Wikipedia talk:WikiProject Mathematics
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Are Wikipedia's mathematics articles targeted at professional mathematicians?
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Abstraction is a fundamental part of mathematics. Even the concept of a number is an abstraction. Comprehensive articles may be forced to use abstract language because that language is the only language available to give a correct and thorough description of their topic. Because of this, some parts of some articles may not be accessible to readers without a lot of mathematical background. If you believe that an article is overly abstract, then please leave a detailed comment on the talk page. If you can provide a more down-to-earth exposition, then you are welcome to add that to the article. Why don't Wikipedia's mathematics articles define or link all of the terms they use?
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Apparently there were some kind of puzzles or codes in the recently released Book of Bill (related to the childrens' TV cartoon Gravity Falls) whose answers included "Triangle" and "Eye of Providence", with the result that those pages have seen massive view spikes. Triangle went from a norm of about 800–900 views per day up to 500,000 views yesterday, and possibly more today.
If anyone wants to have improvements to a mathematical page widely seen, Triangle could use some love.
(I added {{talk page header}} to Talk:Triangle hoping it would forestall some of the graffiti being directed there. Are there other good ways to deal with giant traffic spikes like this?) –jacobolus (t) 22:49, 11 August 2024 (UTC)
- @Jacobolus Triangle was used to be FA. If anyone wants to improve, especially to revive it, I think I can help, but I need a lot of work. Some advices or comments may be required. Whether the goal is to become GA or FA, that implies the article is suitably referenced and on-topic. Dedhert.Jr (talk) 00:58, 12 August 2024 (UTC)
- To be honest I don't care much about GA or FA, but it would be nice if the article were better sourced and more complete. –jacobolus (t) 01:01, 12 August 2024 (UTC)
- Okay. I have made it on my sandbox, and the progress is on the way. For someone who would like to give comments or advice for improvement only, ask me on my talk page. Dedhert.Jr (talk) 03:56, 12 August 2024 (UTC)
- To be honest I don't care much about GA or FA, but it would be nice if the article were better sourced and more complete. –jacobolus (t) 01:01, 12 August 2024 (UTC)
I have some problems while expanding the article. In the case of non-planar triangles, I found out that there are other triangles as in hyperbolic triangle and spherical triangle. However, I also found out that hyperbolic triangles can be constructed by a so-called Thurston triangle [1]. It also contains the area of a hyperbolic triangle by using Gauss–Bonnet theorem, but according to which it is a geodesic triangle. Dedhert.Jr (talk) 11:38, 14 August 2024 (UTC)
- It's unfortunate that we don't yet have an article spherical triangle, and that spherical trigonometry and spherical geometry are so incomplete. These and the many related topics which are currently red links or redirects are on my long-term todo list, but fixing even a few of them properly is a large daunting job and it's hard to get started. I'd eventually like to make a substantial number of diagrams similar to those at Lexell's theorem, but each one takes at least an hour of fiddling, sometimes several. Anyhow, both spherical triangles and hyperbolic triangles are types of geodesic triangles, with edges that are geodesics of their respective spaces.
- What your linked article calls the "Thurston model" of hyperbolic space is a discrete (infinite) polyhedron analogous to the regular icosahedron as a model of a sphere. The vertices are those of the order-7 triangular tiling; if you wanted you could put them all on one branch of a 2-sheet hyperboloid in 3-dimensional Minkowski space of signature (2, 1), and then the flat faces would be space-like triangles in the ambient Minkowski space. You could project from the hyperbolic plane onto those triangles, e.g. using the Gnomonic projection, or you can draw shapes directly in the space of the polyhedron. You could do something similar with any other kind of polyhedron. I don't think the article triangle needs to spend much if any time discussing triangles drawn the surfaces of polyhedra. –jacobolus (t) 18:07, 14 August 2024 (UTC)
Another problem: Do you think the conditions about the importance of similarity and congruence sections should be trimmed away? Not something beneficially useful including the article on triangles in general; HL and HA theorem may be included in Right triangle instead. The same reason for the similarity of triangles via trigonometric functions. However, one exception that I include is its relation with trigonometric function, defining their functions as a ratio between both sides in a right triangle, and then including the law of sines and cosines as well. Dedhert.Jr (talk) 05:43, 15 August 2024 (UTC)
Another problem: The article Triangulation (geometry) is somewhat short and unsourced in some areas. Do you think this article should be expanded, or rather redirected to the section of the article Triangle? Dedhert.Jr (talk) 05:43, 15 August 2024 (UTC)
- Triangulation (geometry) should definitely be its own article, and does not make sense to redirect. But feel free to dramatically expand it. It's a large topic about which whole books have been written. –jacobolus (t) 16:03, 15 August 2024 (UTC)
Ahh, I think something is missing here. Can somebody remind me, or give me more ideas to expand more in my sandbox? I could think of removing "triangles in construction" as in the Flatiron Building and truss; most of these topics are supposed to be triangular prism and isosceles triangle, respectively. The same reason for calculating the median, circumscribed and inscribed triangles, and many more, since they do have their own articles. Dedhert.Jr (talk) 05:43, 15 August 2024 (UTC)
- "Triangles in construction" isn't the best section title or scope, but there should definitely be at least a section about how triangles are the only polygon which is rigid when the side lengths are fixed but the sides can rotate independently about the vertices; this is why triangles are the fundamental shape used in a truss, explains why a 4-bar linkage is the most basic type (a "3-bar linkage" can't move), is a reason triangulation works in surveying, and so on.
