to this page because it's listed as a "vital article" -- this very basic problem with the whole concept of the page is a serious issue that something needs to be done about. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 16:21, 18 July 2008 (UTC)
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| :I disagree about MathWorld being unreliable here. Rather, the person who wrote the broken definition failed to read the MathWorld article thoroughly. [[User:Fredrik|Fredrik Johansson]] 16:31, 18 July 2008 (UTC)
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| :::I haven't read that particular article either. I find MathWorld unreliable ''in general'' as a source for WP. In particular it indulges itself in neologism-making and idiosyncratic organization of information. That would be OK except for its pretensions to be a reference work. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 18:10, 18 July 2008 (UTC)
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| ::Be bold, guys! [[Special:Contributions/86.210.142.101|86.210.142.101]] ([[User talk:86.210.142.101|talk]]) 17:07, 18 July 2008 (UTC)
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| :::Well, this isn't a matter of changing a line or two. The whole premise of the page is wrong, and it's a vital article, at least according to the current list. So some discussion needs to happen first. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 18:10, 18 July 2008 (UTC)
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| :I agree with Trovatore. Also note the first post on this page above, which references [http://en.wikipedia.org/w/index.php?title=Constant&oldid=171745438 an earlier version of this article] for comparison. [[User:Paul August|Paul August]] [[User_talk:Paul August|☎]] 18:31, 18 July 2008 (UTC)
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| ::I don't want to get rid of all the nice content that Randomblue has added. It might make sense in an article called [[list of named constants]] or some such. The "list" format doesn't have to be just a collection of bullets; it can include some exposition, and (in my observation) it's a little looser about the sorts of organizing principle that it can have, even marginally "original" ones, as long as they're not aimed at pushing some sort of point.
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| ::But I really don't think that content can stay under an article called "constant" (and while it's not really on point, I also sort of doubt that any article with "constant" in the name really belongs under "vital articles" for mathematics). --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 09:13, 19 July 2008 (UTC)
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| :This article was nominated for deletion on 7 March 2008. As you can read at the top of this talk page, the result of the [[Wikipedia:Articles for deletion/Constant|discussion]] was: '''merge''' content to [[Mathematical constant]], then '''redirect''' page to [[Constant (disambiguation)]]. It's just that nobody has executed this (yet). --[[User talk:Lambiam|Lambiam]] 21:55, 24 July 2008 (UTC)
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| ::Hmm, but [[mathematical constant]] kind of has the same issue, wouldn't you say? --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 21:57, 24 July 2008 (UTC)
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| :::When ''I'' use the term "mathematical constant" rather than just "constant", it means a number such as ''e'' or π, not just any constant such as, e.g., log(34211/16231). As far as I'm aware that is the common use. Our page [[Constant (disambiguation)]] agrees – which is not surprising since I authored the relevant bit.[http://en.wikipedia.org/w/index.php?title=Constant_(disambiguation)&diff=175032429&oldid=174323220] For another position note that Plouffe's inverter identifies itself as "a database of more than 215,000,000 mathematical constants like Pi, E, Catalan or Euler-Mascheroni constant", where of course not all 215,000,000 entries are equally "significantly" interesting as the four ones named. --[[User talk:Lambiam|Lambiam]] 22:44, 24 July 2008 (UTC)
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| ::::Hmm -- there is certainly a better case for that view for the name ''mathematical constant'' as opposed to just ''constant''. But I'm still uncomfortable with giving a definition that requires the object to be "interesting". Maybe my discomfort would be eased somewhat if there were a way to clarify that this is not a ''mathematical'' definition. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 23:10, 24 July 2008 (UTC)
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| :::::I've edited the lede of [[Mathematical constant]] a bit to clarify that "interesting" is a matter of taste, assuming that readers will understand that applying mathematical definitions will not require one to exercise taste. Please review and see if this assuages your unease. --[[User talk:Lambiam|Lambiam]] 16:22, 25 July 2008 (UTC)
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| == Ahad's Constant ==
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| The article opens with this paragraph: "Constants are real numbers or numerical values which are significantly interesting in some way. The term "constant" is used both for mathematical constants and for physical constants, but with quite different meanings."
