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Again, welcome! --Lst27 (talk) 23:54, 15 Jan 2005 (UTC)

Your reversion of my edit[edit]

Hi, why did you revert my edit to Orthographic projection? Seems to me that the text is now ungrammatical and my edit fixed it. You can't start a sentence with "Orthographic projection is a form of...". Am I missing something? Zvika (talk) 11:02, 8 January 2024 (UTC)[reply]

Sure you can start a sentence that way. Just like you can might a sentence with "Introspection is a form of thinking ..." or "Running is a form of exercise ...". You can conceivably change this to "The orthographic projection ..." and replace one kind of noun with another, but it takes a more substantial rewrite to make sure the end result is grammatical, which your version was not (or if perhaps arguably nominally grammatical, it became awkward and confusing since the new kind of noun didn't match the previous intention of the sentence). –jacobolus (t) 15:23, 8 January 2024 (UTC)[reply]
I encourage you to look at Parallel projection, 3D projection, Map projection, Projection (linear algebra), Projection (set theory), Projection (relational algebra) and probably others, all of which have an article before the word "projection" in the lede. Zvika (talk) 11:38, 10 January 2024 (UTC)[reply]
Yes, there are two different types of nouns involved here. In English you can talk about either the process of projection, or a specific function, a projection. Both versions can be grammatical, and the page Orthographic projection could choose either one in a lead sentence. The sentence could be entirely rewritten to use the version with the article, and that would be fine. There's no particular need to make this change, but if you care strongly you can try rewriting the sentence. You can't just tack the articles on wherever you want though, or you get something awkward and confusing. –jacobolus (t) 15:29, 10 January 2024 (UTC)[reply]

Number Line and Number Axis Are The Same Thing.[edit]

Edit war[edit]

You are involved in an edit war at Cartesian coordinate system. An uninvolved administrator may consider that both the other editor and you did dot respect the WP:3RR rule. If you would have waited a little before your last reverts, I could do them myself, and we could be sure that only the other editor may be blocked.

By the way, I have notified the last talk-page edit of this editor to their last blocking administrator, and suggested an indefinite block, per WP:NOTHERE D.Lazard (talk) 17:47, 9 January 2024 (UTC)[reply]

I would recommend just blocking them temporarily from this specific page. –jacobolus (t) 17:49, 9 January 2024 (UTC)[reply]

They may waste your time with encyclopedic style as well[edit]

My example. (talk) 08:31, 16 January 2024 (UTC)[reply]

I don't understand what you are getting at. Please use full sentences and explain your point clearly. –jacobolus (t) 08:32, 16 January 2024 (UTC)[reply]

They may really waste your with nonsense The latest example. (talk) 08:55, 16 January 2024 (UTC)[reply]

I still have no idea what you are getting at. You need to explain yourself clearly in full sentences, at the relevant talk pages, not make cryptic comments on my user talk page. –jacobolus (t) 08:57, 16 January 2024 (UTC)[reply]

I will work in talk space for a while.[edit]

It's fun editing together, and I like your final edit on Perpendicular. I think we should change the second part of that section (about the dot product.) I will do it on the talk page. Guy vandegrift (talk) 23:12, 28 January 2024 (UTC)[reply]

@Guy vandegrift Feel free to make edits directly to the article. –jacobolus (t) 23:35, 28 January 2024 (UTC)[reply]
It's probably worth making a separate section about vectors and lines in terms of coordinates; should probably go before the section about graphs of linear functions, frankly. –jacobolus (t) 23:37, 28 January 2024 (UTC)[reply]
I will enter the equations soon.Guy vandegrift (talk) 00:11, 29 January 2024 (UTC)[reply]
I'm done editing Perpendicular. I agree with you on moving the section closer to the top and perhaps changing the title. Go ahead and move or rename it. I certainly won't complain!Guy vandegrift (talk) 01:43, 29 January 2024 (UTC)[reply]

You reverted my edit.[edit]

Hello! It seems I've made a pointless edit on Polar coordinate system and you reverted it. However, now I'm confused because I'm not really sure why my edit was incorrect. I'm not a native English speaker so that's why the sentence seems weird to me.

If it's not too much, would you be able to explain to me what does it mean?

