Template:Did you know nominations/Lexell's theorem
- The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.
The result was: rejected by reviewer, closed by BorgQueen talk 16:30, 23 September 2023 (UTC)
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Lexell's theorem
Lexell's theorem
- ... that Lexell's theorem (pictured) holds that spherical triangles with a fixed base and area have their apex on a small circle passing through points antipodal to the base vertices? Source: A.J. Lexell (1784) "Solutio problematis geometrici ex doctrina sphaericorum"
- Reviewed:
Created by Jacobolus (talk). Self-nominated at 20:32, 24 August 2023 (UTC). Post-promotion hook changes for this nom will be logged at Template talk:Did you know nominations/Lexell's theorem; consider watching this nomination, if it is successful, until the hook appears on the Main Page.
I haven't fully checked the article, but my preliminary check suggests that the article meets DYK requirements. No QPQ requires as this appears to be the nominator's first nomination. I also didn't find any close paraphrasing. The main issue here is the hook. It's very technical/specialist and may not be understandable to the average reader. Pinging David Eppstein as he's the resident math expert and may have ideas on a better, more approachable hook. Narutolovehinata5 (talk · contributions) 09:25, 21 September 2023 (UTC)
- WP:DYKINT requires hooks to be "likely to be perceived as unusual or intriguing by readers with no special knowledge or interest". I've usually interpreted that, for mathematics articles, as meaning that the hook should connect to something beyond mathematics. Unfortunately, in this case, almost the only non-mathematical content of the article appears to be the history of famous mathematicians who have done something related to its topic, "Did you know [MATHEMATICIAN] proved [MATHEMATICAL THEOREM]" is unlikely to be perceived as unusual or intriguing. There's a little bit about map projections / spherical interpolation at the end of the "Spherical area coordinates" section but it's very vaguely written and examining the sources suggests that they treat this idea only peripherally, not enough to base a hook around them. There is no requirement that eligible articles get DYK hooks; my usual approach when my own articles become eligible but are irredeemably technical is to not bother trying to get a DYK listing for them. —David Eppstein (talk) 12:13, 21 September 2023 (UTC)
- I wonder if there's a better way to phrase the statement of the theorem to be more accessible in this context. My impression is that the theorem itself is pretty interesting and surprising for most people who have gone through a high school geometry course and have seen how this works on the plane but not studied it on the sphere, but unfortunately I don't know if it can be described in a way friendly to an entirely non-technical audience in just one sentence. (The sticking point is the jargon words "antipodal" and "small circle", but I don't know a way to describe these inline in less than a sentence each.) –jacobolus (t) 13:49, 21 September 2023 (UTC)
- My best shot at simplifying the theorem statement is something like: "... that Lexell's theorem (pictured) holds that every spherical triangle with a fixed base side and fixed area has its third corner on a common circle?" Narutolovehinata5 does that version seem more comprehensible to a layperson or is it still too tricky? –jacobolus (t) 15:03, 21 September 2023 (UTC)
- David Eppstein what about something like, "... that the wide variety of proofs of Lexell's theorem (pictured) provide a tour of methods in spherical geometry." –jacobolus (t) 15:03, 21 September 2023 (UTC)
- Setting aside the question of whether a hook that is entirely mathematical is acceptable, that hook would require a source that expresses the same sentiment, not merely that there exist multiple proofs but that these proofs give some kind of overview of the field. —David Eppstein (talk) 17:29, 21 September 2023 (UTC)
- Maehara/Martini 2023 (which was coincidentally published after the article here was mostly written), says
"As good exercises in geometric intuition with respect to spherical geometry, we present seven proofs of Lexell’s theorem on spherical triangles. This theorem is well suited for such a pedagogical purpose, and in addition, we were motivated to present this collection due to the famous names directly involved in some of the proofs: Leonhard Euler, Jakob Steiner, Carl Friedrich Gauss, Josef-Alfred Serret, and László Fejes Tóth. Some of the important ingredients from spherical geometry that we use are Girard’s theorem, the inscribed angle theorem, and the polar duality theorem, as well as the method of stereographic projection."
