Talk:Arithmetic–geometric mean

Base case
Wouldn't it be simpler to define a[0]=x and g[0]=y and then iterate? The [1] and [n+1] cases are really the same. Or, to keep the g<a property, then a[0]=max(x,y) and g[0]=min(x,y). --Macrakis (talk) 18:46, 29 October 2017 (UTC)
 * That does sound like a good idea. Find us a source that does it that way. Dicklyon (talk) 22:16, 29 October 2017 (UTC)
 * Well, Mathworld for one. I'll see if I can find a better source. --Macrakis (talk) 23:11, 29 October 2017 (UTC)
 * That looks good enough. I'd support re-writing it that way, citing Mathworld. Dicklyon (talk) 23:59, 29 October 2017 (UTC)

Suggested link
I suggest a link at the top of the article to redirect those looking for the Inequality of arithmetic and geometric means. ThomasHales (talk) 00:13, 11 June 2018 (UTC)
 * the link is Already there at See Also at the bottom, no? Cuzkatzimhut (talk) 02:58, 11 June 2018 (UTC)

Transcendental?
Is the AGM of 6 and 24 (given in the example), transcendental? More generally, is the AGM of two algebraic numbers necessarily transcendental? If not, when is it transcendental and when is it not?--Solomonfromfinland (talk) 16:44, 7 December 2018 (UTC)


 * Article talk pages are for discussing improvements to articles. If you have general questions, you can try at the (in this case) Math ref desk.  –Deacon Vorbis (carbon &bull; videos) 16:50, 7 December 2018 (UTC)
 * That's what i was trying to do: get this article improved by telling when the AGM would or would not be transcendental.--Solomonfromfinland (talk) 06:07, 8 December 2018 (UTC)
 * Due diligence on elliptic integrals, as clearly explained in the following. An article is infinitely improved by reading. Read on! Cuzkatzimhut (talk) 15:43, 8 December 2018 (UTC)

inconsistent $g_n$ vs $b_n$
Someone has found it a good idea to call the sequence of geometric means $g_n$ instead of $b_n$ as all classical authors do; this change is present in the first few lines but later in the page, $b_n$ is used. I'm not totally against $g_n$ although I find $b_n$ (i.e., "a and b" rather than "a and g") way more natural in spite of the initials of "arithmetic & geometric", but I do think the page should use the same convention everywhere (and so I suggest to replace the instances of g_n by b_n). What do others think? &mdash; MFH:Talk 14:36, 28 August 2020 (UTC)
 * Eh, using $a$ and $g$ seems clear and reasonable. –Deacon Vorbis (carbon &bull; videos) 14:44, 28 August 2020 (UTC)

Semi-protected edit request on 7 November 2021
The "External links" section contains a link to a presumed calculator website, but the website itself is inoperable, and the only message displayed is "Always an issue with this site so I took it down." which was posted on the 4th of December 2012. I suggest the section to be removed AceMuffins (talk) 17:14, 7 November 2021 (UTC)


 * ✅ Thanks for pointing it out! MrOllie (talk) 17:17, 7 November 2021 (UTC)