- There should probably separately be a discussion of the use of triangles as common decorative elements etc. –jacobolus (t) 16:02, 15 August 2024 (UTC)
- Triangles are definitely not the unique basis for rigid linkages; see Laman graph. The utility graph is I think the simplest triangle-free rigid graph (in 2d). —David Eppstein (talk) 18:04, 15 August 2024 (UTC)
- That's an interesting subject well worth discussing in Laman graph or structural rigidity, but the utilities graph isn't a polygon, and isn't really relevant to the point that the triangle's rigidity is the reason for many of its practical applications. Edit: Maybe Triangle § Rigidity would be a good top-level heading for Triangle. –jacobolus (t) 19:56, 15 August 2024 (UTC)
- @Jacobolus. Okay. I would probably do more research and apply them to my sandbox. One problem here is I still cannot find the sources about the rigidity of a triangle and its tessellation with a hexagon. Dedhert.Jr (talk) 05:55, 16 August 2024 (UTC)
- That's an interesting subject well worth discussing in Laman graph or structural rigidity, but the utilities graph isn't a polygon, and isn't really relevant to the point that the triangle's rigidity is the reason for many of its practical applications. Edit: Maybe Triangle § Rigidity would be a good top-level heading for Triangle. –jacobolus (t) 19:56, 15 August 2024 (UTC)
- Triangles are definitely not the unique basis for rigid linkages; see Laman graph. The utility graph is I think the simplest triangle-free rigid graph (in 2d). —David Eppstein (talk) 18:04, 15 August 2024 (UTC)
Completion
[edit]@jacobolus. The article is done for refactoring and rewriting. But some sources may needed to complete the article. Do you have any comments about something is missing or superfluous in the article? Let me know. Dedhert.Jr (talk) 07:48, 17 August 2024 (UTC)
- Thanks for putting in the time and energy. XOR'easter (talk) 21:18, 19 August 2024 (UTC)
- I've made a smattering of edits to fix small prose matters and fill in some citations. It's still a little under-referenced, so anyone else who'd like to jump in and work on that should feel more than welcome. XOR'easter (talk) 23:30, 19 August 2024 (UTC)
- I appreciate your work, as well as the compliments. Still have problems, however, especially with the sources of Heath's book The Thirteen Books. The first book's Definition 20 describes the isosceles triangle definition according to Euclid, but I think this is a mismatch with the given page in Isosceles triangle, or it is hidden in the Greek writings. Pinging @David Eppstein for further explanation. There is a similar reason for Heath's footnotes being more numerous. Dedhert.Jr (talk) 02:51, 20 August 2024 (UTC)
- Maybe I'm misreading your comment: do you mean there is a mismatch in Euclid's definition, or just with the formatting of the reference? If the former, you should read the Usiskin & Griffin source from both articles. There are two different and incompatible ways of classifying shapes:
- In exclusive classification, all cases must be disjoint: each shape can have only one type
- In inclusive classification, special cases are subsets of more general cases
- As our isosceles triangle article states, Euclid uses an exclusive classification, in which isosceles triangles must have exactly two equal sides and in which equilateral triangles are not isosceles. Many other sources use an inclusive classification in which equilateral triangles are special cases of isosceles triangles. But both remain in use.
- Using an inclusive classification and allowing classes to be subsets of each other can be more flexible and avoids unnecessary case analysis. For instance, when Euclid proves a theorem about isosceles triangles, he would have to prove the same theorem again for equilateral triangles, because the givens from the first theorem would not match the definition needed for the second theorem. And when does a special case become separate from the general case? Maybe isosceles right triangles aren't isosceles triangles, because they are in a different special case class?
- The same issue comes up even more strongly for quadrilaterals, where one may reasonably ask whether parallelograms are trapezoids, whether rectangles or rhombi are parallelograms, and whether squares are rectangles or rhombi. And then one must reconcile this classification with cyclic quadrilaterals, tangential quadrilaterals, orthodiagonal quadrilaterals, kites, bicyclic quadrilaterals, etc. In the isosceles triangle case, either definition was easy enough to write, but for many of these other cases of quadrilaterals, the inclusive definitions are easy to write (it's a quadrilateral for which a specific constraint is true) and the exclusive definitions are much messier (the constraint is true but also some other constraints that would cause it to be a more specific special case are all false).
- Most of the time we use inclusive classification in our Wikipedia articles, but this distinction should be explained. And it's important that this choice be made in a principled way rather than randomly and inconsistently from one article to another because of the sources you happened to read when you were working on the article.
