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)

@Solomonfromfinland: 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 • 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? — MFH:Talk 14:36, 28 August 2020 (UTC)

Eh, using a and g seems clear and reasonable. –Deacon Vorbis (carbon • 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)

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

A minor point on notation

The chart in the top right corner uses "agm" in the legend, but the article says to use AGM or agM.

The note under the chart uses agm(1,x) but the article prefers M(1,x). Blitzer99 (talk) 06:31, 24 August 2024 (UTC)