Knowledge talk:WikiProject Mathematics/Archive/2023/Feb

1371:"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." 3087:

deal with. There are no perfect answers. Some possibilities, none of which will satisfy all authors or all readers: (1) skip proofs altogether but link to a source which includes them, (2) put proof sketches but leave out the details, (3) put proofs in a collapsing section, (4) put proofs in a footnote, (5) put proofs in a floating box to the margin of the main content, (6) put full proofs inline in the text. I think local per-page consensus is probably better to aim for than a blanket site-wide policy. One more thing to notice: Knowledge mobile rendering by default collapses article sections, and readers must tap to expand them; so collapsing elements are clearly not entirely anathema to Knowledge. –

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mathematical arguments, while also being difficult to skim (especially for non experts) and taking significant effort to fully comprehend. If non-specialists hit a wall of formulas or a detailed proof they are likely to be intimidated, discouraged, or bored, and at worst bounce away even if they might be interested in other parts of the page; by contrast, if specialists can’t see a proof they will be unable to fully validate the claims made, and if students can’t see proofs they may develop a false conception about whether/why something is true and what is needed to demonstrate that.

4996: 1629: 3200:, 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 5239:, 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. – 3322:

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. --

40: 4472:"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 3284:, the content is not hidden. The templates collapse top/bottom have been implemented in accordance with this guideline and fallback gracefully to show the content in the absence of JS. I saw some other comments too that screenreaders work fine with collapsed sections (didn't save the link though). So there no accessibility problem with collapsing proofs. It is only 3533:

object, could be a finite set of vertices and edges, an infinite set of boundary points, or a different infinite set of boundary and interior points. Even a point, which you might think of as unavoidably singular, could be considered as equivalent to a line in the projective dual plane, and therefore equivalent to an infinite set of points on that dual line. —

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for the first time and don't yet understand the details, through practitioners in related fields who want a quick reference of concrete results they can use, through historians who want to know the evolution of an idea with numerous citations and experts who want to read generalizations and relations to more advanced topics.

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proofs; references to the reliable sources would do. If the proofs are relevant, they don’t need to be hidden. It’s actually the matter of why we put proofs in the first place. The reason is that proofs are integral parts of mathematics. It’s sometimes important to know how some facts are true not just if they are true. —-

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The problem with proofs (though other kinds of technical content have similar issues, such as large tables of statistical data, detailed timelines, code samples for complicated algorithms, details of chemistry experiments, or full phylogenetic trees) is that they are both necessary to make convincing

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There is no absolute standard by which we can decide what is "irrelevant". Knowledge needs to serve a very wide range of audiences, ranging from members of the general public who have a curiosity about some topic's basic definition and context, through students who are trying to learn about something

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I want to say: I don't like collapsed proofs either. For example, I noticed some people prefer to print out Knowledge articles and then the print-out wouldn't contain collapsed materials. If it is desirable to hide proofs, for a better flow, for example, then a better solution is to put the proofs in

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Anyway, I didn't say the integral *only* computes the area under graphs of functions. But if our standard is what would a layperson or politican understand, you are all assuming way too much mathematical knowledge to think they can parse the sentence "The integral is the continuous analog of the sum"

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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

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The point is to figure out what name is used in recent literature. A google scholar search is generally a much better way to count than a web search, as fewer of the results are complete garbage (e.g. SEO spam, blog posts, plagiarized copies of Knowledge, etc.). Plenty of high school / undergraduate

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Proofs are in many cases irrelevant and distracting to most readers while still being helpful (or even indispensible) for readers who care about the details for one reason or another. Figuring out how to elide tedious or distracting details is a persistent problem that all mathematical writing must

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Thank you for letting me know. I added Template:Redirect to the top of the section. If someone adds an explanation about another notion of delta invariant to wikipedia, I think that they will create separate articles for each notion, or add explanations to existing separate articles for each notion,

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My personal preference is for CS2 because. All. The periods. Annoy. Me. and because I'd rather just have one template than have to figure out which of 10 different cite templates is the best fit for each citation. But the differences are small. As for why: it grew up that way and now it's difficult

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I'd just go for CS1 style as it seems more popular and more or less the same idea as CS2, and the names 'cite journal', 'cite book', etc. are helpful for understanding at a glance what type of source is being cited. But I honestly don't understand why there are two whole separate sets of templates.

