Talk:Erdős–Anning theorem

Erdős–Anning theorem 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: December 6, 2023. (Reviewed version).

GA Review

Passed. L'Orfeo^{Son io} 14:23, 4 December 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:Erdős–Anning theorem/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: L'OrfeoGreco (talk · contribs) 09:06, 5 December 2023 (UTC)[reply]

For a start, I would like to congratulate the contributor(s) on their general effort. I want them to be certain that no corrective comment made by myself is meant to offend them personally or diminish the importance of their contribution to the Wikipedia project. Having made that clear, we can now proceed to my comments and/or suggestions, formulated on the basis of the GA promotion criteria:

1st Criterion: Well-written

a. Language

The article's prose is of an enjoyable pace; its vocabulary is neither too technical, nor too simplistic. Some expressions could be altered to eradicate ambiguity. Bellow are listed my comments and suggestions:

Lead Section. However, it is possible for any finite number of points to have integer distances and not be on a line.

Comment: I take this to be the clarification that the logical equivalence of "if and only if" does not hold for the theorem in question. Expressing this point in a clear manner would probably be of benefit to the random reader.

May I suggest: However, it is... on a line, that is, the equivalence does not hold.

(or something of the sort) L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

Rewrote, because this comment suggests that the intended meaning was not clear: "The theorem cannot be strengthened to give a finite bound on the number of points: there exist arbitrarily large finite sets of points that are not on a line and have integer distances." —David Eppstein (talk) 00:11, 6 December 2023 (UTC)[reply]

Why, the initial expression was not what I took it to be; I overlooked the crucial word "finite". In any case, the rephrasing is certain to further aid understanding. Thank you. L'Orfeo^{Son io} 07:03, 6 December 2023 (UTC)[reply]

Lead Section. The Erdős–Anning theorem inspired the Erdős–Ulam problem on the existence of dense point sets with rational distances.

Suggestion: Link "dense point sets" to dense set to aid understanding (it is linked bellow, but this one is the first mention). L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

Ok, done. —David Eppstein (talk) 00:11, 6 December 2023 (UTC)[reply]

Lead Section, Although there can be no infinite non-collinear set of points with integer distances, there are infinite non-collinear sets of points whose distances are rational numbers

Suggestion: Link "collinear" to Collinearity. L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

Linked first use, in next section. —David Eppstein (talk) 00:11, 6 December 2023 (UTC)[reply]

Rationality versus integrality. For instance, the subset of points on a unit circle obtained by repeatedly rotating by the sharp angle in a 3–4–5 right triangle has this property

Comment: My being more than familiar with mathematics allows me to understand that the "3–4–5 right triangle" is one whose sides have a 3:4:5 ratio. However, it is probable that the random reader won't be able to understand the sentence without some clarification, be it a wikilink or a short reference.

Suggestion: You could use the Special_right_triangle#Common_Pythagorean_triples wikilink, or add the phrase "3:4:5 side ratio", or something of the like. L'Orfeo^{Son io} 11:28, 5 December 2023 (UTC)[reply]

Ok, expanded with wikilink. —David Eppstein (talk) 00:11, 6 December 2023 (UTC)[reply]

Proof. Thus, X lies one of...

Comment: I reckon what was meant here is that it "lies on one of". L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

Yes, fixed. —David Eppstein (talk) 00:16, 6 December 2023 (UTC)[reply]

Proof. By a symmetric argument,...=j

May I suggest that you add the missing range with 0 <= j <= d(B,C)? L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

Ok, done. —David Eppstein (talk) 00:16, 6 December 2023 (UTC)[reply]

Proof. every point set with integer distances and diameter δ has size Ο(δ)

Comment: The Ο(δ) part is not clarified elsewhere.

Suggestion: Maybe add a short descriptive sentence, so that the reader can fully understand what Ο(δ) is. L'Orfeo^{Son io} 11:31, 5 December 2023 (UTC)[reply]

Linked big O notation as an explanation. —David Eppstein (talk) 00:16, 6 December 2023 (UTC)[reply]

Proof. Image caption. Given three non-collinear points A, B, C with integer distances from each other (here, the vertices of a 3–4–5 right triangle)

Suggestion: Link "vertices" to Vertex (geometry). L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

Ok, done. —David Eppstein (talk) 00:42, 6 December 2023 (UTC)[reply]

Proof. Image caption.

Comment: Here, the term "hyperbolas" is preferred over the "hyperbolae" form, used in the Proof section's main text.

Suggestion: To ensure style uniformity, I suggest that you pick one of the two forms. L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

Ok, switched to "hyperbolas" in an attempt to be less technical than "hyperbolae". —David Eppstein (talk) 00:42, 6 December 2023 (UTC)[reply]

Accurate thought, thank you. L'Orfeo^{Son io} 07:09, 6 December 2023 (UTC)[reply]

Proof. Image caption. ...differ by an integer lie on a system of hyperbolas and degenerate hyperbolas...