- If I'm misinterpreting and this was all purely about page numbers then sorry for the off-topic rant. The important part of the Euclid reference is "Book 1, definition 20". —David Eppstein (talk) 04:25, 20 August 2024 (UTC)
- @David Eppstein What I meant is in the article Isosceles triangle, you cited Euclid's definition on page 187 [Heath (1956), p. 187, Definition 20.] But I cannot find that definition on that page. What I meant about Greek letters is, even though I found the "Definition 20" on a different page, I will never find that the definition, and it is possibly written in Greek language. This is why I leave this to you since you are the nominator of that GA. and I have no clue about the article's expansion back of the day. Anyway, thank you for your explanation above. Dedhert.Jr (talk) 05:12, 20 August 2024 (UTC)
- I can check my copy the next time I'm in the office. Are you sure you're looking at Vol.1 of the Dover three-volume edition? There are a lot of different reprints of Heath's translation. If you're reading it in Greek then I think you have a different one; I would have referred to an English translation. —David Eppstein (talk) 05:33, 20 August 2024 (UTC)
- @David Eppstein I have searched it on Heath's citation, which I pointed out in the recent replies. As far as I'm concerned, the page describes the Greek language as the definition and English is probably the further explanation and comments. Look at the page 292 that I linked here [2]. Dedhert.Jr (talk) 05:45, 20 August 2024 (UTC)
- "Heath's citation" is ambiguous. There are many reprints of Heath's translation of Euclid. Again, are you sure you're looking at Vol.1 of the Dover three-volume edition? The link you give is to Book 7 in Vol.2, not to Book 1 in Vol.1. —David Eppstein (talk) 06:09, 20 August 2024 (UTC)
- @David Eppstein Sorry but that source is already linked as a reference or works cited in the Isosceles triangle, see the references:
- Heath, Thomas L. (1956) [1925]. The Thirteen Books of Euclid's Elements. Vol. 1 (2nd ed.). New York: Dover Publications. ISBN 0-486-60088-2.
- Dedhert.Jr (talk) 10:16, 20 August 2024 (UTC)
- Apparently the incorrect link is the fault of User:InternetArchiveBot: [3]. Reported: T372925. —David Eppstein (talk) 17:25, 20 August 2024 (UTC)
- Ideally we should be citing the Cambridge University Press 2nd edition from 1926, which was later reprinted by Dover, and including a link to a scan of the appropriate page with every reference. Unfortunately the internet archive only has a scan of volume 3, and many of their scans of dover reprints are blocked or need to be "checked out" (though they shouldn't be, since the copyright is still 1926, and expired). HathiTrust has a scan of vol 2 (and vol. 3). –jacobolus (t) 15:49, 20 August 2024 (UTC)
- What we need in this case is vol.1. —David Eppstein (talk) 17:31, 20 August 2024 (UTC)
- Is this it?
Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.
XOR'easter (talk) 17:49, 20 August 2024 (UTC)- Yes. And the page number matches, answering Dedhert.Jr's question. —David Eppstein (talk) 18:00, 20 August 2024 (UTC)
- Is this it?
- What we need in this case is vol.1. —David Eppstein (talk) 17:31, 20 August 2024 (UTC)
- @David Eppstein Sorry but that source is already linked as a reference or works cited in the Isosceles triangle, see the references:
- "Heath's citation" is ambiguous. There are many reprints of Heath's translation of Euclid. Again, are you sure you're looking at Vol.1 of the Dover three-volume edition? The link you give is to Book 7 in Vol.2, not to Book 1 in Vol.1. —David Eppstein (talk) 06:09, 20 August 2024 (UTC)
- @David Eppstein I have searched it on Heath's citation, which I pointed out in the recent replies. As far as I'm concerned, the page describes the Greek language as the definition and English is probably the further explanation and comments. Look at the page 292 that I linked here [2]. Dedhert.Jr (talk) 05:45, 20 August 2024 (UTC)
- I can check my copy the next time I'm in the office. Are you sure you're looking at Vol.1 of the Dover three-volume edition? There are a lot of different reprints of Heath's translation. If you're reading it in Greek then I think you have a different one; I would have referred to an English translation. —David Eppstein (talk) 05:33, 20 August 2024 (UTC)
- @David Eppstein What I meant is in the article Isosceles triangle, you cited Euclid's definition on page 187 [Heath (1956), p. 187, Definition 20.] But I cannot find that definition on that page. What I meant about Greek letters is, even though I found the "Definition 20" on a different page, I will never find that the definition, and it is possibly written in Greek language. This is why I leave this to you since you are the nominator of that GA. and I have no clue about the article's expansion back of the day. Anyway, thank you for your explanation above. Dedhert.Jr (talk) 05:12, 20 August 2024 (UTC)
- Maybe I'm misreading your comment: do you mean there is a mismatch in Euclid's definition, or just with the formatting of the reference? If the former, you should read the Usiskin & Griffin source from both articles. There are two different and incompatible ways of classifying shapes:
- I appreciate your work, as well as the compliments. Still have problems, however, especially with the sources of Heath's book The Thirteen Books. The first book's Definition 20 describes the isosceles triangle definition according to Euclid, but I think this is a mismatch with the given page in Isosceles triangle, or it is hidden in the Greek writings. Pinging @David Eppstein for further explanation. There is a similar reason for Heath's footnotes being more numerous. Dedhert.Jr (talk) 02:51, 20 August 2024 (UTC)
Well, the article is down to a handful of uncited statements. I'm not sure that all of them need to be kept in the text. I can try to scrape together the time to work on it more, but maybe someone else would rather take a swing at it. XOR'easter (talk) 18:33, 23 August 2024 (UTC)
- It seems that most of the areas are sourced, only some of the "citation needed"-tags and untagged areas are the remaining problems. Yet, is there anything that can include other related topics of a triangle here? Dedhert.Jr (talk) 01:16, 28 August 2024 (UTC)
Requested move at Talk:Hilbert system#Requested move 20 August 2024
[edit]![](http://upload.wikimedia.org/wikipedia/en/thumb/2/28/Information.svg/30px-Information.svg.png)
There is a requested move discussion at Talk:Hilbert system#Requested move 20 August 2024 that may be of interest to members of this WikiProject. Rotideypoc41352 (talk · contribs) 21:54, 21 August 2024 (UTC)
Uncited and vague statement at Trigonometric functions
[edit]This line in Trigonometric functions is tagged for temporal vagueness and needing a reference: The modern trend in mathematics is to build geometry from calculus rather than the converse.