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| Well, here's one that has been floating around since c. 2004 and hugely [http://www.google.com/search?hl=en&q=Ahad%27s+Constant&btnG=Google+Search discussed] in lots of places and it seems "significantly" interesting and is both a *http://en.wikipedia.org/w/index.php?title=Talk:Constant&action=edit§ion=3physical* as well as a *mathematical* constant:
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| [[Image:Ahads_constant_public_domain_image.jpg|center|400px]]
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| The article would be more complete if [[Talk:Theorem#Ahad.27s_Sphere_of_the_Sun|Ahad's Constant]] were added. Discuss? :-) <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/86.133.83.119|86.133.83.119]] ([[User talk:86.133.83.119|talk]]) 12:08, 5 August 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->
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| :This constant is not notable. The only publication is in the "Letters" column journal of the [[British Astronomical Association|BAA]], an association of ''amateur'' astronomers. Such [http://britastro.org/baa/content/view/46/84/ "Letters to the Editor"] are not peer-reviewed and are not "reliable sources". The "surrounding cosmic illumination", not counting the contribution of the Sun, actually depends on where you are in the universe – although the variation will not be very large in the vicinity of the Solar system.
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| ::A small correction: that is not the *only* publication, albeit in non-refereed journals. There's an inordinate amount of mainstream media and popular culture publications that support this constant and Mr. Ahad's astrophysical theorem of the Sun's radiative zone of pre-eminence. They include the following on and (known) off-line publications: The Mathaba News Network (February 1st, 2007), The American Chronicle, The Daily Star, Writewords.org.uk, Whosreadit.Com, The Muslim Writers Society (July 30th, 2005), Muktadara.Net (Page 71 - "Notable Scientists"), The Luton Herald & Post (August 4th, 2005, p. 29), the Janomot (London: Sep 30-Oct 06, 2005, p. 19) and Bangla Mirror newspapers. From [http://www.publishedauthors.net/aa_spaceagent/news.html] <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/217.36.214.12|217.36.214.12]] ([[User talk:217.36.214.12|talk]]) 14:52, 18 August 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->
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| ==Computability / Definability==
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| I think it would be nice to add one or two new rows for the computability / definability of each constant. What do you think? <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/134.184.131.153|134.184.131.153]] ([[User talk:134.184.131.153|talk]]) 10:40, 6 September 2007 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->
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| ==Chaitin's constant?==
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| Should Chaitin's "constant" be here? It's not actually a real number until you've chosen a computational machine, and I'm not aware of any canonical choices for that. For any such choice, on the other hand, we can make some statements about Ω. For example, for any machine for which the string "0" is a program that simply terminates, Ω > 0.5. We might even know the first digit.
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| [[User:Prumpf|Prumpf]] 14:37, 14 Aug 2004 (UTC)
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| :Okay, I've removed it. I think readding a concrete entry for a particular machine's Ω would be great, but it should be a vaguely natural computational machine, and someone should actually do the math for those digits we can calculate.
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| :[[User:Prumpf|Prumpf]] 13:27, 29 April 2006 (UTC)
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| ==Square roots of 2 and 3? ==
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| Is there any reason why <math>\sqrt{2}</math> and <math>\sqrt{3}</math> are listed as irrational rather than algebraic? [[User:Gkhan|Gkhan]] 16:45, Sep 7, 2004 (UTC)
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| : Exactly what I was wondering. It may make more sense to use R = rational (none of the constants given are rational, I guess) A = algebraic (&irrational), T = transcendental --[[User:AndrewKepert|Andrew Kepert]] 07:05, 7 Oct 2004 (UTC)
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| ::I like this proposal ([R]ational, [A]lgebraic but not rational, [T]ranscendental). Also I would leave out the question marks. It's implicit that if we don't fill in the gap we just don't know. [[User:PizzaMargherita|PizzaMargherita]] 21:23, 1 November 2005 (UTC)
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| == 1? ==
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| Is the number 1 not a mathematical constant? It is used to define the set of [[natural numbers]]. --[[User:Lambyuk|Lambyuk]] 01:44, 13 May 2005 (UTC)
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| :I'll second that. I think [[0_(number)|0]], [[1_(number)|1]] and [[imaginary unit|i]] have a very interesting history behind them (which I didn't have time to write in my tentative entries), and deserve a place in the table for completeness. These numbers are not as obvious as you may think. [[User:PizzaMargherita|PizzaMargherita]] 21:04, 20 November 2005 (UTC)
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| :...so as above, [[0_(number)|zero]], [[1_(number)|unity]] and the [[imaginary unit]] deserve a place in the table, on the basis that:
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| :#They are mathematical constants
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| :#They are not obvious at all—and I find that remark rather insulting to whom spent their lives studying them
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| :#They are part of [[Euler's identity]]. And I quote from the article: "the identity links five fundamental mathematical constants"
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| :#They are arguably more fundamental than many other constants in the list
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| :[[User:PizzaMargherita|PizzaMargherita]] 08:53, 26 February 2006 (UTC)
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| ::Hurrah, it was added today :) [[User:Lambyuk|Lambyuk]] 12:47, 26 February 2006 (UTC)
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| Err, 1 and 0 are not constants. They are numbers. In software development, for example, 0 is a literal, but A=0 would mean A is a constant representing number 0. Secondly, if we have 0 and 1, why not 2, 3 and 4? How about 0x0a? How about [[20_(number)|20]]? It is also very interesting...
