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Frequently asked questions To view an explanation to the answer, click on the [show] link to the right of the question. Are Wikipedia's mathematics articles targeted at professional mathematicians?
No, we target our articles at an
appropriate audience. Usually this is an interested layman. However, this is not always possible. Some advanced topics require substantial mathematical background to understand. This is no different from other specialized fields such as law and medical science. If you believe that an article is too advanced, please leave a detailed comment on the article's talk page. If you understand the article and believe you can make it simpler, you are also welcome to improve it, in the framework of the
BOLD, revert, discuss cycle. Why is it so difficult to learn mathematics from Wikipedia articles?
Wikipedia is an encyclopedia,
not a textbook. Wikipedia articles are not supposed to be pedagogic treatments of their topics. Readers who are interested in learning a subject should consult a textbook listed in the article's references. If the article does not have references, ask for some on the article's talk page or at
Wikipedia:Reference desk/Mathematics. Wikipedia's sister projects
Wikibooks which hosts textbooks, and
Wikiversity which hosts collaborative learning projects, may be additional resources to consider. See also: Using Wikipedia for mathematics self-study Why are Wikipedia mathematics articles so abstract?
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?
Sometimes editors leave out definitions or links that they believe will distract the reader. If you believe that a mathematics article would be more clear with an additional definition or link, please add to the article. If you are not able to do so yourself, ask for assistance on the article's talk page. Why don't many mathematics articles start with a definition?
We try to make mathematics articles as accessible to the largest likely audience as possible. In order to achieve this, often an intuitive explanation of something precedes a rigorous definition. The first few paragraphs of an article (called the
lead) are supposed to provide an accessible summary of the article appropriate to the target audience. Depending on the target audience, it may or may not be appropriate to include any formal details in the lead, and these are often put into a dedicated section of the article. If you believe that the article would benefit from having more formal details in the lead, please add them or discuss the matter on the article's talk page. Why don't mathematics articles include lists of prerequisites?
A well-written article should establish its context well enough that it does not need a separate list of prerequisites. Furthermore, directly addressing the reader breaks Wikipedia's encyclopedic tone. If you are unable to determine an article's context and prerequisites, please ask for help on the talk page. Why are Wikipedia's mathematics articles so hard to read?
We strive to make our articles comprehensive, technically correct and easy to read. Sometimes it is difficult to achieve all three. If you have trouble understanding an article, please post a specific question on the article's talk page. Why don't math pages rely more on helpful YouTube videos and media coverage of mathematical issues?
Mathematical content of YouTube videos is often unreliable (though some may be useful for pedagogical purposes rather than as references). Media reports are typically sensationalistic. This is why they are generally avoided. |
I think it's at a point where only some tidying remains, but I'm not sure when I'll have time to do that tidying. XOR'easter ( talk) 01:26, 24 May 2024 (UTC)
I'd like some advice on how to handle a problem which I encounter quite often in articles covering basic topics that are widely used in other fields.
The typical scenario goes like this: A is a central notion that was introduced a while ago and on which there are plenty of old and recent textbooks. A is now used in many fields outside of mathematics, and maybe in a trendy field such as machine learning. Some people keep adding references to recent textbook or articles on A in the lead.
Sometimes the references are research articles published in obscure journals, and in that case this is not really a problem (even though one might need to remove the same reference several times). But in some cases the references are legit — or at least "legit-looking" — textbooks, and then because Wikipedia does not have very clear guidelines regarding citations in the lead, I am not always sure what to do and end up losing time.
Maybe a concrete example will help: Have a look at the recent [as of 11/06/2024] history of the article Markov chain, more specifically at this diff and this one. Here we have two different IPs located in Romania who are actively monitoring the article and who seem extremely upset that a textbook by a Romanian author is not listed first to back-up:
Of course, that makes me think that the person behind these IPs is either the author of said textbook; or someone who really likes this textbook.
The problem is that, as far as I can tell without reading it, this does indeed seem like a legitimate textbook on Markov chains. In fact, by some metrics it even seems to be a popular textbook: despite being fairly recent, it is already cited 900 times. That is of course impressive...But also not very surprising, considering that it has been the first reference of the Wikipedia article on Markov chains for a while.
(in fact, to try to get an idea of whether most people citing that book actually did so to reference specific properties and theorems, or simply to add a citation after their first use of the phrase "Markov chain". I am not going to copy and copy and paste excerpts, so as not to point fingers; but some authors seem to think that Gagniuc invented Markov chains, others that think that he recently discovered the game-changing fact that the rows of a stochastic matrix sum to 1, etc).