Which is more or less the same idea expressed at length, but doesn't really contain a cute soundbite expression of it. –jacobolus (t) 17:53, 21 September 2023 (UTC)- Honestly both of the new proposals still seem to be pretty jargony to the layperson. They might be interesting to math buffs, but unless you're really interest in math they don't make much sense, at least not enough to encourage people to read the article. Narutolovehinata5 (talk · contributions) 01:36, 22 September 2023 (UTC)
- Hopefully it doesn't sound defensive if I say that I personally find about 50% of DYK hooks to be not interesting enough to give a second glance to, and only ever click through a trivially small proportion of DYK hooks I have ever seen. Many if not most of them seem to me to be of pretty niche interest (for some recent examples, in the past week there was a DYK about how a book led to an (unexplained) controversy in anthropology, how circular domes made ancient temple architecture less austere, how a sociologist studied divorce a century ago, how early 20th century Britain used capital letters as "official lettering", how a naval officer might have been inspired to join the navy by seeing some ships as a child, how a soccer player was recognized for trying to be environmentally friendly, how a TV station wanted to be known as the "cadillac" of TV stations, etc.). So I'm not entirely convinced that "many people aren't excited about this" is a uniform standard for rejection of these. But with that said, I can see how there's not going to be anything obviously shocking or surprising about this theorem to someone who can't make any sense of the statement.
- My experience showing this theorem to people (who have say undergraduate-level technical training in arbitrary subjects) is that many if not most are initially surprised and some are delighted at the result, which is not at all immediately obvious but still fairly straightforward to prove in a number of ways, some of which are quite elegant. But I can appreciate that it's hard to convey the statement of the theorem in a way that is accessible to someone who doesn't at least remember their high school geometry class. I'm happy to take suggestions for other kinds of "hooks". –jacobolus (t) 04:13, 22 September 2023 (UTC)
- I think that's the problem here. If it relies on somewhat specialized knowledge and technical terms that readers may have forgotten about, it may not really be a good fit for DYK. This is not to say that math articles in general are a poor fit for DYK, but it does mean that such articles and hooks do need to be understandable even to people with basic knowledge of math. Maybe David can explain better than I can, but basically, if the issue is that "it's hard to convey the statement of the theorem in a way that is accessible to someone who doesn't at least remember their high school geometry class", then perhaps the article just isn't a good fit for DYK. Narutolovehinata5 (talk · contributions) 05:44, 22 September 2023 (UTC)
- This standard reads kind of like "not everyone would like this, so nobody should see it at all". I personally think many DYK hooks and the articles they point at rely on significant amounts of specialized knowledge (in excess of what is required to understand the statement of Lexell's theorem), and most of the rest are of quite niche interest. Which seems just fine to me – the world is a big and complicated place, and many subjects take a bit of effort to understand, or aren't for everyone. But it sometimes feels like graduate-school level knowledge about e.g. sociology or art history or paleontology are considered to be an easy hurdle for a "general reader", while secondary school level geometry knowledge is taken as an impassable barrier. (As a concrete example, there was recently a link to Palaeorehniidae from DYK – if I click through that article is brimming with sophisticated jargon not known to someone with just a standard high school education, and any curious layperson is going to need to be willing to put significant effort in to click through links of unknown terms to make sense of it. But I personally think it's great to have such articles featured, even if they aren't for everyone.) –jacobolus (t) 06:13, 22 September 2023 (UTC)
- I think that's the problem here. If it relies on somewhat specialized knowledge and technical terms that readers may have forgotten about, it may not really be a good fit for DYK. This is not to say that math articles in general are a poor fit for DYK, but it does mean that such articles and hooks do need to be understandable even to people with basic knowledge of math. Maybe David can explain better than I can, but basically, if the issue is that "it's hard to convey the statement of the theorem in a way that is accessible to someone who doesn't at least remember their high school geometry class", then perhaps the article just isn't a good fit for DYK. Narutolovehinata5 (talk · contributions) 05:44, 22 September 2023 (UTC)
- Honestly both of the new proposals still seem to be pretty jargony to the layperson. They might be interesting to math buffs, but unless you're really interest in math they don't make much sense, at least not enough to encourage people to read the article. Narutolovehinata5 (talk · contributions) 01:36, 22 September 2023 (UTC)
- Maehara/Martini 2023 (which was coincidentally published after the article here was mostly written), says
- Setting aside the question of whether a hook that is entirely mathematical is acceptable, that hook would require a source that expresses the same sentiment, not merely that there exist multiple proofs but that these proofs give some kind of overview of the field. —David Eppstein (talk) 17:29, 21 September 2023 (UTC)