Thanks! Confused.jpg (talk) 12:01, 29 January 2024 (UTC)[reply]

Confused.jpg: The two versions, "there are references to his using polar coordinates" and "there are references to his works using polar coordinates" mean two different things. The former means someone said something along the lines of "Hipparchus used polar coordinates to establish stellar coordinates", whereas the latter probably means someone said something along the lines of "Hipparchus's work XYZ used polar coordinates ...", but is also grammatically ambiguous because it can plausibly be read with "references" as the subject of "using". The cited source is unlikely to support your variant, but I didn't check explicitly; did you?
Arguably this sentence is a bit awkward and might benefit from a rewrite. But it has to be done with care for the details. –jacobolus (t) 12:08, 29 January 2024 (UTC)[reply]
Oh alright, I kind of understand now how my edit changed the meaning of the sentence, and I surely didn't think, nor notice, how it made the sentence ambiguous, thanks for pointing that out.
Not gonna lie, I tried checking the source (after you asked) but I didn't understand enough to be able to provide a valid correction.
It's the second time where I tried to correct something but ended up getting it completely wrong, maybe I should stop doing that.
In any case, thanks for your help and patience, it seems there's a long way until I completely understand how English works. Confused.jpg (talk) 15:25, 30 January 2024 (UTC)[reply]
@Confused.jpg Please feel free to make corrections where you see them. Getting your change reverted is not any kind of personal rebuke, and it happens to everyone all the time including experienced editors. It just means that someone looked at the edit and disagreed. If you ever have a change reverted and you continue to think your version was superior you can start a talk page discussion (either on the other editor's talk page as you did here, or on the article) and talk through the reasons. Decisions on Wikipedia are made by consensus of the editors, not by any individual editor's authority.
In this particular case it might well be worth trying to rewrite this sentence. The original uses a grammatical construction which is a bit unusual and reads a bit awkwardly. All the best. –jacobolus (t) 15:34, 30 January 2024 (UTC)[reply]

Tetrahedron and triangular bipyramid[edit]

Hi. I'm not sure this is the right place to ask about polyhedron. I have planned the article Triangular bipyramid for another improvement to GA, but there is one problem that I could not nominate. Are regular tetrahedrons and tetrahedrons the same synonymously, I have looked up the source [1] that mentioned the triangular bipyramid constructed by two triangular pyramid, but it does not mention the regular, and our article have differentiate both of them. Dedhert.Jr (talk) 08:11, 6 February 2024 (UTC)[reply]

The word "tetrahedron" does not imply regular. Any 4 points in 3-space can be chosen as the vertices of a tetrahedron. If you glued together any 2 tetrahedra sharing a face (or in other words, started from 3 vertices defining a "base" plane, and then picked 2 more vertices on either side of the base and connected each one to the original three vertices), you'd get some flavor of "triangular bipyramid". –jacobolus (t) 08:22, 6 February 2024 (UTC)[reply]
@Jacobolus Yes. But the article is talking about the edge length equal in length case. Do I have to explain the non-regular one as well? This is difficult to find the sources, although we both have modified the article Bipyramid before. Dedhert.Jr (talk) 08:34, 6 February 2024 (UTC)[reply]
Triangular bipyramids (or dipyramids) which do not have equal side lengths seem to be more common than the equal-sided sort in crystallography. I think this article should cover both types. Ones that are "oblique" also come up sometimes I think. I don't think you need to put special attention into the case where the 2 apices are completely arbitrary unrelated points. –jacobolus (t) 08:40, 6 February 2024 (UTC)[reply]
Ahh... In this case, can you help me to find the sources? I'll make sure to add them more. However, one thing that I could not change is the sections, that I'm planning to list all of the eight different deltahedra in WP:GT. By the way, it seems that I could not find the right and oblique triangular bipyramid in neither Google Books nor Google Scholar; they rather explicitly shows the triangular pyramid. Dedhert.Jr (talk) 08:43, 6 February 2024 (UTC)[reply]
Google scholar turns up 18,000 results about this shape, a substantial proportion come from crystallography. I have no idea which sources are especially meaningful/important in that field though. –jacobolus (t) 08:50, 6 February 2024 (UTC)[reply]
@Jacobolus Thank you so much; I thought they do not. I could only found one source [2], but I cannot access the article, and could not the verifiability of this source. Dedhert.Jr (talk) 09:12, 6 February 2024 (UTC)[reply]
@Jacobolus Oh yeah. One more thing. Is it fine to explain the right bipyramid in general [3], and then write its an example as triangular bipyramid? This is the only thing I could think of, but I'm aware that this is challenging the verifiability? Dedhert.Jr (talk) 03:03, 7 February 2024 (UTC)[reply]
Here's e.g. a paper discussing "oblique triangular bipyramids": Alexandrov, Victor (2017). "How many times can the volume of a convex polyhedron be increased by isometric deformations?." Beiträge zur Algebra und Geometrie 58: 549-554. arXiv:1607.06604.pdf. –jacobolus (t) 03:27, 7 February 2024 (UTC)[reply]
In this paper, there is mention of both "right triangular bipyramids" and "Concave tetrahedral/trigonal bipyramidal palladium nanocrystals": Niu, Wenxin; Xu, Guobao (2011). "Crystallographic control of noble metal nanocrystals". Nano Today 6 (3): 265–285. doi:10.1016/j.nantod.2011.04.006. –jacobolus (t) 07:13, 7 February 2024 (UTC)[reply]
@Jacobolus Ah... Sorry for late response. Thank you. I have added this, but are they mentions about the definition of right bipyramid in the last source? Also, does it also mention something more about the nanocrystal. I would like to require more context in that journal, and once again, I cannot access the source, which I subsequently cannot check the verifiability. Thank you so much for the assitance. Dedhert.Jr (talk) 14:01, 11 February 2024 (UTC)[reply]