So, on the one hand I think that reference should be removed from the lead (and probably from the article altogether), because there are tons and tons of excellent textbooks on Markov chains, and I have some suspicions of self-promotion with this one (not to mention that I have no idea whether it is any good). On the other hand, this seems to be a legitimate reference (again, I have not read it) and so I can't really base myself on any clear Wikipedia policy to do so.
I would of course appreciate if someone could help me with this specific example (especially since it looks like some IP users are ready to engage in edit-warring). But I am mostly asking for general guidance here, because it is a problem I encounter regularly.
Best, Malparti ( talk) 23:49, 10 June 2024 (UTC)
Two different stubby articles about the Cut locus were just merged together, but the result is still quite a mess, and some parts are a bit incoherent. Can someone who is more familiar with differential geometry literature take a look and clean it up a bit, ideally adding a couple of better sources? – jacobolus (t) 17:02, 23 June 2024 (UTC)
There is a dispute there which would benefit from additional input; see the last two talk-page sections at Talk:Lagrange inversion theorem. -- JBL ( talk) 17:37, 26 June 2024 (UTC)
Whenever I'm thinking about tables, it reminds me of many tables in mathematical articles, including in geometry. In the past, there was tension about Cairo pentagonal tiling, where a user added tables for something floating things. More strongly, there are many articles about polyhedrons using many tables for representation as spherical polyhedrons, duals, related polyhedrons, and honeycombs together with the vertex configuration. Tetrahedron is another example, which not only contains those, but also contains tables such as the symmetry (and its difference with irregular ones), Coxeter planes, and many more.
My point in asking this is to reduce the excessive tables (unless there is generally being used in higher-class, as in WP:FL). Does Wikipedia actually have some manual of styles about tables? Does WP:WPM (including WP:3TOPE) have some kind of restriction about the tables' usage? Should this be added, whenever possible? Dedhert.Jr ( talk) 01:22, 27 June 2024 (UTC)
I believe the discussion at Wikipedia:Categories_for_discussion/Log/2024_June_21#Category:Symplectic_topology would benefit from more opinions. Mathwriter2718 ( talk) 12:45, 27 June 2024 (UTC)
Some discussion in the article FA Archimedes about its low standard criteria FA. Opinions from a third point of view are voluntarily welcomed. Dedhert.Jr ( talk) 02:27, 29 June 2024 (UTC)
In this deletion discussion, it was just barely decided to delete the article titled Envelope model. The article can be seen here. The originator of envelope models is R. Dennis Cook, noted for Cook's distance and the Cook–Weisberg test for heteroskedasticity. Prof. Cook is now retired.
This seems to have been a deletion without prejeudice to re-creation. About a year after this deletion, Dennis Cook's book An Introduction to Envelopes [1] was published.
Although this topic was primarily the creation of Dennis Cook and some of his Ph.D. advisees, I believe some of his colleagues and students in his graduate courses have also influenced the topic. (In particular, the term "central subspace" was suggested by David Nelson.)
It appears to me that with the publication of the book, the time is ripe to think about re-creating the article, written in a more beginner-friendly way, perhaps under the title Envelope model (statistics) or Envelope (statistics).
The original creator of this article, user:Anthony Appleyard, is reported to have died. Michael Hardy ( talk) 21:34, 29 June 2024 (UTC)
: Michael Hardy ( talk) 21:34, 29 June 2024 (UTC)
In the past couple of days I spent some time researching the name " trammel of Archimedes", sometimes applied to the instrument for the several centuries previously and still often today called an elliptic trammel or elliptic compass (a "trammel" or beam compass is a wooden or metal rod or beam along which slide metal "trammel points", used to draw circles). This is a type of ellipsograph (tool for drawing ellipses). I learned that Archimedes had nothing to do with this tool, which may have been invented in the early 16th century by Leonardo da Vinci, and which operates on the same mathematical principle as a mechanism investigated by Proclus (5th century) based on the one Nicomedes (3rd century BC) used to trisect angles. Circa 1940 the name "trammel of Archimedes" showed up in the work of Robert C. Yates, apparently out of the blue (I speculate this may have been based on some confusion by Yates or whoever he got the name from between Nicomedes and Archimedes). Judging from searches of books/academic papers, the name "trammel of Archimedes" remained quite rare through the 20th century, but there have been a nontrivial number of people calling it that in the past couple of decades, perhaps partly under the influence of webpages like Wikipedia.