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| Similarly, i is the same as 1 but for the complex plane. Just a unit, nothing special. <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/216.55.199.86|216.55.199.86]] ([[User talk:216.55.199.86|talk]]) 20:43, 14 February 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->
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| == New table format: comments? ==
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| I've redone the table in (I hope) a better looking format. It is similar to format used on [[Table of mathematical symbols]]. Any comments? [[User:Paul August|Paul August ]] [[User_talk:Paul August|☎]]
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| Some of the table rows need to be bigger. I would do it myself, but I don't want to mess it up. -Mihirgk
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| == Golden ratio is irrational right? ==
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| Right? (Are all constants that are irrational-but-not-transcendent algebraic?)
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| :All real numbers that are not transcendental are algebraic, because the definition of a transcendental number is a real number that is not algebraic. The golden ratio is irrational and algebraic, being the solution to the equation x<sup>2</sup> - x - 1 = 0 -[[User:GTBacchus|GTBacchus]] 21:24, 1 November 2005 (UTC)
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| == Mill's constant ==
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| Is Mill's constant symbolised by theta (as in the table) or phi (as in it's [[Mill's constant|seperate article]])? --[[User:Saboteur|Saboteur]] 01:11, 31 March 2006 (UTC)
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| :I corrected the article--[[User:Saboteur|Saboteur]] 07:23, 31 March 2006 (UTC)
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| == Hafner-Sarnak-McCurley constant ==
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| Accoring to [http://www.mathworld.wolfram.com/Hafner-Sarnak-McCurleyConstant.html this article],D(1)=6/pi^2,not the HSM constant. It uses sigma for the HSM. We should change the symbol.
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| I just changed the symbol.
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| == Erdos-Borwein constant:algebraic? ==
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| Is the Erdos-Borwein constant ''really'' algebraic? You should make something called I. It will mean "known to be irrational,may be algebraic or transcendental." That would be a good extra symbol.
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| == Landau's constant ==
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| Most precise does not equal most accurate. "Number of known digits" as used in this table means number of digits known to be correct, not number of digits that could be right. [[User:Fredrik|Fredrik Johansson]] 22:57, 6 September 2006 (UTC)
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| : Fredrik, I understand your interpretation of "Number of known digits". Why don't we let the math community of WP decide? Either outcome will be fine with me. [[User:Giftlite|Giftlite]] 23:44, 6 September 2006 (UTC)
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| == Cahen's constant ==
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| The article "http://en.wikipedia.org/wiki/Cahen%27s_constant" give the following value :
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| 0.64341054629...<br><br>
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| What is the true value ?
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| <br><br>
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| cf [http://fr.wikipedia.org/wiki/Discuter:Table_de_constantes_math%C3%A9matiques#Constante_de_Cahen_erron%C3%A9e_?]
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| <br> [[User:Papy77|Papy77]] 15:41, 1 February 2007 (UTC)
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| == Mathematical constint ==
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| Is [[Mathematical constint]] a good redirect? [[User:Constint|Con]][[User talk:Constint|<span style="color:red">stint</span>]] 12:27, 27 February 2007 (UTC)
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| == Red links and external links ==
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| There are so many red links in the table. We should create some pages and remove the external links. [[User:Math Maniac|Math Maniac]] 11:46, 1 March 2007 (UTC)
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| : I created [[Niven's constant]]. <sup>[[User:Over|Over]]</sup>/<sub>[[User talk:Over|Under]]</sub> 13:29, 2 March 2007 (UTC)
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| :: Thanks. [[User:Math Maniac|Math Maniac]] 12:07, 3 March 2007 (UTC)
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| == MRB Constant ==
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| I would like to see if anyone can further expand upon my attempts of researching the following value.
