Over on BIT predicate, we have an IP editor who seems intent on cramming as much off-topic notation-heavy WP:TECHNICAL detail as possible into the history section. More eyes on this would be helpful. — David Eppstein ( talk) 21:50, 28 January 2023 (UTC)
"Even though editors can never 'own' an article, it is important to respect the work and ideas of your fellow contributors. Therefore, be cautious when removing or rewriting large amounts of content, particularly if this content was written by one editor; it is more effective to try to work with the editor than against them—even if you think they are acting as if they "own" the article. [...] In many cases, a core group of editors will have worked to build the article up to its present state and will revert edits that they find detrimental in order, they believe, to preserve the quality of the encyclopedia. Such reversion does not indicate an "ownership" problem [...] Where disagreement persists after such a reversion, the editor proposing the change should first take the matter to the talk page, without personal comments or accusations of ownership. In this way, the specifics of any change can be discussed with the editors who are familiar with the article, who are likewise expected to discuss the content civilly."– jacobolus (t) 02:26, 1 February 2023 (UTC)
I suggest moving this article to the drafts space. I think the subject of this article meets
WP:GNG, but I don't think this article meets the criteria for a stub. I thought about moving this article to the draft space, but
WP:DRAFTIFY said articles older than 90 days should not be draftified without prior consensus at AfD
, so it seems necessary to discuss it first. If someone extends this article, I will withdraw this suggestion. thanks !
SilverMatsu (
talk)
11:22, 31 January 2023 (UTC)
I am not sure that this article is not ready to have its own. It has lack context and many things. Most of the texts, as I glanced at, especially in this part, use many second-person pronouns; however, MOS:YOU mentions that one should avoid such words. Because of these problems, would it be possible to merge it into Roots of unity? Dedhert.Jr ( talk) 15:14, 3 February 2023 (UTC)
would it be possible to merge it into Roots of unity?No. -- JBL ( talk) 22:29, 3 February 2023 (UTC)
You are invited to join the discussion at
Help talk:Citation Style 1§ Proposal: Add parameter |eudml=. Need advice on whether the
European Digital Mathematics Library (Parameter
|eudml=
) meets
WP:GNG. thanks !
SilverMatsu (
talk)
07:06, 4 February 2023 (UTC)
Ya got yer
But where are the cantellate ( great rhombicosidodecahedron is something else) and the omnitruncate? Are they also degenerate? It would be good to note that somewhere. — Tamfang ( talk) 05:39, 5 February 2023 (UTC)
See Wikipedia:Village pump (proposals)#Project-independent quality assessments. This proposes support for quality assessment at the article level, recorded in {{ WikiProject banner shell}}, and inherited by the wikiproject banners. However, wikiprojects that prefer to use custom approaches to quality assessment can continue to do so. Aymatth2 ( talk) 20:23, 6 February 2023 (UTC)
Input is requested at the RfD concerning the target of the redirect page Free term. 66.44.62.177 ( talk) 01:13, 8 February 2023 (UTC)
I randomly came across this village pump that points at the lead sentence is... not hitting the mark. Its too complex for a novice, not useful to an expert, and generally not helpful. I would generally agree. Now I know I should be be bold and change it, but I am not sure how things have changed in the decade since I lasted edited math articles regularly. Here are my thoughts about the sentence, I thought I would see if there was any agreement before I tried changing anything. For reference the sentence currently is:
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data
Here are my issues
Does anyone else on the math project feel it needs a rewrite, or are we generally fine with it as it is? I bring this up here instead of the talk page of the article, because I came across it in the village pump, so I see it as a good community discussion. Thenub314 ( talk) 21:55, 9 February 2023 (UTC)
For example, look at Mensural notation, a very technical and complex subject in music. ... Now look at Integral, which is a very basic concept in maths.I can't imagine trying to discuss this subject with someone who suffers from this degree of misunderstanding about technicality, complexity, and simplicity.
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, their generalizations, momenta and other physical quantities.-- Shmuel (Seymour J.) Metz Username:Chatul ( talk) 17:08, 10 February 2023 (UTC)
The great secret has already been revealed that this mysterious symbol , which is after all only a long S, merely means “the sum of,” or “the sum of all such quantities as.” It therefore resembles that other symbol (the Greek Sigma), which is also a sign of summation. There is this difference, however, in the practice of mathematical men as to the use of these signs, that while is generally used to indicate the sum of a number of finite quantities, the integral sign is generally used to indicate the summing up of a vast number of small quantities of indefinitely minute magnitude, mere elements in fact, that go to make up the total required. Thus , and .
Any one can understand how the whole of anything can be conceived of as made up of a lot of little bits; and the smaller the bits the more of them there will be. Thus, a line one inch long may be conceived as made up of pieces, each of an inch long; or of parts, each part being of an inch long; or of parts, each of which is of an inch long; or, pushing the thought to the limits of conceivability, it may be regarded as made up of an infinite number of elements each of which is infinitesimally small.