Anyway... I think this article would be improved by reorganizing it to discuss the general topic of ellipse drawing, so I proposed at Talk:Trammel of Archimedes § Requested move 1 July 2024 that it should be moved to the title Ellipsograph (which currently redirects there), with "Elliptic trammel" turned into a top-level section. Then we can add other sections about the pins-and-string method for drawing ellipses, as well as various other interesting ellipse drawing tools/methods, and some further discussion about how these tools were used in practice. – jacobolus (t) 05:43, 1 July 2024 (UTC)
Please take a look at talk:mathematics#Overlink issue in lede. -- Trovatore ( talk) 22:02, 3 July 2024 (UTC)
Is 3^^^^3 a proper way of notating Graham's number? voorts ( talk/ contributions) 19:12, 4 July 2024 (UTC)
Hello,
I wrote an article Deficiency (statistics) which was accepted but is still somehow hidden to the public since it does not appear on search engines like Google. Why is that? The article is about a term introduced by Lucien Le Cam in a famous paper called "Sufficiency and Approximate Sufficiency" in the Annals of Mathematical Statistics which was the starting point for Le Cam theory and he later extended in a book.-- Tensorproduct ( talk) 19:57, 4 July 2024 (UTC)
Hi all, I have spent much time over the past week and a half editing the C-class article Riemannian manifold and I think it is ready for a reappraisal. I would also be very happy if others have ideas for how to improve the page or to make it more accessible and readable. I would love to have an image at the top of the page, but I couldn't think of a good one. Mathwriter2718 ( talk) 20:37, 4 July 2024 (UTC)
"in differential geometry, a Riemannian manifold is a (possibly non-Euclidean) geometric space for which traditional geometric notions of distance, angle, and volume from Euclidean geometry are defined. These notions can be defined through reference to an ambient Euclidean space which the manifold sits inside (and indeed any Riemannian manifold may be viewed this way due to the Nash embedding theorems) but the modern notion of a Riemannian manifold emphasizes the intrinsic point of view first developed by Bernhard Riemann, which makes no reference to an ambient space and instead defines the notions of distance, angle, and volume directly on the manifold, by specifying Euclidean inner products on each tangent space with a structure called a Riemannian metric. The techniques of differential and integral calculus can be used to transform this infinitesimal information into genuine geometric data about the manifold, and for example distance between points on the manifold along a path, the arc length, can be determined by integrating the infinitesimal measure of distance along the path given by the metric."
I recommend deferring mention of tangent spaces and Nash embedding theorems past the first paragraph, until such a space as they can be unpacked (briefly but) clearly where mentioned.
Fwiw, I think tazernix lede is good as is. There's no need to complicate matters with endless debate as to the merits of this or that. Tito Omburo ( talk) 17:37, 5 July 2024 (UTC)
"A Riemannian manifold is a geometric space which locally, in the vicinity of each of its points, has the same metrical structure as flat Euclidean space – in the same way that spatial relationships in a small portion of a globe's surface can be modeled using a flat map – including concepts of perpendicularity and angle measure, straightness and curvature, and an infinitesimal definition of distance and volume, based on a formal structure called a Riemannian metric. Using the tools of differential and integral calculus, this local structure can be extended to larger portions of the space, yielding a generalization of Euclidean geometry, Riemannian geometry, in which space might be warped or curved and straight lines are replaced by locally straight curves called geodesics. It is named after Bernhard Riemann, who, building on the work of Carl Gauss, proposed a way of defining and studying such spaces in general."
A Riemannian manifold is a geometric space which locally, in the vicinity of each of its points, has nearly the same metrical structure as flat Euclidean space – in the same way that spatial relationships in a small portion of a globe's surface can be modeled using a flat map – including concepts of perpendicularity and angle measure, straightness and curvature,That should be sufficiently precise for the lead. -- Shmuel (Seymour J.) Metz Username:Chatul ( talk) 18:39, 7 July 2024 (UTC)
"I think it's a clunky way to view it"– It's a sort of hand-wavy view, but it's not detailed enough to be clunky. By comparison, the business about tangent spaces is a very "clunky" way of expressing this idea, a formal definition for a new concept duct taped together from other abstractions previously defined and already at hand. It's not a requirement to define it this way, and most students do not have a clear intuition about the concept of the tangent space for a long time after being introduced to it, but it was convenient for the other proofs people wanted to make.
