Talk:Polygonalization

Polygonalization has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.
Review: February 19, 2023. (Reviewed version).

A fact from Polygonalization appeared on Wikipedia's Main Page in the Did you know column on 17 March 2023 (check views). The text of the entry was as follows:

Did you know... that a simple polygon through all the points of a three-by-three grid must pass straight through some of the points, rather than turning at each of them?

A record of the entry may be seen at Wikipedia:Recent additions/2023/March. The nomination discussion and review may be seen at Template:Did you know nominations/Polygonalization.

Wikipedia

Generation: I thought this was solved?

I read the paper "Connecting Polygonizations via Stretches and Twangs" [1] at least ten years ago. I thought that this set of moves sufficed to connect the space of polygons for a fixed set of points in the plane? 73.5.136.47 (talk) 18:24, 22 November 2022 (UTC)[reply]

They connect a larger space, the "polygonal wraps". The intermediate steps of the connection paths are not polygonalizations. If all you want to do is connect a larger space, the problem is much easier. For instance, the polygonalizations are contained in the space of planar straight line graphs, which are trivially connected by edge insertions and deletions. —David Eppstein (talk) 18:41, 22 November 2022 (UTC)[reply]

GA Review

Passed. Bryan Rutherford (talk) 20:13, 19 February 2023 (UTC)[reply]

The following discussion 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.

This review is transcluded from Talk:Polygonalization/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: Bryanrutherford0 (talk · contribs) 19:59, 15 February 2023 (UTC)[reply]

GA review (see here for what the criteria are, and here for what they are not)

It is reasonably well written.
a (prose, spelling, and grammar): b (MoS for lead, layout, word choice, fiction, and lists):
The prose standard is excellent, and the article satisfies the required sections of MoS. ~~One minor note for clarity: in "Existence", "requiring no three to be in a line is too strong of an assumption" would be more clear with something like "unnecessarily strong" rather than "too strong".~~
Ok, done. —David Eppstein (talk) 02:27, 19 February 2023 (UTC)[reply]
It is factually accurate and verifiable.
a (reference section): b (citations to reliable sources): c (OR): d (copyvio and plagiarism):
The article has a reference section with citations to published sources. I'm not seeing signs of plagiarism from online sources. The sources I could access supported the claims they were cited from. Only one concern: in "Counting", the phrase "at most $54.6^{n}$ polygonalizations" seems to use a rounded figure (the abstract of the cited article says $54.543^{n}$ ); I think it would be better to follow the authors and round where they did.
The intent was to provide the same number of significant figures (three) for both the lower bound and the upper bound. The base of the exponential has been rounded up from 54.543 because rounding up an upper bound in this way preserves correctness while rounding down might not. I do not believe that the upper bound is likely to be close to the actual maximum number of polygonalizations (it is merely the best we can currently prove) so reporting it in greater precision would not be more informative. As evidence that the reference authors themselves don't think that there is some magic reason to round to five digits, see [2] where they rounded to four instead. Another online reference for this problem [3] rounds to two digits. —David Eppstein (talk) 02:27, 19 February 2023 (UTC)[reply]
Fair enough! -Bryan Rutherford (talk) 20:13, 19 February 2023 (UTC)[reply]
It is broad in its coverage.
a (major aspects): b (focused):
I'm not thinking of any other major aspects of the topic that the article doesn't currently address. It also maintains suitable focus and doesn't wander into trivia or tangentially related material.
It follows the neutral point of view policy.
Fair representation without bias:
The article maintains a suitably neutral perspective, not e.g. overblowing the significance of the topic r taking sides on proposed solutions to unsolved problems.
It is stable.
No edit wars, etc.:
The article is stable and has not changed significantly since its creation last year.
It is illustrated by images and other media, where possible and appropriate.
a (images are tagged and non-free content have non-free use rationales): b (appropriate use with suitable captions):
The article is illustrated with clear, relevant images, which have suitable licenses. The first image is an excellent article starter, but the second (the "unflippable polygon") could be improved. Its current placement at the top of the body comes far before the portion of the article ("Generation") that discusses "flipping" pairs of edges to generate new polygons from existing ones, making the purpose of the image unclear where it appears. Indeed, the caption is currently the only place in the article where the word "unflippable" appears, so that I even failed to find an explanation when I searched for that term. This image should be moved to a place in the body where its relevance is more clear, and some elaboration in the caption would probably help, too.
Overall:
Pass/Fail:
An interesting article, and well written! ~~I have only a few small bits of feedback to offer here; it's very close to the standard. -Bryan Rutherford (talk) 22:38, 16 February 2023 (UTC)~~ I'm satisfied that it meets the standard and am approving it. Good work! -Bryan Rutherford (talk) 20:13, 19 February 2023 (UTC)[reply]

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.

Did you know nomination

The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: promoted by Cielquiparle (talk) 18:28, 10 March 2023 (UTC)[reply]

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Comment or view
Article history

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... that a simple polygon through all the points of a 3 × 3 grid must pass straight through some of the points, rather than turning at each of them? Source: Chow et al, doi:10.1080/0025570x.2021.1869493
- ALT1: ... that because the travelling salesman tour of points in the plane cannot cross itself, it forms a polygonalization of the points? Source: Quintas & Supnick, JSTOR 2313333
- Reviewed: Template:Did you know nominations/Muhammad Kamil Tadjudin

Improved to Good Article status by David Eppstein (talk). Self-nominated at 02:29, 20 February 2023 (UTC). Post-promotion hook changes for this nom will be logged at Template talk:Did you know nominations/Polygonalization; consider watching this nomination, if it is successful, until the hook appears on the Main Page.[reply]

General: Article is new enough and long enough
New enough: Long enough:

Policy: Article is sourced, neutral, and free of copyright problems
Adequate sourcing: Neutral: Free of copyright violations, plagiarism, and close paraphrasing:

Hook: Hook has been verified by provided inline citation
Cited: Interesting:

QPQ: Done.

Overall:

@David Eppstein: Good article. Onegreatjoke (talk) 02:47, 20 February 2023 (UTC)[reply]