I see why you reverted this (, but I used VisualEditor and didn't change anything but the params for linking the book title. Sometimes it adds white space to the wiki text by itself. BhamBoi (talk) 07:31, 8 February 2024 (UTC)[reply]

@BhamBoi You can't make this type of edit. It's hugely hugely disruptive. If the visual editor is causing this kind of extreme damage, use the source editor. (That's also a massive bug in the visual editor which should be fixed.) –jacobolus (t) 07:36, 8 February 2024 (UTC)[reply]
I added what I intended to add and published it, there was really no way for me to know what wiki text it was adding… I'll try to be more careful but there is not much I can do when using a core feature as intended. BhamBoi (talk) 07:39, 8 February 2024 (UTC)[reply]
@BhamBoi You can't click "show changes"? If other edits are doing something similar, please don't make them. (For instance, switch to the source editor.) Clobbering all of the intentional whitespace a human put into the citation templates is doing significantly more damage than any benefit that could be had from changing one citation. –jacobolus (t) 07:51, 8 February 2024 (UTC)[reply]
It's not in my normal behavior to preview the changes to wikitext when making a visual edit (maybe I'll start doing that just because of this, but I don't assume that's the norm among editors)... Obviously I didn't intentionally add space to the templates: here's an example video showing that I really could not have known that I was adding whitespace upon publishing my changes without viewing the diff to the wikitext. BhamBoi (talk) 08:02, 8 February 2024 (UTC)[reply]
That's messed up. I've never used the Visual Editor, but the UI you went through there to make a tiny change seems incredibly painfully ineffective, with far too many clicks and boxes to fill. If it additionally has this kind of severe bug, it's probably better if everyone who can just stops using it. –jacobolus (t) 08:10, 8 February 2024 (UTC)[reply]


Hi, jacobolus. Hope all is well. You may want to share your thoughts on Wikipedia:Administrators'_noticeboard/Incidents#User:SheriffIsInTown_and_timesinks. Thank you. HistoriesUnveiler (talk) 18:44, 10 February 2024 (UTC)[reply]

March 2024 GAN backlog drive[edit]

Good article nominations | March 2024 Backlog Drive
March 2024 Backlog Drive:
  • On 1 March, a one-month backlog drive for good article nominations will begin.
  • Barnstars will be awarded.
  • Interested in taking part? You can sign up here or ask questions here.
You're receiving this message because you have reviewed or nominated a good article in the last year.

(t · c) buidhe 02:39, 23 February 2024 (UTC)[reply]

Dialogue and talks in Wikipedia[edit]

This remark would be out of topic on the main Function page, but might clarify some things. First, criticism of behavior fundamentally differs from criticism af a person. The first is a matter of calling to order, the second might (!) be taken as an insult. My observation about "frogs" and "adolescent" clearly referred to behavior.

Second, your question starting with "I'm not clear what you're hoping for" is a bit puzzling. Does it refer to my remark about people barging in in the middle of a dialogue?