Yes, you will say, but what is the use of thinking of anything that way? Why not think of it straight off, as a whole? The simple reason is that there are a vast number of cases in which one cannot calculate the bigness of the thing as a whole without reckoning up the sum of a lot of small parts. The process of “integrating” is to enable us to calculate totals that otherwise we should be unable to estimate directly.
[...]
What kind of definition of integral would you propose that can be understood by a layperson such as a middle school student or a politician without being too imprecise for someone like a math undergraduate?I think this is an extremely difficult question; hence the labeling of my comments as non-constructive, the small font, and the apologies. -- JBL ( talk) 22:52, 11 February 2023 (UTC)
I suggests the following for the firat paragraph:
In mathematics, an integral is, roughly speaking, the sum of infinitely many quantities that are each infinitely small. For example, a surface in a plane can be divided into narrow strips whose areas are approximated by the product of their widths by their lengths; when the widths of the strips tend to zero, their areas tend each to zero, and their number tend to the infinity; the infinite sum of these infinitesimal areas form an integral equal to the area of the surface. Also, the distance traveled by a vehicle, is the product of the speed by the time of the travel; when the speed varies, one divides the time in smaller and smaller intervals. At the limit, the traveled distance is an integral that is the sum of the products of infinitively small time intervals by the instantaneous speed during each interval.
Integration is the process of computing an integral. It is, with differentiation, a fundamental operation of calculus, and is widely used in all mathematics, as well as in physics, and most sciences and technologies that use mathematics.
I have removed the notes and citations, which should be kept is this is accepted. Also, some more linkd should be added; however this must be done with care, as an informal explantion must not be overlinked.
Feel free to improve this draft.
IMO, such informal examples is the best way for explaining what is integration and why it is used almos everywhere. Clearly, if this is accepted, some more work is needed for the remainder of the lead and of the article. D.Lazard ( talk) 16:02, 12 February 2023 (UTC)
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, their generalizations, momenta, other physical quantities, and more abstract physical or mathematical entities. It can be thought of non-rigorously the sum of infinitely many quantities that are each infinitely small. ...?? -- Shmuel (Seymour J.) Metz Username:Chatul ( talk) 22:02, 12 February 2023 (UTC)
Hello, a common method of organising mathematical proofs seems to be to place them inside {{ collapse top}} and {{ collapse bottom}}. This is specified in Wikipedia:WikiProject Mathematics/Proofs. However, this conflicts with two broader guidances Wikipedia:Manual of Style#Scrolling lists and collapsible content and Wikipedia:Accessibility. If there is some reason why the local consensus should override the sitewide consensus, I'd like to know. Otherwise, if this is an oversight, then does anyone have any alternatives that would be suitable? Pinging users who participated in the proceeding discussion on my talkpage: @ DMacks and D.Lazard: Mako001 (C) (T) 🇺🇦 04:54, 9 February 2023 (UTC)
There are different reasons for including or not a proof in Wikipedia. Proofs deserve to be included when they provide insights on a result and the involved concept; in this case, they must be given is plain text and not collapsed. On the other hand, a long techncal proof may have no encyclopedic value if a reference for it is provided.
I see several reasons for providing proofs that are not included in the flow of the text, which are related to WP:Verifiability and WP:LEAST. In many articles, properties or formulas are presented as bulleted lists (for example, List of integrals#Integrals of simple functions and Heronian triangle#Properties of side lengths). In this case, per WP:Verifiability, as source is normally provided for each item. This is rarely done, and when it is done, it is boring for the reader to get access to many sources. So, providing a proof allows readers to verify the assertions without searching in the literature. Also, in some cases, some of the listed properties may appear as "magic", and some readers may want to understand why they are true without accessing the provided source. In both cases, putting the proof in an explanatory footnote seems the best solution. An example of this is Heronian triangle#Properties of side lengths, where I have added such footnotes because I was too lazy for searching the sources.
In my opinion, the cases where collapsed proof are the best solution are rare. The main case is for a rather long proof that is too technical for the article that contain it, and for which a single and not too technical source is hardly to find. I have encountered this in
Homomorphism#Monomorphism and
Homomorphism#Epimorphism. In particular, in the latter section, the sentence the two definitions of epimorphism are equivalent for
sets,
vector spaces,
abelian groups,
modules (see below for a proof), and
groups
requires verifiability, and I do not know any source that does not requires a good knowledge of
category theory. This the reason for which I have added a proof in a collapsed box (at the end of the section, for not breaking the flow).
In summary, for a guideline, I recommend something like For a proof that, otherwise, would break the flow of reading, use a footnote, and reserves collapsed boxes at the end of the section for exceptional cases.