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| Sloan's A037077 ie. one of two real decimal expansions of 1^(1/1)-2^(1/2)+3^(1/3)... or a generalized sum to the divergent series.
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| http://www.research.att.com/~njas/sequences/A037077[http://www.research.att.com/~njas/sequences/A037077]
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| This constant remains a mystery. For instance, before 1998 what was the computation-history of the value that is presently called the MRB Constant? What is the closed form expression (assuming it exists) for the value of this constant? What relation does this constant of infinite dimensional “[[hypercube]]s," have with respect to
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| "[[hypersphere]]s” of dimensions without bound? In what way might this infinite-dimensional constant be used in string theory?
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| Most of my findings can be seen by following the links on Sloan's encyclopedia. From those links you will also come across a few references to more rigorous research done on that value's general form.
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| If you endeavor to research this constant, I will try to help by answering any questions as to what I have already found in the past 9 years.
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| last update--[[User:Marburns|Marvin Ray Burns]] 19:54, 15 April 2007 (UTC)
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| :One formula I didn't see in your documents (perhaps I didn't look hard enough) is the [[Euler transform]] of that series (with 1 subtracted from each term to force convergence):
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| ::<math>s = \sum_{n=1}^\infty 2^{-n-1} \sum_{k=1}^{n+1} (-1)^k {n \choose {k-1}} k^{1/k}</math>
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| :I also tried a few other sequence transformations, but didn't end up with anything fruitful. [[User:Fredrik|Fredrik Johansson]] 09:17, 22 April 2007 (UTC)
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| :::Fredrik Johansson, I have used your reference to the transform as an example of what is required in the article that I am commissioning.--[[User:75.2.16.2|75.2.16.2]] 01:32, 23 April 2007 (UTC)
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| A recent observation about and definition of this constant can be found at http://www.marvinrayburns.com/what_is_mrb.mht[http://www.marvinrayburns.com/what_is_mrb.mht]. I hope that, through the input of interested and knowledgeable people, this constant will qualify for an article on Wikipedia. [[User:Marburns|Marvin Ray Burns]] ([[User talk:Marburns|talk]]) 01:45, 22 April 2009 (UTC)
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| ==Notice: Reward for Article about the MRB Constant==
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| http://en.wikipedia.org/wiki/Wikipedia:Reward_board#MRB_Constant
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| --[[User:Marburns|Marvin Ray Burns]] 00:24, 17 April 2007 (UTC)
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| == Mathematical constants ==
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| This page should be merged with [[Mathematical constants]]. [[User:Jaunt|Jaunt]] 16:50, 12 April 2007 (UTC)
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| == Action by Marvin Ray Burns ==
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| It is obvious that this change needed to be made:
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| http://en.wikipedia.org/w/index.php?title=Mathematical_constant&diff=122317608&oldid=122257451
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| '''The old symbols were larger than the row height of the table.''' <small>—--[[User:Marburns|Marvin Ray Burns]] 21:46, 12 April 2007 (UTC) [[User:Marburns|Marburns]] ([[User talk:Marburns|talk]] • [[Special:Contributions/Marburns|contribs]]) 21:33, 12 April 2007 (UTC).</small><!-- HagermanBot Auto-Unsigned -->
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| ==Approximate Value==
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| <math>\sqrt{-1}</math> is exact and not an approximate value. <math>1.\sqrt{-1}</math> is approximate. Better is the Cartesian representation0.0+1.i. However, the last approximation uses i to define i. I believe it is best to put " <math>\sqrt{-1}</math>exactly ." I'm going to post it and see if anyone has a better -- more accurate—way of displaying it.--[[User:Marburns|Marvin Ray Burns]] 01:55, 15 April 2007 (UTC)
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| == definition ==
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| Is the addition of complex number in the definition really appropriate? The only 'complex constant' I've head of is <math>i</math>, because it's a 'unit'. [[User:Randomblue|Randomblue]] ([[User talk:Randomblue|talk]]) 15:43, 11 December 2007 (UTC)
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| == 2 questioned constants and some suggestions... ==
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| Hi fellow wikipedians!
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| I've been checking all the constants in the list and verified the existence of each red one (except two)
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| via [http://mathworld.wolfram.com/topics/MiscellaneousConstants.html Wolfram MathWorld] (entries
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| in that list, or found by searching that site).