My objection is that, since there is no moderator, the entire discussion becomes fragmented, as on the proverbial fishmarket (oops!). Some restraint may ensure more coherence. Observe that it's happening again to our dialog, impeding all progress! So don't take it personally if I occasionally get out of the melee. Boute (talk) 13:10, 2 March 2024 (UTC)[reply]

@Boute I thought the substantive part of the comment was fine (serving readers, multiple definitions, direct citations to sources), but the introductory aside about frogs and adolescents etc. seemed gratuitous and distracting from the point, and entirely undercut the "restraint is needed to avoid derailing [...] I will set the example in exercising restraint" part of your comment. –jacobolus (t) 17:37, 2 March 2024 (UTC)[reply]
I agree with you that discussions on Wikipedia can often be frustrating for everyone involved, even when people generally agree (let alone when topics get politicized, etc.). –jacobolus (t) 17:38, 2 March 2024 (UTC)[reply]
"I'm not clear what you're hoping for" is a bit puzzling. Does it refer to my remark about people barging in in the middle of a dialogue? – Whoops, I meant to answer this. I thought you were put off by the repeated rejection from multiple authors that an article critic was getting about concern about whether a domain/codomain must be very explicitly described to be part of a set-theoretic structure used as specification of a function. From what I can tell the discussion persisted largely due to the critic's repetitive replies that didn't really seem to engage with what other people were saying. I am not sure what you would prefer as a response in that case: it seems to me that other people can either keep trying to explain/respond, or just ignore the discussion and let the critic talk to themself. –jacobolus (t) 17:45, 2 March 2024 (UTC)[reply]
Indeed, that's why I decided terminating my yearly visit to this article (over the past 10 years I have seen no progress), and coming back in 2025. As regards the codomain issue, since the 1980s I've been regularly asking mathematicians using codomains why they might want it. The answer always amounted to "tradition in certain fields" or "it's a convenience" (without a technical justification). Yet, most definitions for composition of functions with codomains are very restrictive. Of course, since the term codomain exists, it must be covered by an article meant to be encyclopedic, but a solid technical justification would be a genuine added value.
If you have the incentive to continue working on this article, you may find Rogaway's remarks very helpful [4], in particular his remark #18: 'Definitional choices that don't capture strong intuition are usually wrong, they may come back to haunt you". As for the of informal introduction, I recently found very high praise for the educational style of Michael Spivak's Calculus (now in its 4th edition, freely available on the web). Since the perspective of the article must be far wider than calculus (ideally, all of mathematics) the intuitive discussion on functions must also be wider. A suitable preamble to the formal definition might run as follows (after a few examples). (begin excerpt) In our examples, we have been writing f(x) for the "output value" of the function f for a given "input value" x. This immediately raises two questions: (a) for which values of x is f defined? and (b) if x is such a value, what, then, is the value of f(x)? (end excerpt). Answering those questions provides the justification for a simple formal definition to follow.
I hope this helps. Other work currently prevents me from providing more input or even having an occasional look at these pages. Boute (talk) 09:17, 3 March 2024 (UTC)[reply]
The most obvious purpose I can see is to avoid extra bookkeeping. It's easier to say e.g. a square matrix represents a function from and not worry up front about noting that the image might be some restricted subset in degenerate cases. Etc. –jacobolus (t) 09:46, 3 March 2024 (UTC)[reply]

Casting aspersions[edit]

Your commentary towards Airship in the GAN discussion is over the bright line of casting aspersions. You ignored my polite request to strike or remove it and continued responding. You can discuss an editor's actions without making bad-faith assumptions about their motives. I am asking you once again to remove your aspersions or I will block you. ♠PMC(talk) 03:00, 8 March 2024 (UTC)[reply]