— Preceding
unsigned comment added by
D.Lazard (
talk •
contribs)
D.Lazard has already said what I wanted to say but better. But to add his and to respond to jacobolus: I think it's essentially the matter of what proofs we should include and what we shouldn't. To echo D.Lazard, we shouldn't include proofs that merely serve to justify some facts; references to reliable sources are preferrable ways, like any other facts in Wikipedia. However, some proofs do serve to help understand the concepts or the facts discussed in the article. Here is an example: the article Bounded operator includes a (short) proof of the fact that an operator is bounded if and only if it is continuous. This fact can be easily referenced by reliable sources but giving the proof is helpful, since a reader can see how the continuity is used and can also see how the proof actually proves stronger continuity (Lipschitz continuity). Hiding it is not only unnecessary, but would make the article less helpful. There does arise an occasion where we feel a need to give a proof or some short justification to defend ourselves against experts who find the statement suspicious (e.g., some algebraic fact is stated without the Noetherian assumption.) In such a case, the use of footnote is a better solution, since most readers wouldn't care about such technical issues. -- Taku ( talk) 09:12, 11 February 2023 (UTC)
There is actually one more case: de Rham theorem currently redirects to de Rham cohomology; the theorem is discussed there but without a full proof. We could add a collapsed full proof but a better solution is to stop the redirecting and then put a non-hidden full proof to the de Rham theorem article. (By the way, which I think we should do.) —- Taku ( talk) 09:29, 13 February 2023 (UTC)
References
Geometry is often defined or described as the study of the properties/relationships of "geometric figures", but we don't really have a good basic definition/explanation for what that means. The existing article shape seems focused on description of a "single" object of some sort (e.g. a polygon, closed curve, or whatever), and especially with classifying shapes up to similarity (i.e. separating "shape" from "size"), whereas the article configuration (geometry) seems primarily concerned with incidence relations between finitely many / discrete collections of points and lines, rather than e.g. metrical relationships like distance or angle, pencils of lines, arbitrary curves, etc. Should we try to add a new such article, and what would be a good accessible definition? Geometric figure currently redirects to Shape § In geometry which doesn’t seem like it really covers the topic.
Related, geometric object currently redirects to Geometry § Objects which has no basic definition, just a (short, nowhere near exhaustive) list of specific types: {Lines, Planes, Angles, Curves, Surfaces, Manifolds}. Nowhere in that page are such basic concepts (related to geometric objects) defined/discussed as 'locus', 'envelope', 'pencil', 'join', 'meet', 'intersection', etc. Perhaps we could also make a page about that one. Anyone have a suggestion of a good definition, or an idea which sources to look to for one? (And while we're here, mathematical object could use a lot of help.) – jacobolus (t) 01:08, 14 February 2023 (UTC)
1. Geometric figures. [...] A set of points, lines, surfaces, or solids positioned in a certain way in space is generally called a geometric figure. Geometric figures can move through space without change. Two geometric figures are called congruent, if by moving one of the figures it is possible to superimpose it onto the other so that the two figures befome identified with each other in all their parts.2. Geometry. A theory studying properties of geometric figures is called geometry, which translates from Greek as "land-measuring". This name was given to the theory because the main purpose of geometry in antiquity was to measure distances and areas on the Earth's surface.
First concepts of geometry as well as their basic properties, are introduced as idealizations of the corresponding common notions and everyday experiences. [...]
1. A region of space which is bounded in all directions is called a volume. [...]Any collection of points, lines, surfaces, and volumes is called a figure. [...]
2. Geometry is the study of the properties of figures and of the relations between them. [...]
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land', and μέτρον (métron) 'a measure') is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures.
In geometry, a polygon ( /ˈpɒlɪɡɒn/) is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). The bounded plane region, the bounding circuit, or the two together, may be called a polygon.
A shape or figure is a graphical representation of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type.
Graphics (from Ancient Greek γραφικός (graphikós) 'pertaining to drawing, painting, writing, etc.') are visual images or designs on some surface, such as a wall, canvas, screen, paper, or stone, to inform, illustrate, or entertain.
If I understand right, it does seem weird to speak of a figure consisting of one circle and one triangle as a single shape, linguistically speaking. Maybe the shape article should be renamed as a figure? A figure seems a bit more general. —- Taku ( talk) 18:35, 14 February 2023 (UTC)
OK, I have a super basic question because I am rusty. How does the archiving of talk pages work? I thought it was done by bots, but visiting some pages I edited a decade ago, they have these enormous talk pages going back a decade. Is this done manually? Thenub314 ( talk) 15:58, 15 February 2023 (UTC)
Hello, I want to expand and update the contents such as integral, differential, Fourier series, limits of continuity of functions by using two very rich and important books in the book of calculus.
references:
aetemad.iut.ac.ir https://aetemad.iut.ac.ir › filesPDF Essential calculus with applications / by Richard A. Silverman.
stewartcalculus.com https://www.stewartcalculus.com Stewart Calculus Textbooks and Online Course Materials
Mohammad.Hosein.J.Shia ( talk) 09:33, 15 February 2023 (UTC)
Albert Einstein has been nominated for a good article reassessment. If you are interested in the discussion, please participate by adding your comments to the reassessment page. If concerns are not addressed during the review period, the good article status may be removed from the article. Onegreatjoke ( talk) 18:06, 17 February 2023 (UTC)
In Talk:Prime (disambiguation), it is discussed whether Prime should remain a redirect to Prime number or should be moved to Prime (disambiguation).