"sectional curvature (as a Riemannian-geometric notion) in any small region of the sphere is exactly one"– this is not so. The way you "zoom in" on a small portion of the sphere is by expanding the sphere until the portion of interest fills your view (or equivalently, imagine yourself and your natural scale of measurement to be shrinking and shrinking). In the limit as the sphere becomes infinitely large or you become infinitely small, you are left looking at a completely flat surface, indistinguishable in any way from part of a plane. [For a physical example, we don't yet know if the large scale structure of spacetime is flat or not, and we could well imagine the universe being "spherical" or "hyperbolic", but if so the curvature is so slight that it appears flat to within our capacity to measure. The curvature of a spherical, flat, or hyperbolic universe would be very very nearly the same, and you'd need a whopping big length scale to say it had sectional curvature of 1.] – jacobolus (t) 21:40, 7 July 2024 (UTC)
In differential geometry, a Riemannian manifold is a geometric space equipped with, at each point, a copy of the Euclidean space most closely approximating it near that point.or your
In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined.seem fine.
This conversation has slowed down, so I am going to propose yet another lead (not just the first paragraph, but the whole section), attempting to compromise between all of the perspectives I have heard. I think it's really good to at define the terms "Riemannian manifold", "Riemannian metric", and "Riemannian geometry" in the lead. I am also throwing in an image from the ongoing discussion at Talk:Riemannian_manifold#A_couple_of_example_pictures,_not_sure_if_useful; please discuss the image there.
Mathwriter2718 ( talk) 13:27, 10 July 2024 (UTC)
These notions can be defined through reference to an ambient Euclidean space which the manifold sits inside., is inappropriate. Manifolds are intrinsic and not dependent on any particular embedding. For most applications there is no natural embedding. -- Shmuel (Seymour J.) Metz Username:Chatul ( talk) 18:57, 10 July 2024 (UTC)
Any regular surface in three-dimensional Euclidean space has an automatically induced Riemannian structure. Although Nash proved that every Riemannian manifold arises as a submanifold of some (higher-dimensional) Euclidean space and although some Riemannian manifolds are naturally exhibited or defined as such submanifolds, in many contexts Riemannian metrics are more naturally defined or constructed directly, without reference to any Euclidean structure. For example, natural metrics on Lie groups can be defined by using group theory to transport an inner product on a single tangent space to the entire manifold; many metrics with special curvature properties such as constant scalar curvature metrics or Kähler–Einstein metrics are constructed as direct modifications of more generic metrics using tools from partial differential equations.? -- Shmuel (Seymour J.) Metz Username:Chatul ( talk) 08:33, 11 July 2024 (UTC)
There is a new article Quasilinearization which was restored from a deleted form and has been moved directly to main. I know that using linear approximations is very common in optimization and similar problems, and it is of course everywhere in science (first order expansions). I don't know if there are other articles on this, hopefully someone in the applied math area has a better feel for what is already on Wikipedia. For certain I think Quasilinearization can do with better and wider context, but perhaps there is more that should be done. Over to others. Ldm1954 ( talk) 19:27, 6 July 2024 (UTC)
I have recently expanded the article Cube, one of them is the Cube#In architecture. However, one source says that Kaaba is a nearly cube building [2], which I have not included in the article. If that's the case, should this be included elsewhere, the Square cuboid, or keep it in the article Cube but quote what is the source saying? I don't want to have a conflict because of my editing. More opinions are extremely needed. Dedhert.Jr ( talk) 13:03, 8 July 2024 (UTC)
See Talk:Mixing_(mathematics)#Merge_proposal. Please leave comments on that talk page and not here. Mathwriter2718 ( talk) 01:15, 9 July 2024 (UTC)
In 2021, a talk page user pointed out that the definition of the musical isomorphisms on the page musical isomorphism is needlessly complicated. Indeed, since at least 2020, the text itself begrudgingly admits that the second description it gives is "somewhat more transparent" than the first one it gives:
But the problem is actually much more significant than this. Indeed, the definitions as stated are mathematically invalid, as the vector field is not an element of the tangent bundle , which consists of individual vectors. Immediately after this is a parallel discussion on the sharp isomorphism, which suffers from exactly the same defects. Mathwriter2718 ( talk) 02:59, 11 July 2024 (UTC)
Main page | Discussion | Content | Assessment | Participants | Resources |
Mathematics Project‑class | ||||||||||
|
Frequently asked questions To view an explanation to the answer, click on the [show] link to the right of the question. Are Wikipedia's mathematics articles targeted at professional mathematicians?
