Talk:Alhazen's problem/GA1

GA review

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Nominator: David Eppstein (talk · contribs) 20:17, 10 June 2025 (UTC)[reply]

Reviewer: MathKeduor7 (talk · contribs) 17:23, 20 June 2025 (UTC)[reply]

It is the first time I review for GA status. I've read and understood WP:GACR6. Now I'll immediately begin reading the entire article very carefully. I'll keep you informed. MathKeduor7 (talk) 17:23, 20 June 2025 (UTC)[reply]

P.S. I've read and understood the other criteria at Wikipedia:Good article criteria. This will take some time. MathKeduor7 (talk) 17:28, 20 June 2025 (UTC)[reply]

I've just started reading the article's current revision. MathKeduor7 (talk) 17:37, 20 June 2025 (UTC)[reply]

Comment: I've read the very beginning: "Alhazen's problem is a mathematical problem in optics concerning reflection in a spherical mirror. It asks for the point in the mirror where one given point reflects to another."

I think it is a clear presentation, and I've understood it easily by looking at "File:Alhazen-pb.svg" (the image of a reflection in a circular mirror in the plane) illustrating the problem. I haven't checked the references yet, because I plan to first check if the article is well-written and understandable. So, for this little part I've read:

Done MathKeduor7 (talk) 17:50, 20 June 2025 (UTC)[reply]

Comment: I've read the following: "The special case of a concave spherical mirror is also known as Alhazen's billiard problem, as it can be formulated equivalently as constructing a reflected path from one billiard ball to another on a circular billiard table. Other equivalent formulations ask for the shortest path from one point to the other that touches the circle, or for an ellipse that is tangent to the circle and has the given points as its foci."

I think this is also straightforward clear, the layman will probably only need to click to know what is a concave spherical mirror, and imagining a circular billiard table and billiard balls is easy. The equivalent formulations are interesting and not obvious. So, for this little part I've read:

Done MathKeduor7 (talk) 18:01, 20 June 2025 (UTC)[reply]

Comment: Quote: "Although special cases of this problem were studied by Ptolemy, it is named for the 11th-century Arab mathematician Alhazen (Ibn al-Haytham), who formulated it more generally and presented a solution in his Book of Optics. It has no straightedge and compass construction; instead, al-Haytham and others including Christiaan Huygens found solutions involving the intersection of conic sections. According to Roberto Marcolongo, Leonardo da Vinci invented a mechanical device to solve the problem. Later mathematicians, starting with Jack M. Elkin [de] in 1965, solved the problem algebraically as the solution to a quartic equation, and used this equation to prove the impossibility of solving the problem with straightedge and compass."

Historical remarks, reference to notable solutions of some mathematicians (and Leonardo). Not much to comment here, it's obviously clear. Personally, I've got very curious about Leonardo's mechanical device! But let's keep reading in the order. I think it would be a good idea to mention from when is Ptolemy, so that the reader doesn't need to click to know how much time it took for the 1965 algebraic solution. I mean, like not everyone knows Alhazen is from the 11th-century (as it says), and not everyone knows approximate Ptolemy's epoch. @David Eppstein: What do you think of telling (as context) something like "Ptolemy (XXX – YYY AD)"? (or something like that) Just my two cents of course! It's fine as it is:

Done MathKeduor7 (talk) 18:26, 20 June 2025 (UTC)[reply]

I'll continue later. I have some commitments now. MathKeduor7 (talk) 18:27, 20 June 2025 (UTC)[reply]

Comment: I would only change "Researchers have extended this problem and the methods used to solve it to mirrors of other shapes and to non-Euclidean geometry." to "In the ??th century, researchers have [...]." To better inform and make emphasis on the long timeline and evolution (not to mention it's still attracting interest!) of this old problem. Just my two cents of course! It's fine as it is: Done MathKeduor7 (talk) 19:24, 20 June 2025 (UTC)[reply]

Ok, dates for Ptolemy and later researchers added. —David Eppstein (talk) 21:41, 20 June 2025 (UTC)[reply]

My analysis so far:

The lead is really good and meets all requirements of MOS:LEAD.