In Talk:e (mathematical constant)#Requested move 14 February 2023, it is discussed whether e (mathematical constant) should moved to e (number). D.Lazard ( talk) 12:24, 18 February 2023 (UTC)
I’m not sure if a discussion here is sufficient or if I should try a more formal process, but it seems like it might be an improvement to move Gregory's series to arctangent series, since this was discovered independently by Kerala school mathematicians in the 14th–15th century, Gregory in 1671, Leibniz in 1673, and perhaps various others. That article can then be expanded to fill in some of the historical/mathematical details of the separate derivations, as well as subsequent developments, connections to other areas of mathematics, etc.
We already have an article Madhava series which covers various other series as well as this one, but calling this Gregory's series seems to be somewhat pushing a POV, as all of the names "Gregory series", "Leibniz series", "Madhava series", "Nilakantha series", "Gregory–Leibniz series", "Madhava–Gregory series", "Madhava–Leibniz series", "Gregory–Nilakantha series", "Leibniz–Gregory–Nilakantha series", "Madhava–Nilakantha series", etc. can be found in the literature, with no clear preference. The name "arctangent series" also gets regularly used in practice (along with similar names like "arctan series", "inverse tangent series", "Taylor series for arctan", etc.), and it seems to me that a neutral descriptive title would best match Wikipedia:Article titles. Thoughts? – jacobolus (t) 06:55, 17 February 2023 (UTC)
I can agree with what he said Mohammad.Hosein.J.Shia ( talk) 09:45, 17 February 2023 (UTC)
("Gregory's series" OR "Gregory series") -"Madhava-Gregory" -"Leibniz-Gregory" -"Nilakantha-gregory"and likewise for other names, I get:
This discussion shows a redirect from
Arctangent series to
Gregory's series is needed. Done.
D.Lazard (
talk)
12:42, 18 February 2023 (UTC)
Sounds like nobody else thinks there is any issue, so I’ll leave the title at Gregory's series. Hopefully we can still expand this over time, add some more figures, etc. Can anyone find a clear source where one of Madhava of Sangamagrama's followers directly credited him for the Maclaurin series for arctangent? The sources I saw seem to suggest that current scholarly consensus leans more toward this being worked out by one of Madhava's followers in the 15th century, instead of Madhava himself. Madhava series § Madhava's arctangent series quotes "Madhava's own words" but from what I can tell these are not Madhava's words, but those of a later follower. – jacobolus (t) 23:48, 19 February 2023 (UTC)
Hello, according to a discussion, I have read a method in books called Khayyam-Newton expansion in the unification of mathematics. I want to include this article in the Etihad (mathematics) article so that they can get acquainted with the common method of two scientists, one of whom is Iranian and the other is European.
I proceed according to the example This method is obtained in the form of Khayyam's triangle and Newton's union. Mohammad.Hosein.J.Shia ( talk) 09:57, 17 February 2023 (UTC)
I can write an article about this topic Just wants a references Mohammad.Hosein.J.Shia ( talk) 18:55, 17 February 2023 (UTC)
Of course, Pascal's triangle is also a complement to Khayyam's triangle. I mean, according to the Persian, German, English, and Arabic books, this theorem of Khayyam and Pascal's triangle can be generalized for coefficients. Mohammad.Hosein.J.Shia ( talk) 10:01, 19 February 2023 (UTC)
Yes Mohammad.Hosein.J.Shia ( talk) 11:12, 20 February 2023 (UTC)
You are invited to join the discussion at
Talk:Algebraic variety#Merger proposal. --
SilverMatsu (
talk)
23:00, 20 February 2023 (UTC)
I have updated some references in the article Point (geometry). However, I could not find sources for corresponding the footnotes Bracewell 1986 and Schwartz 1950. I have found three sources that correspond to the footnotes. Any assistance would be appreciated. Dedhert.Jr ( talk) 12:44, 23 February 2023 (UTC)
{{
wikicite|ref={{harvid|Name|Year}} |reference=...}}
, which can be wrapped around plain-text citations (or other cite templates with ref=none
set on them) and then highlight/pop up everything inside when used with {{
harvp}}, {{
sfn}}, and the like. This is handy when a paper has been reprinted several times in different books, or when a book was translated from another language edition, or when a paper was split into several parts and published serially across multiple issues of a journal, etc. Downside: it's harder for machines to figure out the citation metadata if you use plain text. Upside: Citation Bot won't come and try to add 50 different useless identifiers from random citation indices. –
jacobolus
(t)
22:32, 24 February 2023 (UTC)
The redirect
Improper point 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/2023 February 26 § Improper point until a consensus is reached. —
Mx. Granger (
talk ·
contribs)
21:54, 26 February 2023 (UTC)
Over on BIT predicate, we have an IP editor who seems intent on cramming as much off-topic notation-heavy WP:TECHNICAL detail as possible into the history section. More eyes on this would be helpful. — David Eppstein ( talk) 21:50, 28 January 2023 (UTC)
"Even though editors can never 'own' an article, it is important to respect the work and ideas of your fellow contributors. Therefore, be cautious when removing or rewriting large amounts of content, particularly if this content was written by one editor; it is more effective to try to work with the editor than against them—even if you think they are acting as if they "own" the article. [...] In many cases, a core group of editors will have worked to build the article up to its present state and will revert edits that they find detrimental in order, they believe, to preserve the quality of the encyclopedia. Such reversion does not indicate an "ownership" problem [...] Where disagreement persists after such a reversion, the editor proposing the change should first take the matter to the talk page, without personal comments or accusations of ownership. In this way, the specifics of any change can be discussed with the editors who are familiar with the article, who are likewise expected to discuss the content civilly."– jacobolus (t) 02:26, 1 February 2023 (UTC)
I suggest moving this article to the drafts space. I think the subject of this article meets
WP:GNG, but I don't think this article meets the criteria for a stub. I thought about moving this article to the draft space, but
WP:DRAFTIFY said articles older than 90 days should not be draftified without prior consensus at AfD
, so it seems necessary to discuss it first. If someone extends this article, I will withdraw this suggestion. thanks !