No, we target our articles at an
appropriate audience. Usually this is an interested layman. However, this is not always possible. Some advanced topics require substantial mathematical background to understand. This is no different from other specialized fields such as law and medical science. If you believe that an article is too advanced, please leave a detailed comment on the article's talk page. If you understand the article and believe you can make it simpler, you are also welcome to improve it, in the framework of the
BOLD, revert, discuss cycle. Why is it so difficult to learn mathematics from Wikipedia articles?
Wikipedia is an encyclopedia,
not a textbook. Wikipedia articles are not supposed to be pedagogic treatments of their topics. Readers who are interested in learning a subject should consult a textbook listed in the article's references. If the article does not have references, ask for some on the article's talk page or at
Wikipedia:Reference desk/Mathematics. Wikipedia's sister projects
Wikibooks which hosts textbooks, and
Wikiversity which hosts collaborative learning projects, may be additional resources to consider. See also: Using Wikipedia for mathematics self-study Why are Wikipedia mathematics articles so abstract?
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?
Sometimes editors leave out definitions or links that they believe will distract the reader. If you believe that a mathematics article would be more clear with an additional definition or link, please add to the article. If you are not able to do so yourself, ask for assistance on the article's talk page. Why don't many mathematics articles start with a definition?
We try to make mathematics articles as accessible to the largest likely audience as possible. In order to achieve this, often an intuitive explanation of something precedes a rigorous definition. The first few paragraphs of an article (called the
lead) are supposed to provide an accessible summary of the article appropriate to the target audience. Depending on the target audience, it may or may not be appropriate to include any formal details in the lead, and these are often put into a dedicated section of the article. If you believe that the article would benefit from having more formal details in the lead, please add them or discuss the matter on the article's talk page. Why don't mathematics articles include lists of prerequisites?
A well-written article should establish its context well enough that it does not need a separate list of prerequisites. Furthermore, directly addressing the reader breaks Wikipedia's encyclopedic tone. If you are unable to determine an article's context and prerequisites, please ask for help on the talk page. Why are Wikipedia's mathematics articles so hard to read?
We strive to make our articles comprehensive, technically correct and easy to read. Sometimes it is difficult to achieve all three. If you have trouble understanding an article, please post a specific question on the article's talk page. Why don't math pages rely more on helpful YouTube videos and media coverage of mathematical issues?
Mathematical content of YouTube videos is often unreliable (though some may be useful for pedagogical purposes rather than as references). Media reports are typically sensationalistic. This is why they are generally avoided. |
I think it's at a point where only some tidying remains, but I'm not sure when I'll have time to do that tidying. XOR'easter ( talk) 01:26, 24 May 2024 (UTC)
I'd like some advice on how to handle a problem which I encounter quite often in articles covering basic topics that are widely used in other fields.
The typical scenario goes like this: A is a central notion that was introduced a while ago and on which there are plenty of old and recent textbooks. A is now used in many fields outside of mathematics, and maybe in a trendy field such as machine learning. Some people keep adding references to recent textbook or articles on A in the lead.
Sometimes the references are research articles published in obscure journals, and in that case this is not really a problem (even though one might need to remove the same reference several times). But in some cases the references are legit — or at least "legit-looking" — textbooks, and then because Wikipedia does not have very clear guidelines regarding citations in the lead, I am not always sure what to do and end up losing time.
Maybe a concrete example will help: Have a look at the recent [as of 11/06/2024] history of the article Markov chain, more specifically at this diff and this one. Here we have two different IPs located in Romania who are actively monitoring the article and who seem extremely upset that a textbook by a Romanian author is not listed first to back-up:
Of course, that makes me think that the person behind these IPs is either the author of said textbook; or someone who really likes this textbook.
The problem is that, as far as I can tell without reading it, this does indeed seem like a legitimate textbook on Markov chains. In fact, by some metrics it even seems to be a popular textbook: despite being fairly recent, it is already cited 900 times. That is of course impressive...But also not very surprising, considering that it has been the first reference of the Wikipedia article on Markov chains for a while.
(in fact, to try to get an idea of whether most people citing that book actually did so to reference specific properties and theorems, or simply to add a citation after their first use of the phrase "Markov chain". I am not going to copy and copy and paste excerpts, so as not to point fingers; but some authors seem to think that Gagniuc invented Markov chains, others that think that he recently discovered the game-changing fact that the rows of a stochastic matrix sum to 1, etc).