Is this remark actually true, and if so, is it worth saying in that spot? It seems to me that talking of a singular "trend" in mathematics is likely to be unsupportable. If one is doing coordinate geometry, one might found it upon properties of the real numbers as developed in real analysis, which is the sophisticated version of/groundwork for/elective taken after calculus. But to a reader for whom geometry is a prereq to calculus, this statement is probably rather puzzling. XOR'easter (talk) 23:21, 21 August 2024 (UTC)
- This seems more or less right, but may be unnecessary here, and could be significantly elaborated. Our description both here and at trigonometry and history of trigonometry is extremely incomplete. As for when this occurred, as concerns trigonometry per se this approach more or less originates with Euler, but picked up steam with Fourier series and then efforts to make them more rigorous in the 19th century, and by studies of elliptic functions, &c. With respect to geometry more generally, I'd also say this is a trend, with pure mathematicians treating geometry as founded in analysis (and its offshoots of topology and set theory), more and more over time starting in the 18th century but since the 20th century almost completely. You could extend this general trend earlier if comparing the gradual substitution of coordinates and analytic geometry in preference to Greek definitions and "synthetic" methods. –jacobolus (t) 00:11, 22 August 2024 (UTC)
- I've given it a go, but I think the article needs some organizing. Also, there is no mention of asymptotes. Tito Omburo (talk) 01:14, 22 August 2024 (UTC)
- I'm not sure the gesture toward G. H. Hardy is any more helpful to readers than the previous vague handwave about trends away from geometry. I'd just cut those prefatory sentences and discuss the broader context more thoroughly in the history section and in history of trigonometry.
- This and related articles could definitely use organizing. There could also be separate articles about tangent (trigonometry) and secant (trigonometry) to go along with sine and cosine, which would leave more room for discussing more specific history, applications, etc. –jacobolus (t) 05:06, 22 August 2024 (UTC)
- A problem with the previous vagueness is that it was an unreferenced point of view. Also, the assertion that there are "two ways" to define the trigonometric functions was flat out wrong. Hardy lists four, not including the first one described in the article (which I found in Bartle and Sherbert). Tito Omburo (talk) 09:58, 22 August 2024 (UTC)
- A minor point: I don't understand why there's so much name-dropping/attribution in your addition. One can write "there is a problem with geometry as a definition.[ref: hardy] there are mutliple modern approaches to fix this: (1)(2)(3)(4).[refs:hardy, bartle-sherbert]" What is added by announcing at the beginning of these sentences that the references at the end of the sentence are written by Hardy and by Bartle--Sherbert? --JBL (talk) 17:54, 22 August 2024 (UTC)
- I'm not married to the wording, but it seems like this is the basic content and sources that should be there. Tito Omburo (talk) 20:31, 22 August 2024 (UTC)
- A minor point: I don't understand why there's so much name-dropping/attribution in your addition. One can write "there is a problem with geometry as a definition.[ref: hardy] there are mutliple modern approaches to fix this: (1)(2)(3)(4).[refs:hardy, bartle-sherbert]" What is added by announcing at the beginning of these sentences that the references at the end of the sentence are written by Hardy and by Bartle--Sherbert? --JBL (talk) 17:54, 22 August 2024 (UTC)
- A problem with the previous vagueness is that it was an unreferenced point of view. Also, the assertion that there are "two ways" to define the trigonometric functions was flat out wrong. Hardy lists four, not including the first one described in the article (which I found in Bartle and Sherbert). Tito Omburo (talk) 09:58, 22 August 2024 (UTC)
- This discussion might better be moved to talk:trigonometric functions, but @Tito Omburo you should give a source for "amplitude function", "method of amplitudes", etc. These are extremely rare names I have never heard of after spending many hundreds of hours researching the specific topic of the trigonometric half-tangent, and can't find any mention of in a google scholar search. –jacobolus (t) 21:45, 22 August 2024 (UTC)
- It's just the amplitude of , but I'll get rid of the neologism. I thought I had seen this in Bourbaki's real variables, but now it seems I was mistaken. Tito Omburo (talk) 22:26, 22 August 2024 (UTC)
- I've given it a go, but I think the article needs some organizing. Also, there is no mention of asymptotes. Tito Omburo (talk) 01:14, 22 August 2024 (UTC)
- "Build geometry from calculus"? What is being referred to here? Michael Hardy (talk) 02:35, 22 August 2024 (UTC)
- I'd say that
The modern trend in mathematics is to build Euclidean geometry from calculus rather than the converse.