SilverMatsu (
talk)
11:22, 31 January 2023 (UTC)
I am not sure that this article is not ready to have its own. It has lack context and many things. Most of the texts, as I glanced at, especially in this part, use many second-person pronouns; however, MOS:YOU mentions that one should avoid such words. Because of these problems, would it be possible to merge it into Roots of unity? Dedhert.Jr ( talk) 15:14, 3 February 2023 (UTC)
would it be possible to merge it into Roots of unity?No. -- JBL ( talk) 22:29, 3 February 2023 (UTC)
You are invited to join the discussion at
Help talk:Citation Style 1§ Proposal: Add parameter |eudml=. Need advice on whether the
European Digital Mathematics Library (Parameter
|eudml=
) meets
WP:GNG. thanks !
SilverMatsu (
talk)
07:06, 4 February 2023 (UTC)
Ya got yer
But where are the cantellate ( great rhombicosidodecahedron is something else) and the omnitruncate? Are they also degenerate? It would be good to note that somewhere. — Tamfang ( talk) 05:39, 5 February 2023 (UTC)
See Wikipedia:Village pump (proposals)#Project-independent quality assessments. This proposes support for quality assessment at the article level, recorded in {{ WikiProject banner shell}}, and inherited by the wikiproject banners. However, wikiprojects that prefer to use custom approaches to quality assessment can continue to do so. Aymatth2 ( talk) 20:23, 6 February 2023 (UTC)
Input is requested at the RfD concerning the target of the redirect page Free term. 66.44.62.177 ( talk) 01:13, 8 February 2023 (UTC)
I randomly came across this village pump that points at the lead sentence is... not hitting the mark. Its too complex for a novice, not useful to an expert, and generally not helpful. I would generally agree. Now I know I should be be bold and change it, but I am not sure how things have changed in the decade since I lasted edited math articles regularly. Here are my thoughts about the sentence, I thought I would see if there was any agreement before I tried changing anything. For reference the sentence currently is:
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data
Here are my issues
Does anyone else on the math project feel it needs a rewrite, or are we generally fine with it as it is? I bring this up here instead of the talk page of the article, because I came across it in the village pump, so I see it as a good community discussion. Thenub314 ( talk) 21:55, 9 February 2023 (UTC)
For example, look at Mensural notation, a very technical and complex subject in music. ... Now look at Integral, which is a very basic concept in maths.I can't imagine trying to discuss this subject with someone who suffers from this degree of misunderstanding about technicality, complexity, and simplicity.
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, their generalizations, momenta and other physical quantities.-- Shmuel (Seymour J.) Metz Username:Chatul ( talk) 17:08, 10 February 2023 (UTC)
The great secret has already been revealed that this mysterious symbol , which is after all only a long S, merely means “the sum of,” or “the sum of all such quantities as.” It therefore resembles that other symbol (the Greek Sigma), which is also a sign of summation. There is this difference, however, in the practice of mathematical men as to the use of these signs, that while is generally used to indicate the sum of a number of finite quantities, the integral sign is generally used to indicate the summing up of a vast number of small quantities of indefinitely minute magnitude, mere elements in fact, that go to make up the total required. Thus , and .
Any one can understand how the whole of anything can be conceived of as made up of a lot of little bits; and the smaller the bits the more of them there will be. Thus, a line one inch long may be conceived as made up of pieces, each of an inch long; or of parts, each part being of an inch long; or of parts, each of which is of an inch long; or, pushing the thought to the limits of conceivability, it may be regarded as made up of an infinite number of elements each of which is infinitesimally small.
