Talk:Mathematical constant

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[edit] Computability / Definability

I think it would be nice to add one or two new rows for the computability / definability of each constant. What do you think? —Preceding unsigned comment added by 134.184.131.153 (talk) 10:40, 6 September 2007 (UTC)

[edit] Chaitin's constant?

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.

Prumpf 14:37, 14 Aug 2004 (UTC)

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.
Prumpf 13:27, 29 April 2006 (UTC)

[edit] Square roots of 2 and 3?

Is there any reason why \sqrt{2} and \sqrt{3} are listed as irrational rather than algebraic? Gkhan 16:45, Sep 7, 2004 (UTC)

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 --Andrew Kepert 07:05, 7 Oct 2004 (UTC)
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. PizzaMargherita 21:23, 1 November 2005 (UTC)

[edit] 1?

Is the number 1 not a mathematical constant? It is used to define the set of natural numbers. --Lambyuk 01:44, 13 May 2005 (UTC)

I'll second that. I think 0, 1 and 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. PizzaMargherita 21:04, 20 November 2005 (UTC)
...so as above, zero, unity and the imaginary unit deserve a place in the table, on the basis that:
  1. They are mathematical constants
  2. They are not obvious at all—and I find that remark rather insulting to whom spent their lives studying them
  3. They are part of Euler's identity. And I quote from the article: "the identity links five fundamental mathematical constants"
  4. They are arguably more fundamental than many other constants in the list
PizzaMargherita 08:53, 26 February 2006 (UTC)
Hurrah, it was added today :) Lambyuk 12:47, 26 February 2006 (UTC)

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? It is also very interesting...

Similarly, i is the same as 1 but for the complex plane. Just a unit, nothing special. —Preceding unsigned comment added by 216.55.199.86 (talk) 20:43, 14 February 2008 (UTC)

[edit] New table format: comments?

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? Paul August ☎

Some of the table rows need to be bigger. I would do it myself, but I don't want to mess it up. -Mihirgk

[edit] Golden ratio is irrational right?

Right? (Are all constants that are irrational-but-not-transcendent algebraic?)

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 x2 - x - 1 = 0 -GTBacchus 21:24, 1 November 2005 (UTC)


[edit] Mill's constant

Is Mill's constant symbolised by theta (as in the table) or phi (as in it's seperate article)? --Saboteur 01:11, 31 March 2006 (UTC)

I corrected the article--Saboteur 07:23, 31 March 2006 (UTC)

[edit] Hafner-Sarnak-McCurley constant

Accoring to this article,D(1)=6/pi^2,not the HSM constant. It uses sigma for the HSM. We should change the symbol.

I just changed the symbol.

[edit] Erdos-Borwein constant:algebraic?

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.

[edit] Landau's constant

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. Fredrik Johansson 22:57, 6 September 2006 (UTC)

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. Giftlite 23:44, 6 September 2006 (UTC)

[edit] Cahen's constant

The article "http://en.wikipedia.org/wiki/Cahen%27s_constant" give the following value : 0.64341054629...

What is the true value ?

cf [1]


Papy77 15:41, 1 February 2007 (UTC)

[edit] Mathematical constint

Is Mathematical constint a good redirect? Constint 12:27, 27 February 2007 (UTC)

[edit] Red links and external links

There are so many red links in the table. We should create some pages and remove the external links. Math Maniac 11:46, 1 March 2007 (UTC)

I created Niven's constant. Over/Under 13:29, 2 March 2007 (UTC)
Thanks. Math Maniac 12:07, 3 March 2007 (UTC)


[edit] MRB Constant

I would like to see if anyone can further expand upon my attempts of researching the following value. 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. http://www.research.att.com/~njas/sequences/A037077[2] 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 “hypercubes," have with respect to "hyperspheres” of dimensions without bound? In what way might this infinite-dimensional constant be used in string theory? 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. 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. last update--Marvin Ray Burns 19:54, 15 April 2007 (UTC)

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):
s = \sum_{n=1}^\infty 2^{-n-1} \sum_{k=1}^{n+1} (-1)^k {n \choose {k-1}} k^{1/k}
I also tried a few other sequence transformations, but didn't end up with anything fruitful. Fredrik Johansson 09:17, 22 April 2007 (UTC)
Fredrik Johansson, I have used your reference to the transform as an example of what is required in the article that I am commissioning.--75.2.16.2 01:32, 23 April 2007 (UTC)

[edit] Notice: Reward for Article!

http://en.wikipedia.org/wiki/Wikipedia:Reward_board#MRB_Constant --Marvin Ray Burns 00:24, 17 April 2007 (UTC)

[edit] Mathematical constants

This page should be merged with Mathematical constants. Jaunt 16:50, 12 April 2007 (UTC)

[edit] Action by Marvin Ray Burns

It is obvious that this change needed to be made: http://en.wikipedia.org/w/index.php?title=Mathematical_constant&diff=122317608&oldid=122257451

The old symbols were larger than the row height of the table. —--Marvin Ray Burns 21:46, 12 April 2007 (UTC) Marburns (talk • contribs) 21:33, 12 April 2007 (UTC).


[edit] Approximate Value

\sqrt{-1} is exact and not an approximate value. 1.\sqrt{-1} 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 " \sqrt{-1}exactly ." I'm going to post it and see if anyone has a better -- more accurate—way of displaying it.--Marvin Ray Burns 01:55, 15 April 2007 (UTC)

[edit] definition

Is the addition of complex number in the definition really appropriate? The only 'complex constant' I've head of is i, because it's a 'unit'. Randomblue (talk) 15:43, 11 December 2007 (UTC)

[edit] 2 questioned constants and some suggestions...

Hi fellow wikipedians! I've been checking all the constants in the list and verified the existence of each red one (except two) via Wolfram MathWorld (entries in that list, or found by searching that site).

There are however two constants which I fail to verify via internet searching: Hughes constant ("Sh") and Jacevicius constant ("J2").

Does anyone else know of these constants and can verify their existence, i.e. justify that they are present in the list? Otherwise, they might be subject for deletion...

Furthermore I find that the following uncategorized constants could be placed in the following fields of mathematics (as far as I understand from checking the articles and/or Wolfram MathWorld);

Any opinions on this? --Dna-Dennis (talk) 15:48, 3 February 2008 (UTC)

'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. -- JocK (talk) 18:41, 5 February 2008 (UTC)
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. Paul August ☎ 18:55, 5 February 2008 (UTC)
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:
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.
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 Wolfram MathWorld nor 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, --Dna-Dennis (talk) 21:38, 5 February 2008 (UTC)
Here's a link to an article about the Hughes Constant: http://aob.oxfordjournals.org/cgi/content/full/89/5/537
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. sam (talk) 05:35, 16 February 2008 (UTC)

[edit] Why are they all pretty small?

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? Brentt (talk) 20:06, 6 May 2008 (UTC)