Talk:Mathematical constant

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1 Chaitin's constant?
2 Square roots of 2 and 3?
3 1?
4 New table format: comments?
5 Golden ratio is irrational right?
6 Mill's constant
7 Hafner-Sarnak-McCurley constant
8 Erdos-Borwein constant:algebraic?
9 Landau's constant

[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:

They are mathematical constants
They are not obvious at all—and I find that remark rather insulting to whom spent their lives studying them
They are part of Euler's identity. And I quote from the article: "the identity links five fundamental mathematical constants"
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)

[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)

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