is generally true, but that the more general statement is false. I'm having trouble coming up with a replacement that is both accurate and concise enough to be in the lead. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:12, 22 August 2024 (UTC) - This statement is basically true from the perspective of a differential geometer, but not from the perspective of an algebraic geometer. I think this statement should be expanded upon or removed because it is just way too vague to be helpful. In the context of trig, it might be more helpful to say that nowadays people define trig functions using calculus and then define angles using trig functions. Mathwriter2718 (talk) 13:39, 22 August 2024 (UTC)
Convex polyhedron
[edit]The article Convex polyhedron is currently under the article's redirection Convex polytope. Our articles have several type of convex polyhedrons: Platonic solid, Archimedean solid, Catalan solid, deltahedron, Johnson solid, and many more. The article convex polyhedron should have redirected into Polyhedron#Convex polyhedra. It seems convex polytope describes the generalization concept. Dedhert.Jr (talk) 09:15, 23 August 2024 (UTC)
- I'll do this change, since readers interested in convex polyhedra need not know dimensions higher than 3. D.Lazard (talk) 09:25, 23 August 2024 (UTC)
The redirect Multiplicity of a restricted root has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2024 August 21 § Multiplicity of a restricted root until a consensus is reached. 136.152.209.125 (talk) 04:24, 24 August 2024 (UTC)
Page move to Piecewise function
[edit]After some discussion at Talk:Piecewise_function#Requested_move_20_July_2024, the page Piecewise was moved to Piecewise function. I still consider this decision nonsensical, and the new title highly confusing. For this reason, I'd like to draw your attention to the move. If nobody else has a problem with it, I'll shut up. - Jochen Burghardt (talk) 18:05, 25 August 2024 (UTC)
In addition, a separate(!) DAB page Piecewise property has been created, which links most of its entries (like "Piecewise continuous") back to Piecewise function, where they are explained more or less satisfactorily. According to Piecewise_function#See_also, "Piecewise property" is a generalization of "Piecewise function"! - Jochen Burghardt (talk) 18:05, 25 August 2024 (UTC)
- According to WP:NOUN the title should be a noun. For example, instead of "French", articles are titled "French language" or "French people". — Rgdboer (talk) 20:08, 25 August 2024 (UTC)
- Or "piecewise property". The problem with "piecewise function" is not grammatical; it is that many of the things defined piecewise are not exactly functions. See e.g. piecewise linear manifold. —David Eppstein (talk) 20:27, 25 August 2024 (UTC)
- I'd move Piecewise property to Piecewise, which if someone wants could be upgraded to a "broad-concept article", and leave a separate article at piecewise function, which should ideally contain quite a bit more discussion of piecewise polynomial "splines", piecewise parametric curves as used in CAD/CAM, and so on. –jacobolus (t) –jacobolus (t) 21:33, 25 August 2024 (UTC)
- My point is that there is no such thing as a piecewise function. Every function can be defined using
if . then . else . endif
(linearizing 2dim math terminology), and every function can be defined without it. This is stated correctly in the 2nd lead sentence. In order to subsume also e.g. piecewise linear manifold, what about "Piecewise definition"? - Jochen Burghardt (talk) 21:52, 25 August 2024 (UTC)every function can be defined without it
While this is maybe true in a very narrow pedantic sense, the concept of a "piecewise function" has a clear, obvious, and useful meaning (which is why it is used in practice), and there are valuable things to say about it as a concept which would not be relevant to an article about "every function". –jacobolus (t) 09:27, 26 August 2024 (UTC)- Given a function by its domain, range, and graph, you can check whether it is piecewise linear, piecewise continuous, etc. (provided additional restrictions to domain and range are met). However, I doubt that you can check whether it is piecewise (without any property); I even don't know what that could mean. Moreover, different properties can require different domain decompositions, e.g. is piecewise differentiable (use , , ) and piecewise monotonic (use , ). Also note the absence of any case distinction from this definition.
- What we can say, however, is what a piecewise definition is (one that has an outermost case distinction on a domain decomposition into finitely many intervals). Based on this, we can define a function to be piecewise xxx if is has some piecewise definition such that each piece satisfies xxx (this is what the article does). Possible, this can also be generalized from total to partial orders to subsume also David Eppstein's piecewise linear manifold example. - Jochen Burghardt (talk) 13:22, 28 August 2024 (UTC)
- Okay, but "take a function and determine whether it is 'piecewise'" is not really something anyone cares much about. Instead, people are interested in proving properties about functions defined or known to be definable in pieces (usually each piece of some specific type, such as constant, polynomial, rational, a linear combination of given basis functions, continuous with bounded derivative, ...), because such functions are extremely common in all sorts of practical applications. Calling these "piecewise functions" is common and well understood (Google scholar turns up 37k results for that phrase – much more common than alternatives I can find, so a good title following WP:COMMONNAME). Deciding that "there is no such thing as a piecewise function" is in my view a semantic quibble that kind of misses the point. –jacobolus (t) 15:54, 28 August 2024 (UTC)
- My point is that there is no such thing as a piecewise function. Every function can be defined using
- I'd move Piecewise property to Piecewise, which if someone wants could be upgraded to a "broad-concept article", and leave a separate article at piecewise function, which should ideally contain quite a bit more discussion of piecewise polynomial "splines", piecewise parametric curves as used in CAD/CAM, and so on. –jacobolus (t) –jacobolus (t) 21:33, 25 August 2024 (UTC)