So, on the one hand I think that reference should be removed from the lead (and probably from the article altogether), because there are tons and tons of excellent textbooks on Markov chains, and I have some suspicions of self-promotion with this one (not to mention that I have no idea whether it is any good). On the other hand, this seems to be a legitimate reference (again, I have not read it) and so I can't really base myself on any clear Wikipedia policy to do so.
I would of course appreciate if someone could help me with this specific example (especially since it looks like some IP users are ready to engage in edit-warring). But I am mostly asking for general guidance here, because it is a problem I encounter regularly.
Best, Malparti ( talk) 23:49, 10 June 2024 (UTC)
Two different stubby articles about the Cut locus were just merged together, but the result is still quite a mess, and some parts are a bit incoherent. Can someone who is more familiar with differential geometry literature take a look and clean it up a bit, ideally adding a couple of better sources? – jacobolus (t) 17:02, 23 June 2024 (UTC)
There is a dispute there which would benefit from additional input; see the last two talk-page sections at Talk:Lagrange inversion theorem. -- JBL ( talk) 17:37, 26 June 2024 (UTC)
Whenever I'm thinking about tables, it reminds me of many tables in mathematical articles, including in geometry. In the past, there was tension about Cairo pentagonal tiling, where a user added tables for something floating things. More strongly, there are many articles about polyhedrons using many tables for representation as spherical polyhedrons, duals, related polyhedrons, and honeycombs together with the vertex configuration. Tetrahedron is another example, which not only contains those, but also contains tables such as the symmetry (and its difference with irregular ones), Coxeter planes, and many more.
My point in asking this is to reduce the excessive tables (unless there is generally being used in higher-class, as in WP:FL). Does Wikipedia actually have some manual of styles about tables? Does WP:WPM (including WP:3TOPE) have some kind of restriction about the tables' usage? Should this be added, whenever possible? Dedhert.Jr ( talk) 01:22, 27 June 2024 (UTC)
I believe the discussion at Wikipedia:Categories_for_discussion/Log/2024_June_21#Category:Symplectic_topology would benefit from more opinions. Mathwriter2718 ( talk) 12:45, 27 June 2024 (UTC)
Some discussion in the article FA Archimedes about its low standard criteria FA. Opinions from a third point of view are voluntarily welcomed. Dedhert.Jr ( talk) 02:27, 29 June 2024 (UTC)
In this deletion discussion, it was just barely decided to delete the article titled Envelope model. The article can be seen here. The originator of envelope models is R. Dennis Cook, noted for Cook's distance and the Cook–Weisberg test for heteroskedasticity. Prof. Cook is now retired.
This seems to have been a deletion without prejeudice to re-creation. About a year after this deletion, Dennis Cook's book An Introduction to Envelopes [1] was published.
Although this topic was primarily the creation of Dennis Cook and some of his Ph.D. advisees, I believe some of his colleagues and students in his graduate courses have also influenced the topic. (In particular, the term "central subspace" was suggested by David Nelson.)
It appears to me that with the publication of the book, the time is ripe to think about re-creating the article, written in a more beginner-friendly way, perhaps under the title Envelope model (statistics) or Envelope (statistics).
The original creator of this article, user:Anthony Appleyard, is reported to have died. Michael Hardy ( talk) 21:34, 29 June 2024 (UTC)
: Michael Hardy ( talk) 21:34, 29 June 2024 (UTC)
In the past couple of days I spent some time researching the name " trammel of Archimedes", sometimes applied to the instrument for the several centuries previously and still often today called an elliptic trammel or elliptic compass (a "trammel" or beam compass is a wooden or metal rod or beam along which slide metal "trammel points", used to draw circles). This is a type of ellipsograph (tool for drawing ellipses). I learned that Archimedes had nothing to do with this tool, which may have been invented in the early 16th century by Leonardo da Vinci, and which operates on the same mathematical principle as a mechanism investigated by Proclus (5th century) based on the one Nicomedes (3rd century BC) used to trisect angles. Circa 1940 the name "trammel of Archimedes" showed up in the work of Robert C. Yates, apparently out of the blue (I speculate this may have been based on some confusion by Yates or whoever he got the name from between Nicomedes and Archimedes). Judging from searches of books/academic papers, the name "trammel of Archimedes" remained quite rare through the 20th century, but there have been a nontrivial number of people calling it that in the past couple of decades, perhaps partly under the influence of webpages like Wikipedia.