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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,

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You are missing my point; I assume I wasn't clear enough. I am not trying to make any claim about what what the limits of a "geometric object" could be, which types of objects should be considered primitives (in one or another context), whether an object should be defined in terms of set theory, or

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I'm going to continue to not be constructive (sorry to all): "continuous" and "domain" are both jargon, and "sum up he continuous values of a function" does not sound to me like it could be deciphered by someone who didn't already know what it meant. An integral of velocity is a displacement (also

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Before you started, the article was already using an inconsistent mix of (full ref in footnote, formatted in CS1) and (harvnb in footnote, manually and inconsistently formatted full ref later). I don't think there is any single consistent style that you can fall back to. So it should be ok to just

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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

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I did a Google search of "arctangent series" and "Gregory's series" and Gregory's series got six times as many hits. People can find arctangent anyway so I don't see how this proposal helps readers. It is not our duty to right great wrongs. As to the various other names there already is a Madhava

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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

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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",

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There are different reasons for including or not a proof in Knowledge. 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

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I don't understand the distinction you are trying to make between single objects and multiple objects. It seems to be a distinction of grammar and convention rather than anything intrinsic. A finite set of points is both a single set and multiple points. A polygon, which you describe as a single

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Sure, there is no perfect solution. In fact, solutions probably would depend on articles. I would however say: if the proofs are irrelevant, those proofs should not be in the article in the first place. Unlike research papers or monographs, in Knowledge, we don’t need to justify the results with

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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

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as it currently exists does not describe any arbitrary collections of geometric primitives, but only certain ones which it considers to be "shapes", which is a small subset of what I would consider to be the universe of "geometric figures". We don't really anywhere a good basic explanation or

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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',

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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

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is both trying to be too technical and failing to be technically accurate. Its tip-toeing around integral as an operator, and what do you say to someone who said "Wait, you said a number and infinity is not a number, my calc prof said so but integrals can be infinite." or "You talk about

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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:

2925:. 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: 3031:

This seems like a problem; that content should be collapsed and only show when a reader tries to expand, and I would assume it would be the same on either desktop or mobile. Why can't the CSS/javascript be set up so that mobile devices can properly expand/collapse these sections?

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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

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Just one more thing before I'll add some references. This article has already used CS1 in the lead, but I didn't notice and accidentally add the sources with CS2 in the references section. Along with inline citations, should I change all of them to inline citations with

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I think that thinking "the area under a function" is a no-go is exactly what leads to an unreadable lead sentence. It captures 90% of the use case of integrals, and what they were originally invented for, and can easily be expanded upon in the next sentence or two.

4698:'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. 3130:

Not every mathematical claim needs to be proven in an encyclopedia article (probably most don’t), but personally I think there are many pages that would benefit from including a few more (collapsed) proofs of statements that are currently just stated. YMMV.

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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?

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which states "Collapsible templates should not conceal article content by default upon page loading." which explicitly contradicts the usage of collapsed proofs. And arguably, if the proofs were expanded by default on page load, it would be following the

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in probability is not about summing a physical quantity over a geometrical shape. It might be better to say that an integral is used to sum up the continuous values of a function in some part of its domain. We could still offer physical examples such as

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If I want to wiki-link from any arbitrary article to "geometric object" or "geometric figure" (or whatever similar term you might prefer, perhaps "configuration" or "arrangement" or ...?) there is currently no good endpoint for that wiki-link to point.