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| There are however two constants which I fail to verify via internet searching:
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| [[Hughes constant]] ("Sh") and [[Jacevicius constant]] ("J<sup>2</sup>").
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| Does anyone else know of these constants and can verify their existence, i.e. justify that they are
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| present in the list? Otherwise, they might be subject for deletion...
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| Furthermore I find that the following uncategorized constants ''could'' be placed in the following fields of
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| mathematics (as far as I understand from checking the articles and/or Wolfram MathWorld);
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| *[[Cahen's constant]] : Number theory (derived from [[Sylvester's sequence]] in Number theory)
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| *[[Laplace limit]]: Calculus (isn't it something like Geometry->Celestial mechanics->Calculus, i.e. Calculus?)
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| *[[Apéry's constant]]: Number theory ([[Apéry's constant|categorized as (analytic) number theory]])
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| *[[Backhouse's constant]]: Number theory ([http://mathworld.wolfram.com/BackhousesConstant.html it's about prime numbers])
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| Any opinions on this?
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| --[[User:Dna-webmaster|Dna-Dennis]] ([[User talk:Dna-webmaster|talk]]) 15:48, 3 February 2008 (UTC)
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| :'Hughes constant' appears to be an emperical constant associated with leave thickness of plants and trees. Seems a rapid delete from list of math constants. -- [[User:JocK|JocK]] ([[User talk:JocK|talk]]) 18:41, 5 February 2008 (UTC)
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| :No opinion on the suggestions. But I do have a request. Could you add citations for the sources you found to the table? That would be ''very'' helpful. If you don't want to add them to the article, adding them here on the talk page would also be helpful. Thanks in advance. [[User:Paul August|Paul August]] [[User_talk:Paul August|☎]] 18:55, 5 February 2008 (UTC)
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| ::Paul, good idea! I've added them as refs to the article (which could help future editors to write entry articles on them). I will repeat them here, and also give links to the entries in OEIS:
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| ::*[[Backhouse's constant]] - [http://mathworld.wolfram.com/BackhousesConstant.html MathWorld] - [http://www.research.att.com/~njas/sequences/A072508 OEIS]
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| ::*[[Bernstein's Constant]] - [http://mathworld.wolfram.com/BernsteinsConstant.html MathWorld] - [http://www.research.att.com/~njas/sequences/A073001 OEIS]
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| ::*[[Alladi-Grinstead Constant]] - [http://mathworld.wolfram.com/Alladi-GrinsteadConstant.html MathWorld] - [http://www.research.att.com/~njas/sequences/A085291 OEIS]
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| ::*[[Lengyel's Constant]] - [http://mathworld.wolfram.com/LengyelsConstant.html MathWorld] - [http://www.research.att.com/~njas/sequences/A086053 OEIS]
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| ::*[[Porter's Constant]] - [http://mathworld.wolfram.com/PortersConstant.html MathWorld] - [http://www.research.att.com/~njas/sequences/A086237 OEIS]
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| ::*[[Lieb's Square Ice Constant]] - [http://mathworld.wolfram.com/LiebsSquareIceConstant.html MathWorld] - [http://www.research.att.com/~njas/sequences/A118273 OEIS]
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| ::I will also see if I can optimize the list format in the article - it's a little tough to edit it as it is.
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| ::JocK, don't worry, I won't delete any constants on my own without consulting you other wikipedians. The problem is that I can't find neither [[Hughes constant]] nor [[Jacevicius constant]] in neither [http://mathworld.wolfram.com/search/help.html Wolfram MathWorld] nor [http://www.research.att.com/~njas/sequences/index.html OEIS (The On-Line Encyclopedia of Integer Sequences)], and I don't find any useful references either by googling. I don't necessarily question their existence, but, the following is important: (1) Are they noteworthy enough to credit an entry in this list? (There are many more other constants which are not currently present in the list). (2) We need to make sure that they have a pure mathematical origin, and are not [[Physical constants]], i.e. measured. JocK, do you have any good links to [[Hughes constant]]? That would be most helpful. My regards, --[[User:Dna-webmaster|Dna-Dennis]] ([[User talk:Dna-webmaster|talk]]) 21:38, 5 February 2008 (UTC)
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| :::Here's a link to an article about the Hughes Constant: http://aob.oxfordjournals.org/cgi/content/full/89/5/537
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| :::It varies from species to species. I'm almost positive the entry here is immature vandalism. It and the Jacevicius constant were added at the same time by a non-registered user. Also, the value for the Hughes constant looks very similar to a date, possibly the birthday of whoever added it? The Jacevicius constant is a value squared. I've never seen a constant represented that way. Why not show the true value by just squaring it? I'd say given the evidence (or lack thereof) these are good to delete. [[User:Sam Etler|sam]] ([[User talk:Sam Etler|talk]]) 05:35, 16 February 2008 (UTC)
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| ==Why are they all pretty small?==
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| Why are all these constants small? Now I know "small" isn't really well defined, but why do constants tend to be close to 0 or 1. Not the most well defined question, but you know what I mean. Has there ever been any discussion in the literature about this? [[User:Brentt|Brentt]] ([[User talk:Brentt|talk]]) 20:06, 6 May 2008 (UTC)
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| ==New section added==
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| I just added a section about the decimal place similarity of irrational constants.
