Talk:No-three-in-line problem

No-three-in-line problem 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.

Article milestones
Date	Process	Result
November 27, 2021	Good article nominee	Listed

A fact from this article appeared on Wikipedia's Main Page in the "Did you know?" column on December 15, 2021.

The text of the entry was: Did you know ... that one can place 16 pawns on a chessboard such that no three pawns lie on the same line?

Untitled

"In 1951, Paul Erdős proved the answer." Well, what is the answer? This is very irritating. N Shar 01:23, 12 January 2006 (UTC)[reply]

GA Review

This review is transcluded from Talk:No-three-in-line problem/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: Eviolite (talk · contribs) 01:44, 25 November 2021 (UTC)[reply]

I'll take a look at this. eviolite (talk) 01:44, 25 November 2021 (UTC)[reply]

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This was a nice read. I have some notes here (I didn't think any of these were too big of a deal, but they seemed a bit awkward):

Lead: This might be more of a me problem, but "form a line" wasn't immediately clear; perhaps "lie on the same line" or just "are collinear" with the link would be better. The next sentence could also be clarified a bit (something like "must" instead of "would", and specifying "horizontal row").
- Done. —David Eppstein (talk) 02:21, 26 November 2021 (UTC)[reply]
Under "Small instances": in which two of the pawns attack each other in the middle four squares of the chessboard—the original source states that they must be on Q 4 (d4) and K 5 (e5), which I think is easier to understand (just saying two of them are fixed), and avoids the issue of having a reflection as a solution. Also, I am not sure if linking to each number of solutions is necessary as this problem is not relevant to the numbers themselves. A {{OEIS}} link with the sequence may also be helpful (instead of just having it in the ref).
- Both done. —David Eppstein (talk) 02:21, 26 November 2021 (UTC)[reply]
Under "general placement methods": an example might be helpful for these in terms of understandability (Wikipedia:Make technical articles understandable#Add a concrete example).
- Example added as an illustration. —David Eppstein (talk) 08:37, 26 November 2021 (UTC)[reply]
Under "Greedy placement": but less is known about the version of the problem where all lines are considered—is this necessary or else can it be reworded? I imagine something like this is hard to get a specific reference for, and it seems implied by saying that the specific case has progress, so not a big deal but something to note.
- Er. I guess I walked into that one. There is a specific reference, some specific progress, and more to say about how little is known for this case. It is a recent paper on which I am a coauthor, and so far only citable as a conference version (the journal version is in submission), which is why I omitted it and wrote about it only in vague terms in the article. But because you asked, I have added it to the article. —David Eppstein (talk) 03:37, 27 November 2021 (UTC)[reply]
The applications and generalizations/variations sections seem more technical than the previous sections, but this doesn't seem to be an issue looking at WP:UPFRONT and WP:ONEDOWN (I am probably around the level of one below computational geometry and found it reasonable enough to understand).

Beyond these things that might do well to be changed, the article meets all other criteria, so I am putting it on hold for now. eviolite (talk) 03:02, 25 November 2021 (UTC)[reply]

@David Eppstein: Thanks, everything looks good now (I've looked over the article again and didn't find any issues on a second pass; my last bullet wasn't really a thing to fix but I see it has been addressed anyway), so happy to pass this review. eviolite (talk) 04:26, 27 November 2021 (UTC)[reply]

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 Theleekycauldron (talk) 11:12, 8 December 2021 (UTC)[reply]

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Comment or view
Article history

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... that one can place 16 pawns on a chessboard so that no three pawns lie on the same line? Source: Dudeney 1917, solution to problem 317
- ALT1: ... that although all solved cases of the no-three-in-line problem have the answer 2n, mathematicians have conjectured that the general solution is approximately 1.814n? Source: Pegg 2005
- ALT2: ... that the no-three-in-line problem has been called "one of the oldest and most extensively studied geometric questions concerning lattice points"? Source: Brass, Moser, & Pach 2005
- ALT3: ... that the no-three-in-line problem in discrete geometry was first posed by Dudeney in 1900 as a puzzle about pawns on a chessboard? Source: Knuth 2008, answer to exercise 242

Reviewed: Template:Did you know nominations/Barton, Kinder and Alderson

Improved to Good Article status by David Eppstein (talk). Self-nominated at 19:34, 27 November 2021 (UTC).[reply]

Freshly nominated GA, no other eligibility issues. Hook facts all check out. QPQ has been done. I personally find ALT0 and ALT3 strongest for a general audience (as a mathematician, I like ALT1). I get some Harvard referencing issues: FelsnerLiottaWismath2003 and Lefmann2008 are not cited anywhere? Could be cited or removed @David Eppstein? But that's nothing that would prevent DYK success. —Kusma (talk) 21:50, 27 November 2021 (UTC)[reply]
- Unused refs removed — thanks for catching this. —David Eppstein (talk) 00:24, 28 November 2021 (UTC)[reply]

ALT0 to T:DYK/P4

Defining the grid size

The example refers to a grid with 10 lines each way as a 10x10 grid. I would guess most people define a Sudoku "box" or a tic-tac-toe game in an outline as a 3x3 grid, yet they are composed of 4 lines each way. Is it standard to define a grid by the number of lines each way or by the number of pigeonholes created? Also, the pawns-on-a-chessboard problem obviously counts pigeonholes rather than intersections. Just wondering . . .Charles Fee (talk) 04:38, 31 January 2022 (UTC)[reply]

It's standard, for mathematical treatments of this problem, to give the grid size as the number of positions available for points in each direction, and to put those points on integer coordinates (at the crossings of integer grid lines) rather than at half-integer coordinates (at the center points of grid squares). That is different from the original formulation of the problem, where the points (chess pawns) were placed at centers of chess squares, but it doesn't make any difference to the results for the problem. —David Eppstein (talk) 06:58, 31 January 2022 (UTC)[reply]

Link to Ramsey theory

This problem of maximizing the size of a set such that no $k$ members have sone common property for some small $k$ sounds connected to Ramsey theory, should there be a link to Ramsey theory in a "See also" page? C7XWiki (talk) 01:46, 12 August 2022 (UTC)[reply]