I suggest that you either describe the term degenerate hyperbolas or provide the reader with a related wikilink. L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

Description added in the second bullet of the proof. —David Eppstein (talk) 00:42, 6 December 2023 (UTC)[reply]

b. Manual of Style

The Lead Section is excellent in terms of content summarisation.The rest of the sections are OK (see "Broad in its coverage" for a suggestion). References are uniform in style and properly tagged for accessibility. Rest OK. L'Orfeo^{Son io} 11:35, 5 December 2023 (UTC)[reply]

2nd Criterion: Verifiable

a. List of all references included

Yes. L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

b. Reliable sources are cited inline

Yes. However, I would like to point out that certain sentences are substantiated by way of citing the whole paper, whilst the specific passage is to be found in no more than one or two pages. Such instances include:

"Rationality versus integrality" section. For instance, the subset of points... in the circle.

Comment: 224-213=11 pages from Heiko Harborth's work are cited; judging by the sentence's length, I guess that only some of them contain the elements required to substantiate this portion of the passage.

Suggestion: It would be great if the nominator gave (a) specific page(s).?
L'Orfeo^{Son io} 13:43, 5 December 2023 (UTC)[reply]

"Rationality versus integrity" section, Adccording to... -Annining theorem.

Comment: The reference here is not just "Erdős, Paul (1985), "Ulam, the man and the mathematician" (PDF), Journal of Graph Theory, 9 (4): 445–449, doi:10.1002/jgt.3190090402, MR 0890232", for the specific mention is made on pages 447 and 448.
L'Orfeo^{Son io} 13:43, 5 December 2023 (UTC)[reply]

"Higher dimensions" section, As Anning... being integral. The quote is to be found on page 600.
L'Orfeo^{Son io} 13:43, 5 December 2023 (UTC)[reply]
Book sources would require specific page numbers, however the standard for journal papers or for papers within edited volumes is to cite the whole page range. This full page range is a necessary part of an accurate citation. The citation templates do not make any provision for citing both the full page range of an article and a specific page or pages within it. —David Eppstein (talk) 00:45, 6 December 2023 (UTC)[reply]
It did occur to me that a contributor of the nominator's experience would certainly have known what seems to be stylistically typical with articles of this sort. Nevertheless, I wanted to be certain, so thank you for the clarification. L'Orfeo^{Son io} 07:34, 6 December 2023 (UTC)[reply]

c. No original research

None traced. L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

d. No copyright violations

None traced by Earwig's copyvio. L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

3rd Criterion: Broad in its coverage

a. Main aspects addressed

In general, the theorem is presented in depth.

However, the "Higher dimensions" section's ending felt somewhat abrupt, as if there was something more to be said. I also noticed that in the lead section it is stated that The same result holds in higher dimensional Euclidean spaces, but no specific reference to "Euclidean spaces" is made in the "Higher dimensions" section.

Maybe the nominator could elaborate a bit on that, at the very least add the "Euclidean spaces" phrase somehow, so as to match the Lead Section. L'Orfeo^{Son io} 11:39, 5 December 2023 (UTC)[reply]

If you look at the source for this statement, it is equally abrupt. There is not much elaboration that could be made without original research. —David Eppstein (talk) 00:47, 6 December 2023 (UTC)[reply]

I see. I was wondering whether anything could be done to make the link between the phrases "in higher dimensional Euclidean spaces" (Lead Section) and "in n-dimensional space" ("Higher dimensions" section) more direct.

That is, if no assumption can be made on what the "n-dimensional space" is based solely on the Erdős–Anning paper (for this would constitute original research), then how can the related clarification "The same result holds in higher dimensional Euclidean spaces" be included in the Lead Section? L'Orfeo^{Son io}

In this context, n-dimensional space and higher dimensional Euclidean spaces are the same thing. It is just a rephrasing of the same statement, rather than copying the exact words of the source a second time. —David Eppstein (talk) 07:59, 6 December 2023 (UTC)[reply]

I see. Thank you for your swift answers. L'Orfeo^{Son io} 08:02, 6 December 2023 (UTC)[reply]

6th Criterion: Illustrated

a. Media are of clearly stated copyright statuses

Yes. L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

b. Media are relevant

Yes. Moreover, two of the article's images were meticulously made by the nominator; they are aesthetically impressive and most helpful to the reader. L'Orfeo^{Son io} 11:27, 5 December 2023 (UTC)[reply]

Review result

All criteria checked. Awaiting the nominator's responses. L'Orfeo^{Son io} 13:52, 5 December 2023 (UTC)[reply]
An excellent article, presented in enjoyably paced and accurately worded prose and impressively illustrated. I would like to congratulate the nominator once again! Promoted to GA status. L'Orfeo^{Son io} 08:06, 6 December 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.