Comment: I'll now download all the references used in this article. It will take some time. MathKeduor7 (talk) 19:28, 20 June 2025 (UTC)[reply]

From now on, I will comment on criteria 1 and 2 of WP:GACR6 for each part of the text. Let's begin! MathKeduor7 (talk) 19:41, 20 June 2025 (UTC)[reply]

Comment: Quote: "The problem comprises drawing lines from two points, meeting at a third point on the circumference (boundary) of a circle and making equal angles with the normal at that point (specular reflection). It belongs to geometrical optics (in which light is modeled using rays rather than waves or particles), and catoptrics, the use of mirrors to control light: it can be used to find the path of a ray of light that starts at one point of space, is reflected from a spherical mirror, and passes through a second point. Although this is a three-dimensional problem, it can immediately be reduced to the two-dimensional problem of reflection in a circular mirror in the plane, because its solution lies entirely within the plane formed by the two points and the center of the sphere." P.S. Reference given was downloaded from http://www.jstor.org/stable/2589403

Yes, it's well-written and summarizes the cited reference content with his own words (as far as I can tell, everything is in accordance with the given reference information). So:

Done MathKeduor7 (talk) 19:49, 20 June 2025 (UTC)[reply]

Comment: The second paragraph of the "Formulation" section cites six different references. It will take some time to read them all, so: that's it for today! MathKeduor7 (talk) 19:54, 20 June 2025 (UTC)[reply]

P.S. I've just noticed some references are to books, not to downloadable journal papers, so I'll use Google Books preview feature! Cya, MathKeduor7 (talk) 19:58, 20 June 2025 (UTC)[reply]

Comment: There are used thirty-nine references in total in this article. Later I will make a list of the ones I have access to and the ones I don't have. Then we will have to think about what to do to for me to check the ones I do not have access yet. I'll probably make this list tomorrow. MathKeduor7 (talk) 01:14, 21 June 2025 (UTC)[reply]

P.S. I never tried https://wikipedialibrary.wmflabs.org/ . Maybe it can help. MathKeduor7 (talk) 01:16, 21 June 2025 (UTC)[reply]

Thankfully, many are freely accessible, and so I managed to get access to all of the first six ones very easily (the only exception: it was a hard one... the book of 100 great problems). This is enough for the next part of the review! Cya, MathKeduor7 (talk) 01:30, 21 June 2025 (UTC)[reply]

You may be able to see much of the relevant part of 100 Great Problems through Google Books: [1]. I have a pdf but I didn't record where I found it. —David Eppstein (talk) 01:49, 21 June 2025 (UTC)[reply]

Thank you! MathKeduor7 (talk) 01:51, 21 June 2025 (UTC)[reply]

Comment: I ask for one week to read and understand thoughtly the first six references (so that I can perhaps give good suggestions to the main author of the article). So: GA review is frozen for likely a week (not more than this, and I may be able to get it sooner!). In addition: I have some commitments next week, and Professor David Eppstein informed me on his user talk page that he will be traveling. That's it for now. Btw, this problem is interesting, and I want to understand it better, I am having fun reading about it. :) MathKeduor7 (talk) 08:34, 21 June 2025 (UTC)[reply]

Comment: As a preparation for the next step of the review, I'll list the first six references the article is using. That's for convenience. MathKeduor7 (talk) 06:54, 23 June 2025 (UTC)[reply]

[1] Neumann, Peter M. (1998), "Reflections on Reflection in a Spherical Mirror", The American Mathematical Monthly, 105 (6): 523–528, doi:10.1080/00029890.1998.12004920, JSTOR 2589403, MR 1626185

[2] Dörrie, Heinrich (1965), "Alhazen's Billiard Problem", 100 Great Problems of Elementary Mathematics, translated by Antin, David, Dover, pp. 197–200, ISBN 978-0-486-61348-2