Yes, you will say, but what is the use of thinking of anything that way? Why not think of it straight off, as a whole? The simple reason is that there are a vast number of cases in which one cannot calculate the bigness of the thing as a whole without reckoning up the sum of a lot of small parts. The process of “integrating” is to enable us to calculate totals that otherwise we should be unable to estimate directly.
[...]
What kind of definition of integral would you propose that can be understood by a layperson such as a middle school student or a politician without being too imprecise for someone like a math undergraduate?I think this is an extremely difficult question; hence the labeling of my comments as non-constructive, the small font, and the apologies. -- JBL ( talk) 22:52, 11 February 2023 (UTC)
I suggests the following for the firat paragraph:
In mathematics, an integral is, roughly speaking, the sum of infinitely many quantities that are each infinitely small. For example, a surface in a plane can be divided into narrow strips whose areas are approximated by the product of their widths by their lengths; when the widths of the strips tend to zero, their areas tend each to zero, and their number tend to the infinity; the infinite sum of these infinitesimal areas form an integral equal to the area of the surface. Also, the distance traveled by a vehicle, is the product of the speed by the time of the travel; when the speed varies, one divides the time in smaller and smaller intervals. At the limit, the traveled distance is an integral that is the sum of the products of infinitively small time intervals by the instantaneous speed during each interval.
Integration is the process of computing an integral. It is, with differentiation, a fundamental operation of calculus, and is widely used in all mathematics, as well as in physics, and most sciences and technologies that use mathematics.
I have removed the notes and citations, which should be kept is this is accepted. Also, some more linkd should be added; however this must be done with care, as an informal explantion must not be overlinked.
Feel free to improve this draft.
IMO, such informal examples is the best way for explaining what is integration and why it is used almos everywhere. Clearly, if this is accepted, some more work is needed for the remainder of the lead and of the article. D.Lazard ( talk) 16:02, 12 February 2023 (UTC)
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, their generalizations, momenta, other physical quantities, and more abstract physical or mathematical entities. It can be thought of non-rigorously the sum of infinitely many quantities that are each infinitely small. ...?? -- Shmuel (Seymour J.) Metz Username:Chatul ( talk) 22:02, 12 February 2023 (UTC)
Hello, a common method of organising mathematical proofs seems to be to place them inside {{ collapse top}} and {{ collapse bottom}}. This is specified in Wikipedia:WikiProject Mathematics/Proofs. However, this conflicts with two broader guidances Wikipedia:Manual of Style#Scrolling lists and collapsible content and Wikipedia:Accessibility. If there is some reason why the local consensus should override the sitewide consensus, I'd like to know. Otherwise, if this is an oversight, then does anyone have any alternatives that would be suitable? Pinging users who participated in the proceeding discussion on my talkpage: @ DMacks and D.Lazard: Mako001 (C) (T) 🇺🇦 04:54, 9 February 2023 (UTC)
There are different reasons for including or not a proof in Wikipedia. Proofs deserve to be included when they provide insights on a result and the involved concept; in this case, they must be given is plain text and not collapsed. On the other hand, a long techncal proof may have no encyclopedic value if a reference for it is provided.
I see several reasons for providing proofs that are not included in the flow of the text, which are related to WP:Verifiability and WP:LEAST. In many articles, properties or formulas are presented as bulleted lists (for example, List of integrals#Integrals of simple functions and Heronian triangle#Properties of side lengths). In this case, per WP:Verifiability, as source is normally provided for each item. This is rarely done, and when it is done, it is boring for the reader to get access to many sources. So, providing a proof allows readers to verify the assertions without searching in the literature. Also, in some cases, some of the listed properties may appear as "magic", and some readers may want to understand why they are true without accessing the provided source. In both cases, putting the proof in an explanatory footnote seems the best solution. An example of this is Heronian triangle#Properties of side lengths, where I have added such footnotes because I was too lazy for searching the sources.
In my opinion, the cases where collapsed proof are the best solution are rare. The main case is for a rather long proof that is too technical for the article that contain it, and for which a single and not too technical source is hardly to find. I have encountered this in
Homomorphism#Monomorphism and
Homomorphism#Epimorphism. In particular, in the latter section, the sentence the two definitions of epimorphism are equivalent for
sets,
vector spaces,
abelian groups,
modules (see below for a proof), and
groups
requires verifiability, and I do not know any source that does not requires a good knowledge of
category theory. This the reason for which I have added a proof in a collapsed box (at the end of the section, for not breaking the flow).
In summary, for a guideline, I recommend something like For a proof that, otherwise, would break the flow of reading, use a footnote, and reserves collapsed boxes at the end of the section for exceptional cases.
