Talk:Moser's circle problem

Comment on gap in 'proof'

Just found this (odd) page.

$f(n)=f(n-1)+\sum _{i=1}^{n-1}\left(2-n+ni-i^{2}\right)$

$=f(n-1)-n^{2}+3n-2+\sum _{i=1}^{n-1}\left(ni-i^{2}\right)$

Well, I guess this is like

f(n) - f(n-1) = C(n)

with c(n) cubic, so the answer is a quartic?

Anyone want to go in and sort this out?

Charles Matthews 17:38, 9 Feb 2004 (UTC)

Regular polygon?

What happens if one divides a circle using an inscribed regular polygon (i.e. "case (a)" as described in the "Lemma" section may occur)? More specifically, given a regular n-gon, what is $f(n)$ = <total number of areas created>? - SigmaEpsilon → ΣΕ 16:38, 15 March 2007 (UTC)

WP:Forum, but I guess it's just 2n... 8.8.202.167 (talk) 02:07, 7 January 2008 (UTC)

this question has a highly nontrivial answer: https://math.mit.edu/~poonen/papers/ngon.pdf . The discussion of this in the article (basically just a table, and sourced only to OEIS) is disappointing. ~2026-28744-62 (talk) 15:33, 17 May 2026 (UTC)

Link to circle

Nothing on this page links to circle and yeah, it should. But the text is pretty dense and I'm not going to figure out where. SchmuckyTheCat (talk) 18:13, 25 June 2018 (UTC)

Done, in the first sentence. Nog642 (talk) 07:38, 1 September 2023 (UTC)

Rename article?

This article's title is kind of terrible. I'm pretty sure the phrase "dividing a circle into areas" is a very general phrase, and doesn't specifically refer to this problem. I think the title "Moser's circle problem" would be better. Nog642 (talk) 07:38, 1 September 2023 (UTC)

I would add that the title is just wrong: it is about cutting a disk into parts. Marc van Leeuwen (talk) 15:02, 30 January 2026 (UTC)

Agree, `Moser's circle problem` is also how most online math educators have referred to the problem (e.g. 3b1b). Cccclimie (talk) 05:34, 13 May 2026 (UTC)

Video explanation

The explanation here is helpful: https://www.youtube.com/watch?v=YtkIWDE36qU " This pattern breaks, but for a good reason | Moser's circle problem " — Preceding unsigned comment added by RichardNeill (talk • contribs) 00:50, 5 October 2023 (UTC)

Requested move 13 May 2026

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: moved. (closed by non-admin page mover) Jeffrey34555 (talk) 06:13, 20 May 2026 (UTC)

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Dividing a circle into areas → Moser's circle problem – The original name of this article was chosen way back in 2004, where there was no common way to refer to this problem online. Now, though, the problem is almost always referred to as `Moser's circle problem` when being discussed, especially after 3Blue1Brown's video popularized both the problem in general and specifically the name Moser's circle problem. The current name gives an okay overview of what the problem is, but we no longer need a descriptive title now that there is a precise commonly agreed upon name. Given that an unofficial move request has been sitting in the talk page for three years with no objections (see top of talk page), this move appears to be uncontroversial.

References

Cccclimie (talk) 16:35, 13 May 2026 (UTC)

Support - (This is mostly a repeat of what I said at the Technical Requests page.) Assuming the article does not cover any exercises that are not Moser's circle problem, that should be the title because the current title is a process that does not conform with WP:PRECISION, and per Cccclimie it is unnecessary as a descriptive title. ---DOOMSDAYER520 (TALK|CONTRIBS) 16:58, 13 May 2026 (UTC)

Support. I concur with Cccclimie and Doomsdayer520 in the entirety—the new title would be clearer and more precise (there are many ways to divide a circle into areas (pizza-cutting, for instance), and the article already refers specifically to the one associated with the problem commonly known as Moser's circle problem) and slightly more concise. LieutenantZipp (talk) 19:55, 13 May 2026 (UTC)

The current title is certainly terrible. I suggest notifying WT:WPM of this RM. ~2026-28744-62 (talk) 15:35, 17 May 2026 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Better historical sourcing

I mentioned this above, but: This question was surely known long before 1949. The venue of Moser's publication is one hint in this direction, but also the question of a regular n-gon had already been considered in the 1930s. That question is strictly harder but the answers turn out to coincide for odd n (so you can't solve that version without solving the easy version). See https://math.mit.edu/~poonen/papers/ngon.pdf for historical references to this question. That article and its references should be mined for historical information (and mathematical content!). ~2026-28744-62 (talk) 12:27, 20 May 2026 (UTC)

also the oeis sequence https://oeis.org/A000127 has several links and references that look to be of higher quality than anything currently in this article. ~2026-28744-62 (talk) 12:30, 20 May 2026 (UTC)

I definitely agree that the article could benefit from more history, surely someone documented this problem before moser's 1949 paper (I've found some earlier documentation of the series itself from the oeis page, but not of the link between the series and the circle problem). Cccclimie (talk) 16:31, 21 July 2026 (UTC)