Well, I see that you have chosen to respond to Airship at WT:GAN again and not even acknowledge this post, let alone strike your aspersions, so I have blocked you for 24 hours. I will be happy to remove it if you acknowledge this post and confirm you will strike your bad-faith comments. ♠PMC(talk) 03:15, 8 March 2024 (UTC)[reply]
@Premeditated Chaos I didn't notice your talk page comment here until now, but this seems like an entirely disproportionate and entirely unnecessary site block, frankly quite abusive. Can you please lift it? I'd really like to get back to productively editing articles now, which was what I was otherwise in the middle of working on. Airship asked a concrete question about why people had a problem with math GARs, to which I was responding in good faith. We were in the middle of a conversation, and I was in the middle of replying to concrete questions. If you like I am entirely happy to not reply any further on Wikipedia talk:Good article nominationsjacobolus (t) 03:25, 8 March 2024 (UTC)[reply]
As I stated, I am happy to remove the block when you are willing to remove your bad-faith aspersions towards another editor. If you feel the need for me to be specific, your entire first paragraph accusing another editor in good standing of being on a power trip and personal crusade to remove GA status is absolutely beyond the pale. ♠PMC(talk) 03:36, 8 March 2024 (UTC)[reply]
@Premeditated Chaos I can't make any edit at all. I am happy to strike the line you didn't like.
Here was my comment that was otherwise interrupted there, and couldn't go through:
Inre "WP:CALC" per se, math articles are not fundamentally different than any other kind of articles, in the sense that factual claims should typically be sourced to reliable sources. However, there are some differences in the way that plays out in practice: Specifically, it doesn't make any sense to try to add a separate citation to every step in a proof or derivation or every example calculation, which is the kinds of questions WP:CALC is focused on. Sometimes the argument from a paper needs several paragraphs to summarize/transmit in the body of an article, and requiring separate footnotes at the end of every paragraph of this doesn't help anyone. If a published paper contains a quick proof sketch it seems entirely fine (when otherwise appropriate in context) for an article to expand that for the sake of novice readers, and vice versa if the published paper contains a detailed proof it's fine to give a quick paraphrase. It also seems fine to use different variable names, add intermediate variables for legibility, simplify or reorder a proof, do non-novel types of algebraic manipulation, etc., so long as the idea is fundamentally the same. If you have a specific example in mind of where you are curious whether "WP:CALC" or "WP:BLUE" seems like an applicable standard or whether a claim should be cited to a specific source, people can give a clear opinion about it.
jacobolus (t) 03:44, 8 March 2024 (UTC)[reply]
Confirming you are willing to strike or remove the entire first paragraph if I unblock you? I frankly have no interest or comment about the underlying dispute; it was the comments about his motivation that I consider problematic. ♠PMC(talk) 03:48, 8 March 2024 (UTC)[reply]
@Premeditated Chaos That is correct. I am happy to strike the first paragraph. I still think GAR is a waste of time, and I would be happy to leave it to folks who care. –jacobolus (t) 03:50, 8 March 2024 (UTC)[reply]
Unblocked, thank you. ♠PMC(talk) 03:59, 8 March 2024 (UTC)[reply]

Divison by zero[edit]

Hi Jacobolus, sorry if I overwrote your changes after your reversion.

There are couple questions that I'd like your input on. Do you think it makes sense to restrict to real functions? The statements make sense for complex functions too; that's why I removed the word "real".

The reason I required the numerator to be nonzero in addition to the denominator being zero is because this is necessary for the ratio to tend to infinity, as you surely know.

Do you think it is really necessary to require the denominator to be positive away from the point in question. It is pretty standard to say that 1/x tends to infinity as x approaches 0, and not just as x approaches 0 from the right. Maybe the denominator should be assumed nonzero in some punctured neighborhood, but I couldn't figure out an easy way to say this without making the statement sound more technical. Maybe you can figure out a way to do it.

In any case, we should be calling 0/0 the indeterminate form, not f(x)/g(x). Ebony Jackson (talk) 21:20, 9 March 2024 (UTC)[reply]

I tried to make my comments clearer on the "Division by zero" Talk page, so that we're not editing at cross purposes. Maybe you or someone else can incorporate them in a way that makes sense to you. Ebony Jackson (talk) 21:35, 9 March 2024 (UTC)[reply]
I replied on talk:division by zero. –jacobolus (t) 23:02, 9 March 2024 (UTC)[reply]

In appreciation[edit]

