Talk:Problem of Apollonius/GA1

GA Review

Protonk comments

As a general note, I am not a specialist. I consider myself sharp enough to pick this sort of thing up after having it beaten over my head repeatedly, but this is not my forte nor my vocation. I won't attempt to check statements for validity or factual accuracy (except statements made outside the purview of geometry).

Thank you so much, Proton! Your review is wonderful and nicely complementary to Dan's just above it. You put your finger on some key things that needed improving. I'll try to fix these up today.  :) Willow (talk) 11:53, 19 August 2008 (UTC)

• Images Image tags all check out. Each image seems to provide some good illustration of this obviously geometric problem.
• Style/MOS

• Lead seems good as far as length and breadth are concerned
• "...are sometimes called Apollonius circles, although the term is ambiguous." Ambiguous links directly to Circles of Apollonius. I gather that I am to understand this to mean the sentence "These "circles of Apollonius" should not be confused with the Apollonian circles, which have a different technical definition." highlights the ambiguity. Is there a better way to make this notion clear to the reader?

I expanded this discussion and also improved the disambiguation page, Circles of Apollonius. Willow (talk) 16:25, 19 August 2008 (UTC)

• "These objects may be arranged in any way and may cross one another; however, they are usually taken to be distinct." Would this be improved if a link to Distinct were provided? That article doesn't really help the reader too much and it might be considered a dicdef, so YMMV.

Your suggestion of the link to distinct was great, so I added it and also fleshed this idea out more. Willow (talk) 16:25, 19 August 2008 (UTC)

• "In practice, two circles are tangent if they coincide or intersect at only one point; this is also true for a line and a circle" Couldn't this be better stated by showing the two plane counterexamples for circles?

Again, excellent suggest that I took over. I also expanded the discussion here as well. Willow (talk) 16:25, 19 August 2008 (UTC)

• "Apollonius' problem can also be formulated as the problem of locating one or more points such that the differences of its distances to three given points equal three known values" This should be explained as carefully as the geometric formulation of the problem. Links to the trilateration page don't seem immediately helpful.

Yes, it does seem as though trilateration is, umm, ripe for improvement. I tried to explain the second formulation more thoroughly, and clarify the connection to navigation systems such as GPS. I also moved up the definitions of internal and external tangencies, since they seemed to flow nicely after the definition of tangency itself. Willow (talk) 22:53, 19 August 2008 (UTC)

• Blue links. Several persons and concepts are linked multiple times throughout the piece. Unless you intend to link them multiple times (e.g. linking to Newton in the lead and again in the applications), following links should be removed.

Since people sometimes read articles out of order, or skip around to the sections they care about, I generally give a link every section or every few sections. I'll go through the article, though, and see if I went overboard somewhere, as I'm wont to do. Thank you! :) Willow (talk) 12:04, 19 August 2008 (UTC)

As a note, I really like how this article uses links for internal navigation. Don't touch those. Protonk (talk) 14:15, 19 August 2008 (UTC)

• Do the sources describe Van Roomen's method as flawed because of the inability to construct it with a compass and straightedge? I can certainly see that it could be judged as not a 'real' solution to the problem, but flawed brings to mind underlying error.

You and Dan both had the same association, so I changed "flaw" to "drawback". I chose "flaw" originally mainly because I liked its sound, a punchy monosyllable that wakes the reader up. I was also thinking of Van Roomen's proof as a diamond with a single imperfection. The idea the sources convey is just that his proof left something to be desired, since it wasn't yet known whether Apollonius' problem could be solved by ruler and straightedge, until Viète's proof. Willow (talk) 12:04, 19 August 2008 (UTC)

• Newton's and Van Roomen's solutions are written in past tense, but Viète's is written in present tense.

Again — oops.

OK, I think this has been fixed? Willow (talk) 22:53, 19 August 2008 (UTC)

• Is the bolded "point, point, point" notation (PPP) common to a student of this discipline? Should be quickly explained or (more drastically) dispensed with?

You make a very good point! I've tried now to explain it quickly at the beginning of that section. The notation does seem to be generally used in sources written after 1950, and maybe earlier; I need to check that. Originally, the "Special cases" section was above the History section, so that I didn't need to explain the notation. Willow (talk) 12:04, 19 August 2008 (UTC)

• Solution by inversion section: "...orange circle CG in Figure 6 crosses the red, blue and green given circles at right angles" I don't see red or green circles. Only black, pink and orange (in figure 6).

Thank you for catching that! At Jakob's suggestion, I'd changed the colors of several Figures, to help people understand them, but I missed a few color-specific references in the text. :( I think that I've caught them all now, though. :) Willow (talk) 16:35, 19 August 2008 (UTC)

• "If two of the three given circles are disjoint" Disjoint might benefit from a link.

I changed it to "If two of the three given circles do not intersect", which is consistent with the rest of the article. No need to introduce new words like "disjoint" if we don't have to. :) Willow (talk) 16:35, 19 August 2008 (UTC)

• "...Apollonius' problem degenerates to the CCP limiting cases," Perhaps a more direct link? limiting cases for CCP

Thank you, that was YAES (yet another excellent suggestion). ;) Willow (talk) 16:35, 19 August 2008 (UTC)

• The rest looks ok.

• Sourcing and claims

• Is there a source independent from John Casey (mathematician) that claims he refined Van Roomen's method independent from Newton almost 200 years after the publication of the Principia? That doesn't seem unbelievable, just unlikely.

I feel a little silly for not realizing that; I'm a little too trusting sometimes. :P Let me check my sources more carefully and get back to you with a more precise and verifiable statement. Willow (talk) 11:53, 19 August 2008 (UTC)

• Format

• I like the format and layout.
• POV No problems.

Overall this is an impressive article. I understood a good portion of it (more than I thought I would) and I felt that care was taken in writing it. I'll be happy to pass this article as soon as the quibbles above are dealt with. On hold. Protonk (talk) 04:51, 19 August 2008 (UTC)

• Updates: Once the Viète solution tense and differences of distances problem statement issues are fixed, I'll be happy to pass this article. As an aside, it is interesting to see how circle packing theorems intersect with Mathematics of paper folding, see this TED talk. Protonk (talk) 16:44, 19 August 2008 (UTC)
  • PS Another link related to your aside. This seems off-topic from the present article, though. —David Eppstein (talk) 17:28, 19 August 2008 (UTC)

Cool! :) I'd never heard of TED conferences or Robert Lang before, but I was fascinated; thank you, dead people! :) I've never learned origami, although I do like to make talking puppets out of paper for my nieces and god-daughter. :) You're motivating me to watch all those origami videos on YouTube, like this one. :) Willow (talk) 22:53, 19 August 2008 (UTC)

• Excellent job, Protonk. Even if you did point out all the things I missed. No, I don't mind! - Dan Dank55 (talk)(mistakes) 18:38, 19 August 2008 (UTC)