- I wonder if there's a better way to phrase the statement of the theorem to be more accessible in this context. My impression is that the theorem itself is pretty interesting and surprising for most people who have gone through a high school geometry course and have seen how this works on the plane but not studied it on the sphere, but unfortunately I don't know if it can be described in a way friendly to an entirely non-technical audience in just one sentence. (The sticking point is the jargon words "antipodal" and "small circle", but I don't know a way to describe these inline in less than a sentence each.) –jacobolus (t) 13:49, 21 September 2023 (UTC)
- WP:DYKINT requires hooks to be "likely to be perceived as unusual or intriguing by readers with no special knowledge or interest". I've usually interpreted that, for mathematics articles, as meaning that the hook should connect to something beyond mathematics. Unfortunately, in this case, almost the only non-mathematical content of the article appears to be the history of famous mathematicians who have done something related to its topic, "Did you know [MATHEMATICIAN] proved [MATHEMATICAL THEOREM]" is unlikely to be perceived as unusual or intriguing. There's a little bit about map projections / spherical interpolation at the end of the "Spherical area coordinates" section but it's very vaguely written and examining the sources suggests that they treat this idea only peripherally, not enough to base a hook around them. There is no requirement that eligible articles get DYK hooks; my usual approach when my own articles become eligible but are irredeemably technical is to not bother trying to get a DYK listing for them. —David Eppstein (talk) 12:13, 21 September 2023 (UTC)
I'm really sorry about this, but after looking at the article again and checking for any possible material, I just don't think there's anything suitable here that would work as a layperson-friendly DYK hook. If there was anything that caught my attention I would have proposed a hook myself, but it seems there isn't any and David also agrees. Sorry to be the bringer of bad news but given the content it's probably just not the right fit for DYK. Narutolovehinata5 (talk · contributions) 03:08, 23 September 2023 (UTC)
- That's fair. It's probably not worth bothering to try to engage in the future with community processes like this, which are generally biased against technical contributions, no matter how significantly technical authors try to bend over backwards to make high quality articles which are as accessible as possible (e.g. in this article, I spent probably 50 hours making diagrams as attractive and legible as possible to make them accessible to the widest possible audience.) Goes with a broader societal stigma against mathematics: It's easy to dismiss contributions as just for "math buffs" without seriously trying to understand or engage with them. –jacobolus (t) 04:20, 23 September 2023 (UTC)
- Just because something is technical or scientific doesn't inherently make it impossible to be featured on DYK. We've featured many science and math hooks in the past, David Eppstein can attest to that. Maybe this article didn't work out but that doesn't mean other concepts don't have potential. Narutolovehinata5 (talk · contributions) 04:49, 23 September 2023 (UTC)
- If even terms like "spherical triangle", "circle", "proof", "area", and "corner" are just an insurmountable level of jargon for DYK, then there's no way it's worth the trouble to go through a monthlong process for inevitable rejection at the end. Better to write articles as I want for myself, and promote them independently of Wikipedia's internal community processes. For example, here are the responses from the math reddit about a month ago: "Great job!", "I’m super impressed :)", "the image looks amazing!", "Dude,great work! Really impressive! And thank you for your contribution!", "If only all wikipedia articles were written like this one 😍", "Great work!", "I just wanted to thank you for taking your time to do this.", "Great article OP!", "Wow this was amazing. Have you considered publishing this ...", "That article rocks!", "I really like the proof section. Many articles on math Wikipedia neglect proofs and often they are a bit annoying to track down in literature. You present them in a clear and nice way with an appropriate amount of detail, good job on that. And the illustrations are absolutely stellar as well." – making a post there requires no special process, the result is much more encouraging, I got some decent substantive feedback as well, and there was even some meaningful conversation about the mathematics involved. –jacobolus (t) 04:59, 23 September 2023 (UTC)
- Just because something is technical or scientific doesn't inherently make it impossible to be featured on DYK. We've featured many science and math hooks in the past, David Eppstein can attest to that. Maybe this article didn't work out but that doesn't mean other concepts don't have potential. Narutolovehinata5 (talk · contributions) 04:49, 23 September 2023 (UTC)
- That's fair. It's probably not worth bothering to try to engage in the future with community processes like this, which are generally biased against technical contributions, no matter how significantly technical authors try to bend over backwards to make high quality articles which are as accessible as possible (e.g. in this article, I spent probably 50 hours making diagrams as attractive and legible as possible to make them accessible to the widest possible audience.) Goes with a broader societal stigma against mathematics: It's easy to dismiss contributions as just for "math buffs" without seriously trying to understand or engage with them. –jacobolus (t) 04:20, 23 September 2023 (UTC)