The Barnstar of Integrity
For your commitment to the project. I have thought many things of you (as I am sure you have of me) but that is one thing I have never doubted. ~~ AirshipJungleman29 (talk) 03:09, 12 March 2024 (UTC)[reply]
Thanks. Sorry to get heated. I'll try to tone down my initial responses, even when feeling frustrated.
(To be honest the biggest part of the daily frustration is how mediocre so many important wikipedia articles are, and how limited and uncoordinated expert editor attention is to work on it. Reading articles I haven't seen before, Wikipedia is simultaneously an amazing testament to years of dedicated collaboration, and a constant stark reminder of how far short it falls of its potential and its "responsibility" as the canonical source about every topic. There's just an overwhelming amount that needs to be done.) –jacobolus (t) 03:45, 12 March 2024 (UTC)[reply]
Tell me about it. The other thing about Mongolian history is that many articles were created to focus on the wrong things, or simply not created at all, and of course no one bothers to have a look at the whole. I noticed the other day that Mongol invasions of the Levant and Mongol raids into Palestine are essentially the same article, and have been duplicating each other since 2008! ~~ AirshipJungleman29 (talk) 11:55, 12 March 2024 (UTC)[reply]

Question concerning Munsell Color System diagram[edit]

The Munsell color system, showing: a circle of hues at value 5 chroma 6; the neutral values from 0 to 10; and the chromas of purple-blue (5PB) at value 5.

Hi, jacobolus.

I hope you are doing well. My name is Michał and I am writing a scientific paper about the formalization of psychological theories. I would like to use your cool diagram of the Munsell Color System in the paper. Please let me know if that is fine with you and if so how would you like me to cite it?

Thank you very much in advance for your responce

Best wishes

Michał MichalPS (talk) 20:07, 12 March 2024 (UTC)[reply]

Hi Michał. You can certainly use this diagram, so long as you abide by the terms of the CC-BY-SA-3.0 license, which you can read at Specifically, any modifications you make to the diagram must be released under the same license, and you must give appropriate credit, for instance by including my name (Jacob Rus) the URL of the diagram (, and a mention of the CC-BY-SA-3.0 license. The exact position and formatting of these would depend on the formatting of your paper and the other images therein. If you click "more info" at the CC license description page there is further detail about this. –jacobolus (t) 20:20, 12 March 2024 (UTC)[reply]
Great, thank you very much! I do not plan to edit the diagram and I will credit you accordingly.
Thank you once again
Best wishes
Michał MichalPS (talk) 20:48, 12 March 2024 (UTC)[reply]

The previous page is less than updated[edit]

Newton's iteration in today's numerical analysis is much more than Raphson's version, which is the only version presented in the previous page. Furthermore, the convergence properties should be presented immediately after the method.

The previous page includes too much elementary stuff. This is a reference page, not a place for explanation. Fangong00 (talk) 01:19, 21 April 2024 (UTC)[reply]

@Fangong00 – Please take your concerns to talk:Newton's method. Wikipedia articles are intended for a general audience including readers with a wide range of preparation and interests. The first few sections of this particular article must be accessible to an audience of people with a high school level education, but I found your replacement version very difficult to make sense of even for people with extensive technical background.
Feel free to make the case on the talk page that this article needs to be written in a more general fashion with more advanced material toward the front. If you can establish a consensus for that position, it's possible it would stand. I am skeptical that you'll succeed at that though, as there are many other editors who are concerned that technical articles remain accessible (see WP:TECHNICAL). In any event, even if people do agree with you, the style and content of the early sections needs to be much clearer and more carefully written than your version. Perhaps you can recruit someone with strong writing skills to help you write a version which is more advanced but still legible. –jacobolus (t) 01:48, 21 April 2024 (UTC)[reply]
Aside: If you don't get enough engagement at talk:Newton's method, we can also try starting a discussion at the Wikiproject Mathematics talk page, where many of the participants are professional mathematicians or other serious experts. –jacobolus (t) 01:55, 21 April 2024 (UTC)[reply]

This cardinal feature should be on both the pages : METALLIC MEANS & PYTHAGOREAN TRIPLES[edit]

Relation between Metallic Ratios and Pythagorean triples

Metallic Ratios in Primitive Pythagorean Triangles

Metallic means are precisely represented by primitive Pythagorean triples.

In a primitive Pythagorean triple, if the difference between hypotenuse and longer leg is 1, 2 or 8, such Pythagorean triple accurately represents one particular metallic mean. The cotangent of the quarter of smaller acute angle of such Pythagorean triangle equals the precise value of one particular metallic mean.