[3] Chen, Tieling; Ilukor, Paul; Koo, Reginald (March 2024), "The one-cushion escape from snooker in a circular table", Recreational Mathematics Magazine, 11 (18): 99–109, doi:10.2478/rmm-2024-0006

[4] Peterson, Ivars (March 3, 1997), "Billiards in the Round", The Mathematical Tourist, retrieved 2025-06-05

[5] Poirier, Nathan; McDaniel, Michael (2012), "Alhazen's hyperbolic billiard problem", Involve, 5 (3): 273–282, doi:10.2140/involve.2012.5.273, MR 3044613

[6] Drexler, Michael; Gander, Martin J. (1998), "Circular billiard", SIAM Review, 40 (2): 315–323, Bibcode:1998SIAMR..40..315D, doi:10.1137/S0036144596310872

That's it for now. MathKeduor7 (talk) 06:57, 23 June 2025 (UTC)[reply]

Comment: Quoting the 2nd paragraph of "Formulation" section: "The same problem can be formulated with the two given points inside the circle instead of outside.[1] In this case the solution describes the path of a billiards ball reflected within a circular billiards table,[2][3] as Lewis Carroll once suggested for billiards play.[4] Because the two chords of the circle through the given points and the reflection point form equal angles with the circle, they form the two equal sides of an isosceles triangle inscribed within the circle, with the two given points on these two sides. Another equivalent form of Alhazen's problem asks to construct this triangle.[2][5] For points near each other within the solution, in general position, there will be two solutions, but points that are farther apart have four solutions.[6]"

I intend to analyze this paragraph tomorrow. MathKeduor7 (talk) 07:57, 23 June 2025 (UTC)[reply]

Drexler/Gander is also JSTOR 2653338 in case that's easier for you to access. —David Eppstein (talk) 08:53, 23 June 2025 (UTC)[reply]

Thank you, Professor David Eppstein! I had already got all six ones! ^^ Btw, when I think about it... Sometimes I will need help here, maybe from my great friend GregariousMadness, who has university library access and a lot of expertise in geometry. ^^ @GregariousMadness: Hi, friend! Do you have some time to help me reviewing this article? MathKeduor7 (talk) 10:13, 23 June 2025 (UTC)[reply]

@GregariousMadness: Would you be interested (and have time to) review the section "Alhazen's_problem#Algebraic"? Many nice references and a lot of advanced math! It sounds fun, haha. ^^ MathKeduor7 (talk) 10:23, 23 June 2025 (UTC)[reply]

Comment: "The same problem can be formulated with the two given points inside the circle instead of outside." can be understood by a toddler and is backed by the Ref [1] in its very first page. Clearly written and very well referenced, so: Done MathKeduor7 (talk) 10:35, 23 June 2025 (UTC)[reply]

The entire 2nd paragraph of "Formulation" section is pretty clear and well-written (even more with the pictures), so all I need is to check if everything is fully backed by the given references. And I'll do that tomorrow! MathKeduor7 (talk) 11:54, 23 June 2025 (UTC)[reply]

Comment: "In this case the solution describes the path of a billiards ball reflected within a circular billiards table,[2][3] as Lewis Carroll once suggested for billiards play.[4]" follows from the stated references (note: Refs [3] and [4] don't mention the word "Alhazen" specifically, but they are about related mathematical billiard tables with point-sized balls, but again, the article just says short infos about them with Lewis Carroll etc, and you can check it at https://mathtourist.blogspot.com/2020/05/billiards-in-round.html for example, that it's relevant to the article IMHO), so, one more positive check towards GA: Done MathKeduor7 (talk) 23:50, 23 June 2025 (UTC)[reply]

Note: I need some days of rest. Checking references is exhausting, but I'll go till the end! MathKeduor7 (talk) 00:34, 24 June 2025 (UTC)[reply]