- Or "piecewise property". The problem with "piecewise function" is not grammatical; it is that many of the things defined piecewise are not exactly functions. See e.g. piecewise linear manifold. —David Eppstein (talk) 20:27, 25 August 2024 (UTC)
- I agree that the term “piecewise property” seems problematic since, unlike continuity or differentiability, it’s not something a function can have or not. “Piecewise-linear” is a property that a space or a function, etc. can have but that’s different. Since other editors have made the same point, I have started a move proposal: “piecewise property” -> “piecewise” at talk:Piecewise_property#Requested_move_26_August_2024. —- Taku (talk) 08:16, 26 August 2024 (UTC)
What about Piecewise-defined property? Surely we agree that a given definition of a property can be piecewise (or not)? The piecewise functions of calculus are perhaps piecewise elementary functions, for example. 100.36.106.199 (talk) 10:37, 28 August 2024 (UTC)
- I've been an advocate of piecewise-defined, as grammatically preferable to the other options. Tito Omburo (talk) 10:57, 28 August 2024 (UTC)
- Or, if it must be a noun, piecewise definition. —David Eppstein (talk) 17:49, 28 August 2024 (UTC)
- +1 for piecewise definition; that seems to get best at the correct concept. Piecewiseness is not a property of functions, but it is a property of definitions. --Trovatore (talk) 19:26, 28 August 2024 (UTC)
- Sounds good to me, for the general concept article. Tito Omburo (talk) 19:42, 28 August 2024 (UTC)
- Piecewise definition sounds good to me, too. XOR'easter (talk) 02:19, 29 August 2024 (UTC)
- Sounds good to me, too. - Jochen Burghardt (talk) 11:52, 29 August 2024 (UTC)
- Sure, let's do it. 100.36.106.199 (talk) 16:15, 29 August 2024 (UTC)
- Or, if it must be a noun, piecewise definition. —David Eppstein (talk) 17:49, 28 August 2024 (UTC)
Rhombic icosahedron and Springer
[edit]The Springer source [4] states that it is false in our Wikipedia that rhombic icosahedron is the dual polyhedron of a pentagonal gyrobicupola. I am surprised this fact still exists nowadays. Any thoughts? Dedhert.Jr (talk) 11:13, 26 August 2024 (UTC)
- The Springer source is correct. The rhombic icosahedron has adjacent degree-5 and degree-3 vertices, so the dual should have adjacent pentagons and triangles, as shown in the figure in the Springer source. The pentagonal gyrobicupola has the correct numbers of faces of each type but incorrect adjacencies; its pentagons and triangles are not adjacent. I will remove this mistake from our article. —David Eppstein (talk) 17:22, 26 August 2024 (UTC)
Updates to "Math theorem" Templates: Improved style and new proof parameters
[edit]Currently, there are two templates for inserting formatted theorems and proofs into articles: {{Math theorem}} and {{Math proof}} In many cases, however, the proof of a theorem directly follows the theorem. The formatting when juxtaposing these templates is not great, however:
Theorem — My theorem statement.
My proof statement.
I have written a modified version of {{Math theorem}} (see {{Math theorem/sandbox}}, at [this revision]) to improve the formatting by incorporating the proof as a new parameter for {{Math theorem}}, and also bringing the default formatting of theorems in line with typical math texts:
Theorem. My theorem statement.
Please join the conversation at Template talk:Math theorem there if you have opinions about the proposed change. The-erinaceous-one (talk) 04:50, 2 September 2024 (UTC)
- Can you give examples of articles where you think this template should be used? Personally I find that most of the time ordinary paragraphs are sufficient for theorem statements and proofs (in some articles where authors put theorems in flashy boxes, sometimes with color, etc., I have found the decorations more distracting than helpful). Proofs are helpful in particular in articles that are directly about a theorem or a few theorems, or occasionally in articles where a particular theorem is fundamentally important to the topic, but in cases I'm thinking of collapsing the proofs would defeat the point of including them. Most of the rest of the time I'd skip the proofs altogether (proofs in external resources can be linked from footnotes, or if a proof seems distracting but necessary, it could be put in a footnote in full). –jacobolus (t) 06:35, 2 September 2024 (UTC)
- I envision the new version of the template replacing the current {{Math theorem}} template and also being used anywhere else that a formal theorem statement could be useful. As you noted, many pages currently display theorems and proofs in boxes, which I agree are undesirable. Editors might sometimes intentionally add boxes around theorems and proofs, but I think in many cases they simply use {{Math theorem}} because they assume it is the "standard" Wikipedia formatting of theorems. By updating the template, we would improve the formatting across all of those pages that use it and discourage editors from doing ad-hoc formatting of theorems (e.g., boxes and colors).
- Regarding the formatting of proofs, I'm not married to the idea of making the proofs collapsed by default, or, in fact collapsible by default. We could choose the default to not make proofs collapsible and then allow editors to enable it using a parameter flag. I am also looking into adding another parameter that allows displaying the proof in a footnote, although I personally find this a worse option than a collapsible box since it requires readers to scroll up and down if they want to see the theorem while reading the proof.
- One example of a page that would benefit from a nicely formatted Theorem template is Liouville's theorem (Hamiltonian). Despite the name of the page including "theorem", there is not a formal statement of the theorem. The closest thing it has is
The distribution function is constant along any trajectory in phase space.
- but this doesn't state the formal assumptions of the theorem. The-erinaceous-one (talk) 22:58, 2 September 2024 (UTC)
- I was looking around for an example of a proof in the footnote, but didn't find one quickly. Here's what I have tried for the {{Math theorem}} template.
