Talk:Quadrature (geometry)

I restored the article for the following reasons.

1. Such actions shouldn't be made without full discussion.
2. The article has 5 interwikis which are the real articles, not redirections.
3. The term quadrature had no connection with Numerical integration for 2000 years (until Wallis time), it was considered only as geometrical construction. The article's content also doesn't contain Numerical integration.

LGB (talk) 11:09, 29 April 2013 (UTC)

: I've added a new section Definite integral#Geometrical to reflect this separate method. Fgnievinski (talk) 01:40, 30 April 2013 (UTC)

:: OK. Maybe it should be useful to add the same link (Main article: Quadrature (mathematics)) into Numerical integration#History. LGB (talk) 11:05, 30 April 2013 (UTC)

{{requested move/dated|Quadrature (mathematics)}}

:Quadrature (geometry) → {{no redirect|Quadrature (mathematics)}} – This would revert a move done without discussion by {{u|Fgnievinski}} on 25 September 2023. After the move, they removed the part of the article devoted to the use of the term in integral calculus, probably because they consider unrelated the two uses of term (area conputation and integral computation). I edited recently the article, and the new version shows that the two meanings are deeply related and deserve to be explained in the same article. So, the present vesion of the article is no more restricted to geometry, and this makes the article title confusing. Also, AFAIK, the article covers presently all uses of "quadrature" in mathematics, and the proposed title is thus the most correct one. D.Lazard (talk) 16:40, 22 April 2025 (UTC) — Relisting. Bensci54 (talk) 16:36, 30 April 2025 (UTC)

:While we are discussing quadrature in Euclid, etc. it would be good to give a brief synopsis of Elements book 2. It’s e.g. unfortunate not to mention the gnomon (difference of two squares) here — and our article about gnomons does a poor job explaining its context and practical use for greek geometry. –jacobolus (t) 16:56, 22 April 2025 (UTC)

:Oppose: the mathematical technique of numerical quadrature is outside of the scope of the present article. It notes the term "quadrature" is old-fashioned and the modern term is "squaring". So, Squaring (geometry) seems the preferred term. fgnievinski (talk) 07:39, 23 April 2025 (UTC)

::You misread the lead: it says that in the sense of buildong square the modern word is squaring. But the next paragraph and the last section of the article say essentially that "quadrature" was a synonym of "integral" (until the 19th century, I believe, but I have no source fo that).

::It is clear that numerical computation of integrals does not belong to this article, but the fact that quadrature was a synonym of integral has nothing to do with numerical computation and belongs to this article at least for historical reasons. Note that the article has a section {{alink|Integral calculus}} that is not really about geometry. Also, the phrases "solving a differential equation by quadrature" and "reducing a differential equation to quadrature" are often used in Wikipedia and must be redirected somewhere. Numerical quadrature is a wrong link for them, since these phrases have nothing to do with numerical computation. These phrases could be redirected to ordinary differential equation, but, in any case, "quadrature" deserve to have a WP:Broad concept article, and this page is the natural place for that. D.Lazard (talk) 08:56, 23 April 2025 (UTC)

:::If numerical computation of integrals does not belong to this article, then it cannot be titled "Quadrature (mathematics)", as numerical methods are part of mathematics.

:::Also note tkhe current article only has a section about history. As such, it could be merged into Area#History. fgnievinski (talk) 12:08, 23 April 2025 (UTC)

:The parenthetical "geometry" seems possibly misleading, since what we are talking about in the original meaning of the term is not geometry in a broad modern sense, but specifically an idiosyncratic quirk in Euclid's Elements and some other works of Greek deductive geometry, in which the areas of two arbitrary shapes could be compared by (sometimes infinite) cut-and-paste reconstruction of each into a single square, which could then be compared by side length. My (amateur and unstudied) understanding is that other ancient geometry styles (Babylonian, Egyptian, Indian, Chinese, ...) including practical Greek/Roman work measured areas in more or less the modern style, by comparing the area of an arbitrary shape to the area of a bunch of little unit squares. {{pb}} It's a bit of a tricky organization problem, and somewhat contrary to usual Wikipedia organization guidelines, but I think it might be fine to focus on varying historical meanings of the word quadrature in this article rather than specifically on one sense of it, since that is likely to be helpful to readers unfamiliar with the term who come here to try to get a basic idea what it means. That would also be the least work compared to the content we already have, which is sort of a mishmash. If we go for such a scheme, then the article should include some discussion of the history of integration and then of numerical integration. In that version it would be fine to go for the title Quadrature (mathematics). {{pb}} An alternative would be to make the article's focus more narrow, targeted to the version in Euclid (etc.), but then include a section right after the lead discussing the various other meanings of the word, sort of a mini disambiguation page, linking out to articles about the history of integration, modern numerical integration, etc. {{pb}} In any event, @D.Lazard, I'm not a big fan of the new first sentence, "quadrature is an old-fashioned term ...", which doesn't seem to keep with expectations about Wikipedia's tone/style. –jacobolus (t) 17:34, 30 April 2025 (UTC)

::I like the counterproposal of an article about the term "quadrature", titled Quadrature (mathematics), touching on numerical integration and possibly merging portions into Area#History. fgnievinski (talk) 15:47, 2 May 2025 (UTC)

:Support: Quantifying an area by quadrature has been a mainstay of mathematical development from the beginning. Reducing the topic to an aspect of geometry is wrong. — Rgdboer (talk) 22:49, 1 May 2025 (UTC)

:As one more aside: does anyone have any clear survey works by mathematical historians about quadrature as found in Euclid etc.? It would be helpful to describe this in a way that explains how the concept evolved in its early history, what terminology was used in Greek ("τετραγωνισμὸς"?) and what it meant originally vs. for later commentators, some about how relevant proofs were written in Greek, and so on. I am an amateur at best here (as are the rest of us, I am guessing). –jacobolus (t) 18:07, 2 May 2025 (UTC)