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| More on this coming soon!
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| [[User:Quantum Anomaly|Quantum Anomaly]] ([[User talk:Quantum Anomaly|talk]]) 04:48, 1 July 2008 (UTC)
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| :I really doubt that these "patterns" are statistically significant. There are more than 40 constants listed in this article. If you pick a random digit (0-9) 40 times, there is a 0.5% chance that you will get 10 or more 9s. Doesn't sound very high, but if you take 40 random numbers (between 0 and 1), the probability that 10 or more will contain the digit 9 at the same decimal place somewhere in their first 20 decimal places is 1-(1-0.005)<sup>20</sup> or about 10%. And if you don't specify in advance that it is the digit 9 you are looking for the probability of finding a "pattern" is even higher. Try a simulation - with 40 random numbers I think there is a greater than 50% chance of finding the same digit (not necessarily 9) at the same decimal place somwehere in the first 20 places in 10 or more of them.
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| :This is an example of the [[Texas sharpshooter fallacy]] - if you look hard enough at a large enough volume of data, you will find some patterns. But this is meaningless unless you form an [[ex-ante]] hypothesis before looking at the data.
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| :Even though these "patterns" may be just conincidence, they could still be mentioned in the article ''if'' you could cite a [[WP:RS|reliable third-party source]] where they are discussed. But I am afraid that at the moment your footnote "Observation first noted by Seth Lewis" does not qualify as a reliable source. Unless you can find a source, I think this section should be removed. [[User:Gandalf61|Gandalf61]] ([[User talk:Gandalf61|talk]]) 12:49, 1 July 2008 (UTC)
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| :I see you have removed the [[silver ratio]] because it is 1+sqrt(2), so obviously the decimal expansions of these two constants are related. Note that the [[golden ratio]], phi, is (1+sqrt(5))/2, so anywhere there is a 9 in the decimal expansion of sqrt(5), the corresponding digit in the decimal expansion of phi can only be a 4 or a 9 - so the decimal expansions of these two constants are also related.
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| :Unless you can quite soon provide an independent reference to show these coincidences in decimal expansions have been noted and discussed elsewhere, I am seriously considering removing this section on the grounds that it is apparently [[WP:NOR|original research]]. [[User:Gandalf61|Gandalf61]] ([[User talk:Gandalf61|talk]]) 08:28, 2 July 2008 (UTC)
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| ::Okay, now 3 days since my first post on this, and no response from anyone, so I am removing the new section on the grounds that it is unsourced, and so likely OR. Removed text is shown below. If someone can provide a [[WP:RS|reliable source]] that discusses these "patterns" then I have no objection to re-instating the section. [[User:Gandalf61|Gandalf61]] ([[User talk:Gandalf61|talk]]) 08:32, 4 July 2008 (UTC)
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| :::I agree with the removal. Your analysis is correct, and any inclusion of examples of interesting patterns would need to be supported with reliable sources indicating ''why'' they are significant. Given that these decimal expansions go on forever, it seems inevitable that patterns like the ones removed will occur. --[[User:Johnuniq|Johnuniq]] ([[User talk:Johnuniq|talk]]) 01:01, 5 July 2008 (UTC)
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| ::::Well it seems there is a consensus that the section doesn't belong. That's fine, but I think some have misunderstood my intentions in posting it. I never claimed to understand the reason for the frequent occurrence of nines. I made no statements that would require a "reliable third-party source". The nines are there and they speak for themselves. The purpose of the post was to draw attention to this trend so that the community could see this and share ideas, explore further, etc. If there is a better place for this than Wikipedia then I am open to suggestions, but I don't feel it should be written off as insignificant so quickly. When the decimals of these irrational constants are displayed in a line graph the numbers appear not to be random. Just because nobody has identified any specific patterns yet doesn't mean that the possibility should not be investigated. As far as I'm concerned it is an open question, so where does such a question belong if not here?