Theorem. Mathy mathy math.[proof 1]
- The-erinaceous-one (talk) 23:27, 2 September 2024 (UTC)
- I would recommend against replacing the previous template, since authors who used it were intending the behavior as provided at the time, not an entirely different appearance chosen by someone else later. I also disagree that Liouville's theorem (Hamiltonian) would benefit from having parts of it wrapped in boxes or reformatted. Ordinary paragraphs are working fine there. In my opinion you should make a new template under a new name if you want it, and then adopt it on pages you write yourself or do significant work on, but should leave other pages alone. Aside: your sandbox version probably has some kind of malformed HTML which causes it to render outside of a colon-indented talk page response (which uses a definition list element). –jacobolus (t) 23:44, 2 September 2024 (UTC)
- It looks like the existing template does not work well in lists either. [Edit: I placed an example here, but it broke our ability to use the "reply" editor]. The-erinaceous-one (talk) 00:07, 3 September 2024 (UTC)
- Regarding Liouville's theorem (Hamiltonian), I think a weakness of that page is that it is difficult to figure out what "the theorem" actually says. First you have to search through the page to find the quoted text I copied above (which is not clearly labeled as the theorem). Then, you have to reconstruct and/or guess what the assumptions of the theorem are from the rest of the article. The-erinaceous-one (talk) 00:13, 3 September 2024 (UTC)
- In other words, it's a typical explanation of something that physicists call a theorem. XOR'easter (talk) 02:31, 3 September 2024 (UTC)
- I would recommend against replacing the previous template, since authors who used it were intending the behavior as provided at the time, not an entirely different appearance chosen by someone else later. I also disagree that Liouville's theorem (Hamiltonian) would benefit from having parts of it wrapped in boxes or reformatted. Ordinary paragraphs are working fine there. In my opinion you should make a new template under a new name if you want it, and then adopt it on pages you write yourself or do significant work on, but should leave other pages alone. Aside: your sandbox version probably has some kind of malformed HTML which causes it to render outside of a colon-indented talk page response (which uses a definition list element). –jacobolus (t) 23:44, 2 September 2024 (UTC)
- The-erinaceous-one (talk) 23:27, 2 September 2024 (UTC)
- Skimming through links at Special:WhatLinksHere/Template:Math theorem and Special:WhatLinksHere/Template:Math proof, these templates aren't really all that widely used, and in my opinion most of the articles where they are used would be improved by avoiding the templates (and sometimes taking out the proofs). YMMV. –jacobolus (t) 06:51, 2 September 2024 (UTC)
- Their usage might not be ubiquitous, but 400+ pages is not insignificant and improving the available template(s) would improve those pages and making nicely formatted theorems and proofs easier. Regardless, the {{Math theorem}} template already exists and is used, so the question is whether the proposed changes would be improvements---not whether we should completely stop using it. The-erinaceous-one (talk) 23:01, 2 September 2024 (UTC)
- Also, many of the pages I've opened up use the templates multiple times, so the total number of uses is well over 400. The-erinaceous-one (talk) 00:34, 3 September 2024 (UTC)
- Yeah, if it were up to me at least half of those would not have any such template. But it's disruptive to make changes like this at large scale. People should feel free to use this list as inspiration for finding articles which could be improved, including by removing the templates. –jacobolus (t) 01:45, 3 September 2024 (UTC)
- Also, many of the pages I've opened up use the templates multiple times, so the total number of uses is well over 400. The-erinaceous-one (talk) 00:34, 3 September 2024 (UTC)
- Their usage might not be ubiquitous, but 400+ pages is not insignificant and improving the available template(s) would improve those pages and making nicely formatted theorems and proofs easier. Regardless, the {{Math theorem}} template already exists and is used, so the question is whether the proposed changes would be improvements---not whether we should completely stop using it. The-erinaceous-one (talk) 23:01, 2 September 2024 (UTC)
- I agree with @jacobolus that we don't want to put too much emphasis on proofs. Many articles would actually benefit from removing some of their proofs. This has been discussed multiple times on WPM. From the Proofs section of MOS:MATH:
A downside of including proofs is that they may interrupt the flow of the article, whose goal is usually expository. Use your judgment; as a rule of thumb, include proofs when they expose or illuminate the concept or idea; don't include them when they serve only to establish the correctness of a result.
In many cases it would be more beneficial to work on replacing the proofs with some suitable references to reputable sources instead of incorporating them into some new template. PatrickR2 (talk) 03:19, 3 September 2024 (UTC)- Even without the issue of incorporating proofs or not, I often find the current template (and the new template) which wraps the result in a "template box" to be distracting and annoying. In articles that discuss multiple results, it gives undue weight to those that happen to have an official name of "Theorem of Such-and-such" compared with those results that don't. That unnecessarily breaks the flow of exposition. Better use something less intrusive like "Theorem of such-and-such: statement ..." in the text itself. One case where the template could be justified is an article or section dedicated to a single theorem. But most of the time, the use of the template seems misguided to me. PatrickR2 (talk) 03:28, 3 September 2024 (UTC)
- There are two different matters: how to update the current theorem template and whether its use is appropriate. I commented on the first in the talk page of the template and so here I comment on the second. As someone who actually likes using the template (and the one who actually imported the template from French Wikipedia), I think it depends on how it is used within an article. I agree in some instances, boxes can be jarring especially if there are too many of them. On the other hand, emphasizing a statement in some way is a good idea in some other instances. The axiom of choice articles gives a good example in my opinion: since the article is about a single statement. (As the proof template, I have never used it personally but apparently some people like it) —- Taku (talk) 08:26, 3 September 2024 (UTC)
Square bipyramid proposal to split
[edit]Discussion on splitting article the square bipyramid is ongoing. See Talk:Octahedron#Create a square bipyramid or regular octahedron article. More opinions are welcome. Dedhert.Jr (talk) 11:08, 4 September 2024 (UTC)
Eigenmode vs. eigenmodes (redirects)
[edit]Currently,
- eigenmode redirects to Eigenvalues and eigenvectors, and
- eigenmodes redirects to Normal mode.
This is obviously confusing, because eigenmodes ([[eigenmode]]s
) and eigenmodes ([[eigenmodes]]
) are different link destinations.
