Talk:Squaring the circle/GA1

GA Review

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Reviewer: Ovinus (talk · contribs) 00:28, 23 May 2022 (UTC)

Exciting. Article looks good on first glance. Ovinus (talk) 00:28, 23 May 2022 (UTC)

Thoughts:

• because there are rational numbers arbitrarily close to pi, and many such constructions have been found – sure, but I think more to the point, there are constructible numbers arbitrarily close to pi. The more-interesting constructions, like Ramanujan's, use irrational numbers. Ovinus (talk) 00:58, 23 May 2022 (UTC)
  • The irrational constructible numbers do not provide more-accurate approximations than the rational ones; how could they? But I think the explanation for why good approximations exist is misplaced in the lead, so I removed the "because" clause. —David Eppstein (talk) 07:07, 25 May 2022 (UTC)
    • Cool. And all I meant was that a reader might think that only constructions of rational approximants are particularly good, or even possible, instead of the many approximations which construct irrational lengths. I like how it is now. Ovinus (talk) 07:43, 25 May 2022 (UTC)
• Perhaps name the method that Antiphon used (method of exhaustion) Ovinus (talk) 00:58, 23 May 2022 (UTC)
  • Done. —David Eppstein (talk) 07:07, 25 May 2022 (UTC)
• "since any polygon can be squared" was this known? (I assume you just triangulate it) Ovinus (talk) 00:58, 23 May 2022 (UTC)
  • I added a footnote to Euclid II.14. —David Eppstein (talk) 07:12, 25 May 2022 (UTC)
• Mention neusis construction in History Ovinus (talk) 00:58, 23 May 2022 (UTC)
  • Do we have a neusis construction for squaring the circle? I don't think the use of the quadratrix or Archimedes spiral are quite the same thing? My impression is that neusis, at least in its more strict definitions, can solve some higher-order algebraic problems like trisection or cube-doubling but isn't powerful enough for circle-squaring. Knorr's section on Archimedes' neuses discusses only trisection and heptagon construction (with also the tangent to a spiral early in the Archimedes chapter), for instance. —David Eppstein (talk) 07:28, 25 May 2022 (UTC
    • Ah I should have been more specific. Indeed neusis can't solve this problem. I meant in the sentence "Therefore, more powerful methods than compass and straightedge constructions..." but perhaps there are other constructions you didn't think fit to mention. Neusis was just the one that came to mind, since it can solve those problems. (Didn't know paper folding could though!) Ovinus (talk) 07:43, 25 May 2022 (UTC)
      • Ok, that makes more sense. Added. Fortunately the existing reference already covers this. —David Eppstein (talk) 18:35, 25 May 2022 (UTC)
• I'd like one sentence in History that says something about later professional work being mostly about finding clever approximations Ovinus (talk) 00:58, 23 May 2022 (UTC)
  • Ok, added. —David Eppstein (talk) 07:01, 26 May 2022 (UTC)
• "roughly and informally" what is the difference between these things Ovinus (talk) 00:58, 23 May 2022 (UTC)
  • I tightened the wording there and now neither word appears. —David Eppstein (talk) 06:56, 26 May 2022 (UTC)
• In Construction by Konchanski, what is r in the diagram? Radius of the circle? Ovinus (talk) 00:58, 23 May 2022 (UTC)
  • Appears to be, yes. I updated the caption to say so. —David Eppstein (talk) 00:38, 26 May 2022 (UTC)
• Any info on how Ramanujan found his approximation? Or was this one of his "determined empirically" pieces of divine inspiration Ovinus (talk) 00:58, 23 May 2022 (UTC)
  • Ramanujan writes "This value was obtained empirically, and it has no connection with the preceding theory." It's easy to obtain it from the continued fraction representation of
    $$\pi ^{4}=97+{\cfrac {1}{2+{\cfrac {1}{2+{\cfrac {1}{3+{\cfrac {1}{1+{\cfrac {1}{16539+\cdots }}}}}}}}}}$$
    by stopping just before the huge term 16539. Why $\pi ^{4}$ has a huge term in its continued fraction is beyond me, though. —David Eppstein (talk) 19:16, 25 May 2022 (UTC)
    • Fascinating stuff. Ovinus (talk) 07:56, 26 May 2022 (UTC)
• "seem to have become prevalent" is the source cautious enough for this, or is "became prevalent" fine Ovinus (talk) 00:58, 23 May 2022 (UTC)
  • Replaced by "became prevalent". —David Eppstein (talk) 19:47, 25 May 2022 (UTC)
• I named Milü in History, but if you don't want it there, I'd suggest putting it in Constructions using 355/133. Ovinus (talk) 00:58, 23 May 2022 (UTC)
  • I think history is a better place for this. —David Eppstein (talk) 18:36, 25 May 2022 (UTC)

Sources look great, citations are formatted nicely, prose is clear and engaging (and appropriately fun in places). Ovinus (talk) 00:58, 23 May 2022 (UTC)

@Ovinus: I think that's all comments responded to; please take another look. —David Eppstein (talk) 07:01, 26 May 2022 (UTC)

All looks good; passing. Ovinus (talk) 07:56, 26 May 2022 (UTC)