— Preceding
unsigned comment added by
D.Lazard (
talk •
contribs)
D.Lazard has already said what I wanted to say but better. But to add his and to respond to jacobolus: I think it's essentially the matter of what proofs we should include and what we shouldn't. To echo D.Lazard, we shouldn't include proofs that merely serve to justify some facts; references to reliable sources are preferrable ways, like any other facts in Wikipedia. However, some proofs do serve to help understand the concepts or the facts discussed in the article. Here is an example: the article Bounded operator includes a (short) proof of the fact that an operator is bounded if and only if it is continuous. This fact can be easily referenced by reliable sources but giving the proof is helpful, since a reader can see how the continuity is used and can also see how the proof actually proves stronger continuity (Lipschitz continuity). Hiding it is not only unnecessary, but would make the article less helpful. There does arise an occasion where we feel a need to give a proof or some short justification to defend ourselves against experts who find the statement suspicious (e.g., some algebraic fact is stated without the Noetherian assumption.) In such a case, the use of footnote is a better solution, since most readers wouldn't care about such technical issues. -- Taku ( talk) 09:12, 11 February 2023 (UTC)
There is actually one more case: de Rham theorem currently redirects to de Rham cohomology; the theorem is discussed there but without a full proof. We could add a collapsed full proof but a better solution is to stop the redirecting and then put a non-hidden full proof to the de Rham theorem article. (By the way, which I think we should do.) —- Taku ( talk) 09:29, 13 February 2023 (UTC)
References
Geometry is often defined or described as the study of the properties/relationships of "geometric figures", but we don't really have a good basic definition/explanation for what that means. The existing article shape seems focused on description of a "single" object of some sort (e.g. a polygon, closed curve, or whatever), and especially with classifying shapes up to similarity (i.e. separating "shape" from "size"), whereas the article configuration (geometry) seems primarily concerned with incidence relations between finitely many / discrete collections of points and lines, rather than e.g. metrical relationships like distance or angle, pencils of lines, arbitrary curves, etc. Should we try to add a new such article, and what would be a good accessible definition? Geometric figure currently redirects to Shape § In geometry which doesn’t seem like it really covers the topic.
Related, geometric object currently redirects to Geometry § Objects which has no basic definition, just a (short, nowhere near exhaustive) list of specific types: {Lines, Planes, Angles, Curves, Surfaces, Manifolds}. Nowhere in that page are such basic concepts (related to geometric objects) defined/discussed as 'locus', 'envelope', 'pencil', 'join', 'meet', 'intersection', etc. Perhaps we could also make a page about that one. Anyone have a suggestion of a good definition, or an idea which sources to look to for one? (And while we're here, mathematical object could use a lot of help.) – jacobolus (t) 01:08, 14 February 2023 (UTC)
1. Geometric figures. [...] A set of points, lines, surfaces, or solids positioned in a certain way in space is generally called a geometric figure. Geometric figures can move through space without change. Two geometric figures are called congruent, if by moving one of the figures it is possible to superimpose it onto the other so that the two figures befome identified with each other in all their parts.2. Geometry. A theory studying properties of geometric figures is called geometry, which translates from Greek as "land-measuring". This name was given to the theory because the main purpose of geometry in antiquity was to measure distances and areas on the Earth's surface.
First concepts of geometry as well as their basic properties, are introduced as idealizations of the corresponding common notions and everyday experiences. [...]
1. A region of space which is bounded in all directions is called a volume. [...]Any collection of points, lines, surfaces, and volumes is called a figure. [...]
2. Geometry is the study of the properties of figures and of the relations between them. [...]
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Geometry (from Ancient Greek γεωμετρία (geōmetría) 'land measurement'; from γῆ (gê) 'earth, land', and μέτρον (métron) 'a measure') is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures.
In geometry, a polygon ( /ˈpɒlɪɡɒn/) is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain (or polygonal circuit). The bounded plane region, the bounding circuit, or the two together, may be called a polygon.
A shape or figure is a graphical representation of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type.
Graphics (from Ancient Greek γραφικός (graphikós) 'pertaining to drawing, painting, writing, etc.') are visual images or designs on some surface, such as a wall, canvas, screen, paper, or stone, to inform, illustrate, or entertain.
If I understand right, it does seem weird to speak of a figure consisting of one circle and one triangle as a single shape, linguistically speaking. Maybe the shape article should be renamed as a figure? A figure seems a bit more general. —- Taku ( talk) 18:35, 14 February 2023 (UTC)
OK, I have a super basic question because I am rusty. How does the archiving of talk pages work? I thought it was done by bots, but visiting some pages I edited a decade ago, they have these enormous talk pages going back a decade. Is this done manually? Thenub314 ( talk) 15:58, 15 February 2023 (UTC)
Hello, I want to expand and update the contents such as integral, differential, Fourier series, limits of continuity of functions by using two very rich and important books in the book of calculus.
references:
aetemad.iut.ac.ir https://aetemad.iut.ac.ir › filesPDF Essential calculus with applications / by Richard A. Silverman.
stewartcalculus.com https://www.stewartcalculus.com Stewart Calculus Textbooks and Online Course Materials
Mohammad.Hosein.J.Shia ( talk) 09:33, 15 February 2023 (UTC)
Albert Einstein has been nominated for a good article reassessment. If you are interested in the discussion, please participate by adding your comments to the reassessment page. If concerns are not addressed during the review period, the good article status may be removed from the article. Onegreatjoke ( talk) 18:06, 17 February 2023 (UTC)
In Talk:Prime (disambiguation), it is discussed whether Prime should remain a redirect to Prime number or should be moved to Prime (disambiguation).