Anyway... I think this article would be improved by reorganizing it to discuss the general topic of ellipse drawing, so I proposed at Talk:Trammel of Archimedes § Requested move 1 July 2024 that it should be moved to the title Ellipsograph (which currently redirects there), with "Elliptic trammel" turned into a top-level section. Then we can add other sections about the pins-and-string method for drawing ellipses, as well as various other interesting ellipse drawing tools/methods, and some further discussion about how these tools were used in practice. – jacobolus (t) 05:43, 1 July 2024 (UTC)
Please take a look at talk:mathematics#Overlink issue in lede. -- Trovatore ( talk) 22:02, 3 July 2024 (UTC)
Is 3^^^^3 a proper way of notating Graham's number? voorts ( talk/ contributions) 19:12, 4 July 2024 (UTC)
Hello,
I wrote an article Deficiency (statistics) which was accepted but is still somehow hidden to the public since it does not appear on search engines like Google. Why is that? The article is about a term introduced by Lucien Le Cam in a famous paper called "Sufficiency and Approximate Sufficiency" in the Annals of Mathematical Statistics which was the starting point for Le Cam theory and he later extended in a book.-- Tensorproduct ( talk) 19:57, 4 July 2024 (UTC)
Hi all, I have spent much time over the past week and a half editing the C-class article Riemannian manifold and I think it is ready for a reappraisal. I would also be very happy if others have ideas for how to improve the page or to make it more accessible and readable. I would love to have an image at the top of the page, but I couldn't think of a good one. Mathwriter2718 ( talk) 20:37, 4 July 2024 (UTC)
"in differential geometry, a Riemannian manifold is a (possibly non-Euclidean) geometric space for which traditional geometric notions of distance, angle, and volume from Euclidean geometry are defined. These notions can be defined through reference to an ambient Euclidean space which the manifold sits inside (and indeed any Riemannian manifold may be viewed this way due to the Nash embedding theorems) but the modern notion of a Riemannian manifold emphasizes the intrinsic point of view first developed by Bernhard Riemann, which makes no reference to an ambient space and instead defines the notions of distance, angle, and volume directly on the manifold, by specifying Euclidean inner products on each tangent space with a structure called a Riemannian metric. The techniques of differential and integral calculus can be used to transform this infinitesimal information into genuine geometric data about the manifold, and for example distance between points on the manifold along a path, the arc length, can be determined by integrating the infinitesimal measure of distance along the path given by the metric."
I recommend deferring mention of tangent spaces and Nash embedding theorems past the first paragraph, until such a space as they can be unpacked (briefly but) clearly where mentioned.
Fwiw, I think tazernix lede is good as is. There's no need to complicate matters with endless debate as to the merits of this or that. Tito Omburo ( talk) 17:37, 5 July 2024 (UTC)
"A Riemannian manifold is a geometric space which locally, in the vicinity of each of its points, has the same metrical structure as flat Euclidean space – in the same way that spatial relationships in a small portion of a globe's surface can be modeled using a flat map – including concepts of perpendicularity and angle measure, straightness and curvature, and an infinitesimal definition of distance and volume, based on a formal structure called a Riemannian metric. Using the tools of differential and integral calculus, this local structure can be extended to larger portions of the space, yielding a generalization of Euclidean geometry, Riemannian geometry, in which space might be warped or curved and straight lines are replaced by locally straight curves called geodesics. It is named after Bernhard Riemann, who, building on the work of Carl Gauss, proposed a way of defining and studying such spaces in general."
A Riemannian manifold is a geometric space which locally, in the vicinity of each of its points, has nearly the same metrical structure as flat Euclidean space – in the same way that spatial relationships in a small portion of a globe's surface can be modeled using a flat map – including concepts of perpendicularity and angle measure, straightness and curvature,That should be sufficiently precise for the lead. -- Shmuel (Seymour J.) Metz Username:Chatul ( talk) 18:39, 7 July 2024 (UTC)
"I think it's a clunky way to view it"– It's a sort of hand-wavy view, but it's not detailed enough to be clunky. By comparison, the business about tangent spaces is a very "clunky" way of expressing this idea, a formal definition for a new concept duct taped together from other abstractions previously defined and already at hand. It's not a requirement to define it this way, and most students do not have a clear intuition about the concept of the tangent space for a long time after being introduced to it, but it was convenient for the other proofs people wanted to make.