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| [[User:Quantum Anomaly|Quantum Anomaly]] ([[User talk:Quantum Anomaly|talk]]) 21:33, 8 July 2008 (UTC)
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| :::::I think the issue is that Wikipedia is supposed to be a repository of verifiable information, [[WP:NOT#OR|not a forum or source of original research]]. Sure, you demonstrated an interesting pattern, but one can find lots of patterns that are essentially just outcomes of one particular roll of the dice. So, this section would need a reliable source showing (or at least claiming) that the particular patterns really are significant. I'm sure Google can find newsgroups and mailing lists discussing mathematical issues, and that is where these patterns could be pursued. --[[User:Johnuniq|Johnuniq]] ([[User talk:Johnuniq|talk]]) 03:22, 9 July 2008 (UTC)
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| ----
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| <small>''Removed text''</small>
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| It is interesting to note the frequent occurrence of [[Irrational_number|irrational]] constants having the number nine in the 12th and/or 14th decimal places.<ref>Observation first noted by Seth Lewis</ref> This pattern confirms a relationship between irrational constants and hints at the possibility of underlying [[Self-similarity|self-similarity]] of a larger scale.
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| <center>A working list of irrational constants with nine in their 12th decimal place:</center>
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| {| border="0" cellspacing="0" cellpadding="0" width="90%"
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| |- valign="top"
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| | align="right" | <tt>
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| [[Pi]]<font color="646464">:</font>
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| [[golden ratio|Phi]]<font color="646464">:</font>
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| [[Apéry's constant|Apéry's Constant]]<font color="646464">:</font>
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| [[Square root of 5|The Square Root of 5]]<font color="646464">:</font>
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| [[Copeland-Erd%C5%91s_constant|Copeland-Erdös Constant]]<font color="646464">:</font>
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| [[Landau-Ramanujan constant|Landau-Ramanujan Constant]]<font color="646464">:</font>
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| [[Sierpi%C5%84ski's_constant|Sierpiński's Constant]]<font color="646464">:</font>
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| [[E_(mathematical_constant)|e]]<font color="646464">:</font>
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| [[Omega constant|Omega Constant]]<font color="646464">:</font>
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| </tt>
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| | align="left" | <tt>
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| <font color="white">0</font>3.14159265358<font style="background-color:yellow">'''9'''</font>793238462643383279
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| <font color="white">0</font>1.61803398874<font style="background-color:yellow">'''9'''</font>894848204586834365
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| <font color="white">0</font>1.20205690315<font style="background-color:yellow">'''9'''</font>594285399738161511
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| <font color="white">0</font>2.23606797749<font style="background-color:yellow">'''9'''</font>789696409173668731
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| <font color="white">0</font>0.23571113171<font style="background-color:yellow">'''9'''</font>232931374143475359
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| <font color="white">0</font>0.76422365358<font style="background-color:yellow">'''9'''</font>220662990698731250
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| <font color="white">0</font>2.58498175957<font style="background-color:yellow">'''9'''</font>253217065893587383
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| <font color="white">0</font>2.71828182845<font style="background-color:yellow">'''9'''</font>045235360287471352
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| <font color="white">0</font>0.56714329040<font style="background-color:yellow">'''9'''</font>783872999968662210
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| </tt>
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| |}
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| <center>A working list of irrational constants with nine in their 14th decimal place:</center>
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| {| border="0" cellspacing="0" cellpadding="0" width="90%"
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| |- valign="top"
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| | align="right" | <tt>
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| [[Pi]]<font color="646464">:</font>
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| [[golden ratio|Phi]]<font color="646464">:</font>
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| [[Square root of 2|The Square Root of 2]]<font color="646464">:</font>
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| [[Erd%C5%91s-Borwein_constant|Erdős-Borwein Constant]]<font color="646464">:</font>
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| [[Apéry's constant|Apéry's Constant]]<font color="646464">:</font>
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| [[Feigenbaum constants|Feigenbaum Delta Constant]]<font color="646464">:</font>
