Talk:Fermat's right triangle theorem/GA1

GA Review

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Reviewer: RoySmith (talk · contribs) 21:05, 24 March 2021 (UTC)[reply]

I'm starting this review. My plan is to do two major passes through the article, first for prose, the second to verify the references. In general, all my comments will be suggestions which you can accept or reject as you see fit. -- RoySmith (talk) 21:05, 24 March 2021 (UTC)[reply]

Checklist

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):
It is factually accurate and verifiable.
a (reference section): b (citations to reliable sources): c (OR): d (copyvio and plagiarism):
It is broad in its coverage.
a (major aspects): b (focused):
It follows the neutral point of view policy.
Fair representation without bias:
It is stable.
No edit wars, etc.:
It is illustrated by images and other media, where possible and appropriate.
a (images are tagged and non-free content have fair use rationales): b (appropriate use with suitable captions):
Overall:
Pass/Fail:

Prose

Lead section

Regarding the ordering of the 6 formulation bullet-points, if this is commonly known as "Fermat's right triangle theorem", it seems odd that forulation is not the first bullet. Is there some logic to why they're in that order?

Regarding the accompanying figure, why the circles? I haven't yet read the rest of the article, so maybe that's explained later on, but at this point I'm just left wondering about them. The caption doesn't refer to them at all, hence the mystery.

Squares in arithmetic progression

"In 1225, Fibonacci was challenged to find". Who challenged him? I have a Monty Python-esqe mental image of some rogue leaping out of the shadows, sword drawn, demanding a proof. The sentence also parses ambiguously. I initially read it as listing several properties the triples should have: 1) they are equally spaced, 2) they form an arithmetic progression, and then started getting parse failures. I think (but I'm not sure), "which" is better than "that" here, but could also be left out completely. So, something like, "...for triples of equally spaced square numbers (i.e. an arithmetic progression), and for the spacing between these numbers (which he called a congruum)", although I'm not sure that's what you're trying to say.

(pausing here, I'll pick it up later, but this may be slow going)

"they would form two integer-sided right triangles in which the pair {\displaystyle (d,b)}(d,b) gives one leg and the hypotenuse of the smaller triangle and the same pair also forms the two legs of the larger triangle." Are a, b, c, d here the same a, b, c, d in the figure at the top? I think not, and that's really confusing. If I'm understanding this correctly, this is (a, c) in the figure.

You refer to "one leg and the hypotenuse". From the examples here, it looks like it's always the shorter leg. Is it always the shorter leg? If so, why not just say "the shorter leg" and remove the ambiguity. Or is this a hedge against a 45-45-90 triangle?

Areas of right triangles

"Fermat was inspired not by Fibonacci but by an edition of Diophantus published by Claude Gaspar Bachet de Méziriac". Add the dates, "not by Fibonacci's 1225 treatment, but by the 15xx (16xx?) edition of..." Looping back to the lead, the first date mentioned in the article is 1225, but it took me a bit to sort out that it's referring to what Fibonacci did 350 years prior to Fermat. The lead should mention up front when Fermat published his theorem.

Fermat's proof

"he wrote a proof in his copy of Bachet's Diophantus, which his son discovered and published posthumously." Clarify that you're talking about Fermat's son, not Bachet's son.

That does it for my comments on the prose. I'll come back and do another pass for the other GA criteria, but probably not today.

Notes section

"The fact that there can be no two right triangles that share two of their sides". We may be back into snot-nosed kid territory, but this is only true if the triangles are non-overlapping. I'm not sure, but it's possible it also only applies in a plane. Which brings me to wondering if somewhere in the lead you should mention that everything here only applies to plane geometry.

References

No issues with non-WP:RS.