Consider a primitive Pythagorean triple (a,b,c) in which a < b < c and c - b ∈ {1, 2, 8}. Such Pythagorean triangle (a,b,c) yields the precise value of a particular metallic mean as follows :

where θ is the smaller acute angle of the Pythagorean triangle and

For example, the primitive Pythagorean triple 20-21-29 incorporates the 5th metallic mean. Cotangent of the quarter of smaller acute angle of the 20-21-29 Pythagorean triangle yields the precise value of the 5th metallic mean. Similarly, the Pythagorean triangle 3-4-5 represents the 6th metallic mean. Likewise, the Pythagorean triple 12-35-37 gives the 12th metallic mean, the Pythagorean triple 52-165-173 yields the 13th metallic mean, and so on. [1] (talk) 10:40, 21 April 2024 (UTC)[reply]


  1. ^ Rajput, Chetansing; Manjunath, Hariprasad (2024). "Metallic means and Pythagorean triples | Notes on Number Theory and Discrete Mathematics". Bulgarian Academy of Sciences.{{cite web}}: CS1 maint: numeric names: authors list (link)

I don't understand why you posted this on my talk page. –jacobolus (t) 10:47, 21 April 2024 (UTC)[reply]

Lemniscate functions and number theory[edit]

Hi Jacobolus,

I know you like digging old stuff and your expertise would be greatly appreciated here: [5].

Regards! A1E6 (talk) 19:52, 22 April 2024 (UTC)[reply]

@A1E6 I don't feel qualified to figure this out quickly, and don't want to spend too much time on it in the immediate future, sorry. –jacobolus (t) 19:58, 22 April 2024 (UTC)[reply]

DYK for Descartes' theorem[edit]

On 23 April 2024, Did you know was updated with a fact from the article Descartes' theorem, which you recently created, substantially expanded, or brought to good article status. The fact was ... that the discovery of Descartes' theorem in geometry came from a too-difficult mathematics problem posed to a princess? The nomination discussion and review may be seen at Template:Did you know nominations/Descartes' theorem. You are welcome to check how many pageviews the nominated article or articles got while on the front page (here's how, Descartes' theorem), and the hook may be added to the statistics page after its run on the Main Page has completed. Finally, if you know of an interesting fact from another recently created article, then please feel free to suggest it on the Did you know talk page.

 — Amakuru (talk) 00:03, 23 April 2024 (UTC)[reply]

Hook update
Your hook reached 15,382 views (640.9 per hour), making it one of the most viewed hooks of April 2024 – nice work!

GalliumBot (talkcontribs) (he/it) 03:29, 24 April 2024 (UTC)[reply]

The redirect Turing recognizable has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Anyone, including you, is welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2024 May 4 § Turing recognizable until a consensus is reached. 1234qwer1234qwer4 20:02, 4 May 2024 (UTC)[reply]

Modifying comment pages[edit]

You wrote "It is inappropriate to make spelling changes to comments on talk pages." I see no mention of spelling explicitly at WP:Talk page guidelines. Because there is no change of meaning nor any criticism of the original editors, it's hard for me to see why this would be frowned upon. And because it achieves the positive objective of removing an incorrect spelling that might otherwise be imitated, I considered it a positive contribution. —Quantling (talk | contribs) 17:49, 24 May 2024 (UTC)[reply]

@Quantling It is generally considered rude to make any kind of edit to other editors' comments, though sometimes people do stuff like fixing wiki syntax or template parameter errors, especially if they break formatting for other comments. I even find this to be excessive a lot of the time, but various people run "linters" which display annoying error messages for syntax errors on pages. But this spelling fix is not necessary, and we definitely don't want to have a precedent that everyone's comments get repeatedly copyedited by other Wikipedians. There's a high chance to cause annoyance or even disputes, for no real benefit. (Of course please fix spelling mistakes in articles.) You can see discussion on the policy page you linked, under WP:OTHERSCOMMENTS: It is not necessary to bring talk pages to publishing standards, so there is no need to copy edit others' posts. Doing so can be irritating. The basic rule, with exceptions outlined below, is to not edit or delete others' posts without their permission. The later exceptions include "Attributing unsigned comments", "Fixing format errors that render material difficult to read", and "Fixing layout errors", but not making spelling changes. –jacobolus (t) 00:12, 25 May 2024 (UTC)[reply]
@Quantling I archived the old comments. Does that help? –jacobolus (t) 01:20, 25 May 2024 (UTC)[reply]