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| [[Feigenbaum constants|Feigenbaum Alpha Constant]]<font color="646464">:</font>
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| [http://mathworld.wolfram.com/RiemannZetaFunctionZeros.html 1st 0] of [[Riemann zeta function|Riemann Zeta Function]]<font color="646464">:</font>
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| [[Kepler-Bouwkamp constant|Kepler-Bouwkamp Constant]]<font color="646464">:</font>
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| </tt>
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| | align="left" | <tt>
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| <font color="white">0</font>3.1415926535897<font style="background-color:yellow">'''9'''</font>3238462643383279
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| <font color="white">0</font>1.6180339887498<font style="background-color:yellow">'''9'''</font>4848204586834365
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| <font color="white">0</font>1.4142135623730<font style="background-color:yellow">'''9'''</font>5048801688724209
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| <font color="white">0</font>1.6066951524152<font style="background-color:yellow">'''9'''</font>1763783301523190
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| <font color="white">0</font>1.2020569031595<font style="background-color:yellow">'''9'''</font>4285399738161511
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| <font color="white">0</font>4.6692016091029<font style="background-color:yellow">'''9'''</font>0671853203820466
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| <font color="white">0</font>2.5029078750958<font style="background-color:yellow">'''9'''</font>2822283902873218
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| 14.1347251417346<font style="background-color:yellow">'''9'''</font>3790457251983562
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| <font color="white">0</font>0.1149420448532<font style="background-color:yellow">'''9'''</font>6200701040157469
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| </tt>
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| |}
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| <font color="646464" size="1">• In the numbers above, the last decimal is truncated, not rounded.</font>
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| <font color="646464" size="1">• 14.134... is known as "the imaginary part of the first nontrivial zero of the Riemann zeta function". It has been abbreviated in the table above. </font>
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| The significance of nine in an irrational constant is also a theme of the [[Feynman point]].
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| ==Section "Equations" (removed)==
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| A [http://en.wikipedia.org/w/index.php?title=Golden_ratio&diff=223928252&oldid=223802162 new section titled "Equations"] was added below "Calculation". I was going to remove the "Equations" and add the following to the bottom of "Calculation". However, the new section was reverted, a decision that I support (but failed to do myself due to lack of boldness). The expressions are quite cute, so here they are:
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| This result can be rearranged
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| :<math>\varphi = \frac{1 + \sqrt{5}}{2} = .5 + \sqrt{5} * .5 = \sqrt{\frac{5 + \sqrt{5}}{5 - \sqrt{5}}}</math>
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| --[[User:Johnuniq|Johnuniq]] ([[User talk:Johnuniq|talk]]) 04:13, 7 July 2008 (UTC) | |
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| == Reverting "Anton's constant" ==
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| I have <s>twice</s> four times now reverted an anonymous contributor who has added "Anton's constant" (value=6) to the table of mathematical constants. No source, no Google hits, no article, wikilinks are to [[6 (number)]] and [[rational number]], so I am assuming this is complete nonsense. [[User:Gandalf61|Gandalf61]] ([[User talk:Gandalf61|talk]]) 10:51, 15 October 2008 (UTC)
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| == Golden ratio ==
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| The table in this article says that the golden ratio is known to 3.14x10^9 places, while 5^0.5 is known to only 10^6 places. But the golden ratio is equal to (1+5^0.5)/2 so they must both be known to the same number of places. Which is right?
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| [[User:Ehrenkater|Ehrenkater]] ([[User talk:Ehrenkater|talk]]) 21:11, 22 November 2008 (UTC)
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| == Still start class? ==
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| Looks pretty good to me... a big fat bold article in the middle of the mathematics vital articles is annoying. [[User:Leon math|Leon math]] ([[User talk:Leon math|talk]]) 22:12, 4 January 2009 (UTC)
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| == Decimal expansions ==
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| Shouldn't we include the approximate decimal values of the constants? I'm surprised no one's said anything about that. I hope I didn't miss anyone's comment... [[User:Leon math|Leon math]] ([[User talk:Leon math|talk]]) 22:15, 4 January 2009 (UTC)
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| :Decimal expansions of constants and, where appropriate, number of known decimal digits are given in a big table near the end of the article. [[User:Gandalf61|Gandalf61]] ([[User talk:Gandalf61|talk]]) 09:38, 5 January 2009 (UTC)
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