Talk:Gelfond's constant

Correction

Regarding the new section "Interesting facts", I think that the first sentence should refer to "Gelfond's constant", not Gelfond-Schneider. Also, it isn't clear see why this is interesting. Explaining the link to the j-function would make things clearer.  —Daphne A 12:29, 25 August 2006 (UTC)

Reference for $\pi +e^{\pi }\,$

I added MathWorld's reference for Nesterenko's proof, but can't check it at the moment. Could someone please verify? --Tardis 20:51, 2 April 2007 (UTC)

Isn't "The number $e^{\pi }-\pi \approx$ 19.9991..., is almost an integer." and "Notice that $e^{\pi }-20=3.140692633\approx \pi$ itself." the same thing mathematically?

Yes, but it's coming at the same fact from two different perspectives. That makes the fact much easier to process for people unfamiliar with Gelfond's constant, and the principle applies for any mathematics-related articles in general. --54x 08:04, 4 October 2007 (UTC)

Numerical Value

The iteration was wrong. I corrected it with the help of Wolfram's website and a spreadsheet but I do not understand why it works. Anybody would like to give a motivation for this formula? And what will seed values other than $1/{\sqrt {2}}$ do? HannsEwald (talk) 11:11, 30 November 2007 (UTC)

It does work. I don't know why. I'm not sure that it is computationally that useful. I suppose you just need a calculator with sqrt but middle school kids have calculators that will do e^pi. Using 50 place accuracy it gets the best accuracy after 5 iterations. 23+65/462=23.1406926406926... gives 11 digits correctly.--Gentlemath (talk) 06:05, 30 March 2009 (UTC)

(-1)^(-i)

The algebraic manipulation leading to (-1)^(-i) is interesting, but also a bit confusing: it should be explained why one cannot write e^π = (e^(-iπ))^i = (-1)^i , or the -1 in the above as e^(-iπ), which yields e^(-π) = 0.04.... — MFH:Talk 22:32, 24 October 2009 (UTC)

One can write either of these things. Complex exponentiation is multivalued, and for the Gelfond–Schneider theorem to apply it suffices that one of the possible values of (−1)⁻ⁱ is the number we want, i.e., e^π. In general, the values of (−1)⁻ⁱ = (−1)ⁱ are all numbers of the form e^(2k+1)π, where k is an integer. — Emil J. 13:15, 2 November 2009 (UTC)

While e^π is a value of (-1)ⁱ, it is misleading to write e^π = (e^(iπ))^(-i), since the latter is really a set of values. —Preceding unsigned comment added by 209.147.97.202 (talk) 20:15, 23 April 2011 (UTC)

Instance citable in Scientific American?

The main page of this article could be improved if Gelfond's constant was ever cited by Martin Gardner in his 1960s and 1970s magazine column, Mathematical Games, (published for a significant period of time in Scientific American) magazine? If anybody knows of an instance where the number was used and cited, please mention it here, or in the main page of this article.

If Gelfond's constant is relevant to the volume of a multi-dimensional sphere, it ought to pop up frequently in a "tiling the sphere" game. There was at least one column by Martin Gardner where he discussed the minimum number of radio towers to place on the Moon, or on Mars, and that is something that is definitely related to the concept of "tiling a sphere. Since minimizing the number of radio towers in a situation like that involves economization and conservation of limited resources, there are probably a number of computer military simulations about the establishment or destruction of radio broadcasting/receiving towers. Dexter Nextnumber (talk)

How about in hex?

Just as there are lots of people that like staring at decimal expansions of irrational numbers, there are bound to be lots of people who get the same kind of satisfaction staring at hexadecimal expansions.

I think the main article could be improved if someone were to give the hexadecimal equivalent of the decimal series in the article. True, they are the same number but for the shift in base, but I still think it would improve the main article.

And giving it to 20 digits might be helpful also. Dexter Nextnumber (talk) 23:00, 14 February 2010 (UTC)

Switching number and exponent?

If e to the power of pi is Gelfond's constant, then what is pi to the power of e?

The main article should indicate whether this other constant has a name, or whether it has any interesting properties at all. Dexter Nextnumber (talk) 04:10, 15 February 2010 (UTC)

pi**e = 22.45915771836 87.102.44.18 (talk) 15:53, 27 April 2016 (UTC)

Geometric peculiarity reference?

The reference [4] in Geometric peculiarity is not complete. Can it be verified? "Connolly, Francis. University of Notre Dame[full citation needed]"

Is the Geometric peculiarity statement even valid?

John W. Nicholson (talk) 02:23, 6 January 2013 (UTC)

I don’t know about the reference, but the statement is obviously valid, this is just the power series for exp.—Emil J. 15:16, 7 January 2013 (UTC)

Reference for the name 'Gelfond's constant' ?

The article does not provide any reference for the name 'Gelfond's constant'. As far as I see, the name was given by MathWorld, but Wikipedia does not have to follow without secondary source. The attribution to Gelfond is rather gratuitous and not very respectful of him and previous mathematicians. 147.210.245.180 (talk) 16:56, 24 September 2013 (UTC)