In Talk:e (mathematical constant)#Requested move 14 February 2023, it is discussed whether e (mathematical constant) should moved to e (number). D.Lazard ( talk) 12:24, 18 February 2023 (UTC)
I’m not sure if a discussion here is sufficient or if I should try a more formal process, but it seems like it might be an improvement to move Gregory's series to arctangent series, since this was discovered independently by Kerala school mathematicians in the 14th–15th century, Gregory in 1671, Leibniz in 1673, and perhaps various others. That article can then be expanded to fill in some of the historical/mathematical details of the separate derivations, as well as subsequent developments, connections to other areas of mathematics, etc.
We already have an article Madhava series which covers various other series as well as this one, but calling this Gregory's series seems to be somewhat pushing a POV, as all of the names "Gregory series", "Leibniz series", "Madhava series", "Nilakantha series", "Gregory–Leibniz series", "Madhava–Gregory series", "Madhava–Leibniz series", "Gregory–Nilakantha series", "Leibniz–Gregory–Nilakantha series", "Madhava–Nilakantha series", etc. can be found in the literature, with no clear preference. The name "arctangent series" also gets regularly used in practice (along with similar names like "arctan series", "inverse tangent series", "Taylor series for arctan", etc.), and it seems to me that a neutral descriptive title would best match Wikipedia:Article titles. Thoughts? – jacobolus (t) 06:55, 17 February 2023 (UTC)
I can agree with what he said Mohammad.Hosein.J.Shia ( talk) 09:45, 17 February 2023 (UTC)
("Gregory's series" OR "Gregory series") -"Madhava-Gregory" -"Leibniz-Gregory" -"Nilakantha-gregory"and likewise for other names, I get:
This discussion shows a redirect from
Arctangent series to
Gregory's series is needed. Done.
D.Lazard (
talk)
12:42, 18 February 2023 (UTC)
Sounds like nobody else thinks there is any issue, so I’ll leave the title at Gregory's series. Hopefully we can still expand this over time, add some more figures, etc. Can anyone find a clear source where one of Madhava of Sangamagrama's followers directly credited him for the Maclaurin series for arctangent? The sources I saw seem to suggest that current scholarly consensus leans more toward this being worked out by one of Madhava's followers in the 15th century, instead of Madhava himself. Madhava series § Madhava's arctangent series quotes "Madhava's own words" but from what I can tell these are not Madhava's words, but those of a later follower. – jacobolus (t) 23:48, 19 February 2023 (UTC)
Hello, according to a discussion, I have read a method in books called Khayyam-Newton expansion in the unification of mathematics. I want to include this article in the Etihad (mathematics) article so that they can get acquainted with the common method of two scientists, one of whom is Iranian and the other is European.
I proceed according to the example This method is obtained in the form of Khayyam's triangle and Newton's union. Mohammad.Hosein.J.Shia ( talk) 09:57, 17 February 2023 (UTC)
I can write an article about this topic Just wants a references Mohammad.Hosein.J.Shia ( talk) 18:55, 17 February 2023 (UTC)
Of course, Pascal's triangle is also a complement to Khayyam's triangle. I mean, according to the Persian, German, English, and Arabic books, this theorem of Khayyam and Pascal's triangle can be generalized for coefficients. Mohammad.Hosein.J.Shia ( talk) 10:01, 19 February 2023 (UTC)
Yes Mohammad.Hosein.J.Shia ( talk) 11:12, 20 February 2023 (UTC)
You are invited to join the discussion at
Talk:Algebraic variety#Merger proposal. --
SilverMatsu (
talk)
23:00, 20 February 2023 (UTC)
I have updated some references in the article Point (geometry). However, I could not find sources for corresponding the footnotes Bracewell 1986 and Schwartz 1950. I have found three sources that correspond to the footnotes. Any assistance would be appreciated. Dedhert.Jr ( talk) 12:44, 23 February 2023 (UTC)
{{
wikicite|ref={{harvid|Name|Year}} |reference=...}}
, which can be wrapped around plain-text citations (or other cite templates with ref=none
set on them) and then highlight/pop up everything inside when used with {{
harvp}}, {{
sfn}}, and the like. This is handy when a paper has been reprinted several times in different books, or when a book was translated from another language edition, or when a paper was split into several parts and published serially across multiple issues of a journal, etc. Downside: it's harder for machines to figure out the citation metadata if you use plain text. Upside: Citation Bot won't come and try to add 50 different useless identifiers from random citation indices. –
jacobolus
(t)
22:32, 24 February 2023 (UTC)
The redirect
Improper point 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/2023 February 26 § Improper point until a consensus is reached. —
Mx. Granger (
talk ·
contribs)
21:54, 26 February 2023 (UTC)