"sectional curvature (as a Riemannian-geometric notion) in any small region of the sphere is exactly one"– this is not so. The way you "zoom in" on a small portion of the sphere is by expanding the sphere until the portion of interest fills your view (or equivalently, imagine yourself and your natural scale of measurement to be shrinking and shrinking). In the limit as the sphere becomes infinitely large or you become infinitely small, you are left looking at a completely flat surface, indistinguishable in any way from part of a plane. [For a physical example, we don't yet know if the large scale structure of spacetime is flat or not, and we could well imagine the universe being "spherical" or "hyperbolic", but if so the curvature is so slight that it appears flat to within our capacity to measure. The curvature of a spherical, flat, or hyperbolic universe would be very very nearly the same, and you'd need a whopping big length scale to say it had sectional curvature of 1.] – jacobolus (t) 21:40, 7 July 2024 (UTC)
In differential geometry, a Riemannian manifold is a geometric space equipped with, at each point, a copy of the Euclidean space most closely approximating it near that point.or your
In differential geometry, a Riemannian manifold is a geometric space on which many geometric notions such as distance, angles, length, volume, and curvature are defined.seem fine.
This conversation has slowed down, so I am going to propose yet another lead (not just the first paragraph, but the whole section), attempting to compromise between all of the perspectives I have heard. I think it's really good to at define the terms "Riemannian manifold", "Riemannian metric", and "Riemannian geometry" in the lead. I am also throwing in an image from the ongoing discussion at Talk:Riemannian_manifold#A_couple_of_example_pictures,_not_sure_if_useful; please discuss the image there.
Mathwriter2718 ( talk) 13:27, 10 July 2024 (UTC)
These notions can be defined through reference to an ambient Euclidean space which the manifold sits inside., is inappropriate. Manifolds are intrinsic and not dependent on any particular embedding. For most applications there is no natural embedding. -- Shmuel (Seymour J.) Metz Username:Chatul ( talk) 18:57, 10 July 2024 (UTC)
Any regular surface in three-dimensional Euclidean space has an automatically induced Riemannian structure. Although Nash proved that every Riemannian manifold arises as a submanifold of some (higher-dimensional) Euclidean space and although some Riemannian manifolds are naturally exhibited or defined as such submanifolds, in many contexts Riemannian metrics are more naturally defined or constructed directly, without reference to any Euclidean structure. For example, natural metrics on Lie groups can be defined by using group theory to transport an inner product on a single tangent space to the entire manifold; many metrics with special curvature properties such as constant scalar curvature metrics or Kähler–Einstein metrics are constructed as direct modifications of more generic metrics using tools from partial differential equations.? -- Shmuel (Seymour J.) Metz Username:Chatul ( talk) 08:33, 11 July 2024 (UTC)
There is a new article Quasilinearization which was restored from a deleted form and has been moved directly to main. I know that using linear approximations is very common in optimization and similar problems, and it is of course everywhere in science (first order expansions). I don't know if there are other articles on this, hopefully someone in the applied math area has a better feel for what is already on Wikipedia. For certain I think Quasilinearization can do with better and wider context, but perhaps there is more that should be done. Over to others. Ldm1954 ( talk) 19:27, 6 July 2024 (UTC)
I have recently expanded the article Cube, one of them is the Cube#In architecture. However, one source says that Kaaba is a nearly cube building [2], which I have not included in the article. If that's the case, should this be included elsewhere, the Square cuboid, or keep it in the article Cube but quote what is the source saying? I don't want to have a conflict because of my editing. More opinions are extremely needed. Dedhert.Jr ( talk) 13:03, 8 July 2024 (UTC)
See Talk:Mixing_(mathematics)#Merge_proposal. Please leave comments on that talk page and not here. Mathwriter2718 ( talk) 01:15, 9 July 2024 (UTC)
In 2021, a talk page user pointed out that the definition of the musical isomorphisms on the page musical isomorphism is needlessly complicated. Indeed, since at least 2020, the text itself begrudgingly admits that the second description it gives is "somewhat more transparent" than the first one it gives:
But the problem is actually much more significant than this. Indeed, the definitions as stated are mathematically invalid, as the vector field is not an element of the tangent bundle , which consists of individual vectors. Immediately after this is a parallel discussion on the sharp isomorphism, which suffers from exactly the same defects. Mathwriter2718 ( talk) 02:59, 11 July 2024 (UTC)