Suggestion: the plural redirect [[eigenmodes]]
should point to Eigenvalues and eigenvectors, just like the singular version. Thoughts? — sbb (talk) 03:30, 5 September 2024 (UTC)
- The word “mode” (with or with prefix) does not appear at Eigenvalues and eigenvectors; should it? 100.36.106.199 (talk) 10:36, 5 September 2024 (UTC)
- I believe that the best way forwards is to look at all of the articles on eigenfunction, eigenmode, eigenstate, eigenvector and normal mode collectively, then discuss what to merge and what to redirect. As part of this, the redirects for singular and plural should be brought into alignment with each other after looking at what links to what.
- My first take is that eigenfunctions and eigenvectors should be in the same article, but I could make a case for keeping them separate. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:52, 5 September 2024 (UTC)
- Clearly the target of any of these links should not depend on whether it is plural or not. That's easy to fix.
- I think Eigenfunction should be kept separate from Eigenvalues and eigenvectors, since the latter article is necessarily focused on linear endomorphisms in general, whereas the former should be focused on the specific application to function spaces. It's fine to leave a summary in Eigenvalues and eigenvectors § Eigenvalues and eigenfunctions of differential operators pointing to Eigenfunction as a main article. –jacobolus (t) 17:25, 5 September 2024 (UTC)
- A mode is a standing wave. See eg https://www.feynmanlectures.caltech.edu/I_49.html#Ch49-S5
- In mathematical models of wave systems these standing waves appear as "eigenfunctions", also called "eigenvectors" in some representations. A mode, a wave concept, is not a synonym for "eigenfunction", a mathematical concept.
- Absent a significant reliable reference, "eigenmode" should be deleted. The word is redundant by repeating itself. Similarly "eigenmodes". Without a reference having these pages is misinformation. Johnjbarton (talk) 15:34, 5 September 2024 (UTC)
- According to Eigenmode expansion, eigenmode is a specific term-of-art for solutions of the Maxwell equation along a waveguide. This usage seems to be consistent with many of the hits in a cursory Google scholar search. Tito Omburo (talk) 17:19, 5 September 2024 (UTC)
- Thanks, but I disagree with your characterization based on the three sources in that page. None of these references define "eigenmode" and as far as I can tell they only use the word as a modifier as in "eigenmode propagation algorithm".
- The solutions to Maxwell's equations along a waveguide seems to be just "modes". Jackson discusses "wave guides" in section 8.3 and says:
- "There will be a spectrum of eigenvalues and corresponding solutions which form an orthonormal set. These different solutions are called the modes of the waveguide.
- Here is a review of quantum optics that uses the word 'mode' many times, but 'eigenmode' rarely and inconsistently.
- Fabre, Claude, and Nicolas Treps. "Modes and states in quantum optics." Reviews of Modern Physics 92.3 (2020): 035005.
- My guess is that "eigenmode" has a specific technical meaning like you say. But what meaning?
- Based on what we know so far, "eigenmode" should redirect to Eigenmode expansion since at least the word is used there. Johnjbarton (talk) 19:38, 5 September 2024 (UTC)
- Ok I think I found a review that sorts this out at least for radio waves:
- Huang, Shaode, Jin Pan, and Yuyue Luo. "Study on the relationships between eigenmodes, natural modes, and characteristic modes of perfectly electric conducting bodies." International Journal of Antennas and Propagation 2018.1 (2018): 8735635.
- Eigenmode expansion method (EEM) [3], singularity expansion method (SEM) [4], and characteristic mode analysis (CMA) [5] are three common modal analysis methods in electromagnetic engineering. The three modal analysis methods result in three different kinds of modes generally, that is, eigenmodes, natural modes, and characteristic modes, respectively.
- Huang, Shaode, Jin Pan, and Yuyue Luo. "Study on the relationships between eigenmodes, natural modes, and characteristic modes of perfectly electric conducting bodies." International Journal of Antennas and Propagation 2018.1 (2018): 8735635.
- Based on this reference (and thus restricted to the corresponding field), "eigenmode" is not a synonym for "eigenvector" or "normal mode", but a specialized term related to the "eigenmode expansion method". Johnjbarton (talk) 19:57, 5 September 2024 (UTC)
- Ok I think I found a review that sorts this out at least for radio waves:
- According to Eigenmode expansion, eigenmode is a specific term-of-art for solutions of the Maxwell equation along a waveguide. This usage seems to be consistent with many of the hits in a cursory Google scholar search. Tito Omburo (talk) 17:19, 5 September 2024 (UTC)
Help needed on several elementary articles
[edit]Farkle Griffen made many edits on several elementary articles including Variable (mathematics), Mathematical object, Indeterminate (variable) and several others. Generally, these article are of low quality, but IMO, most of their edits are disimprovements, as consisting generally of misinterpretations of randomly chosen sources. One of their typical edit is to change the first sentence of Variable (mathematics) from "In mathematics, a variable is a symbol, typically a letter that is used for naming a mathematical object, often a number" to "In mathematics, a variable is a symbol, typically a letter, that holds a place for constants, often numbers".
I must stop to revert them, because WP:3RR, and because of the lack of third party input, I cannot open an ANI thread for disruptive editing (this appears as content dispure).
So, I need some help. D.Lazard (talk) 18:36, 5 September 2024 (UTC)
- Mathematical object seems broadly improved. Variable and indeterminate seem tricky to me. There's at least one way these are different, in that variables usually have a domain, while indeterminates are purely formal symbols. (E.g., random variable, real variable, etc.) But many people in casual discourse make no such distinction. Tito Omburo (talk) 18:53, 5 September 2024 (UTC)