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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

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it is best to err in the direction of too chatty and novice-friendly than the other way. Ideally a non-technical reader should be able to read the first 2–3 sections and have at least a vague idea what concept is being defined and what its context

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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

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is a way of computing the area under a function, or more generally the volume under the graphs of functions of more than one variable. The region under the graph of a function may have an irregular shape (so that the familiar formula of

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I put it here because on Refdesk (with which I am better acquainted than with Projects) my last sentence is likely to provoke "that belongs on the relevant Talk page(s)." Because you ask nicely I'll try it there, omitting that sentence.

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doesn't mean that editors who care about specific pages can't make arguments for their preferred versions or ask other editors to go to the talk page and establish some consensus before making significant changes. To quote that page,

2179:(though that article's lead is too technical) or 'continuous' which many readers will have heard of before (though Knowledge in general needs a much better basic explanation of what 'continuous' / 'continuum' means than provided at 4937:

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.

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No need to draftify. The content of this article is essentially reduced to an implicit link to the definition given in another article. So, I'll redirect this article to the anchor that I have already added in that article.

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in geometry refers to the collection of geometric objects and their specified (or derived) relationships, rather than a physical picture drawn on a piece of paper. I think it would be useful to have a better definition of

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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

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The point of collapsing the proofs is that it is effectively the same as removing them for that part of the audience who wants to skim past or ignore them, except they can still be seen for that part of the audience who is

4876: 3153:, you can give a footnote a name, like "Proof", which displays in the article like this . This would make it clear where the proof is, leave it acessible to all readers, but still move it out of the way. Would this work? 2815:

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.

3048:: Hmm, I'm seeing the same thing. You would have to ask the WMF why the Minerva skin (mobile view) doesn't work with collapsible content properly. In any case, we need to focus on what we are able to do something about. 2375:

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

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to read for many (if not most) readers (i.e. anyone using a mobile device). Setting all proofs to auto expand would "solve" the accessibility problem, but would make (for want of a better term) "a bit of a mess".

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This addition is much too physics-specific for my taste. It makes it look like integrals are only used for physical quantities. Many integrals are unphysical. Areas and volumes can be but are not always physical.

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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

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sort of hints that long proofs are not suitable for WP. For example, considering the Homomorphism page, I think it would be better to cite the proofs that require a good knowledge of category theory, than to do

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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.

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reliable sources are preferrable ways, like any other facts in Knowledge. However, some proofs do serve to help understand the concepts or the facts discussed in the article. Here is an example: the article

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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

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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?

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Bracewell, Ronald N. The Fourier transform and its applications. Third edition. McGraw-Hill Series in Electrical Engineering. Circuits and Systems. McGraw-Hill Book Co., New York, 1986. xx+474 pp. ISBN:

5029:. 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. 63: 4102:

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.

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That aside, your combative behavior over this constructive edit (calling it an "attack" and talking about "hurting my feelings") has been disturbing. One expects more maturity from a professor. See

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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

3604:, 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. 2968:

It should be technically possible to implement this in such a way that a print stylesheet expands them automatically, though many readers may prefer to have proofs collapsed even when printing.

2003:"the area under a function" is a meaningless phrase. But also it is false that this is what they were originally invented for -- no one is or ever has been interested in computing areas under 1295: 3364:

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.) —-

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Well, collapsing the proof usually makes the article more readable (unless the article itself is about the proof of something), especially if there are multiple proofs and each one is long.

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I have painful memories of trying as a teenager to make sense of such language in "Calculus for the Practical Man", and I only started to understand Calculus when I read a copy of Thomas's

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Schwartz, L. Théorie des distributions. Tome I. (French) Publ. Inst. Math. Univ. Strasbourg, 9. Actualités Scientifiques et Industrielles , No. 1091 Hermann & Cie, Paris, 1950. 148 pp.

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it into a separate page is widely endorsed. What's forbidden is the slash to indicate a subpage, and the general idea of each article needing to be its own topic. We already do that: for

3515:'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, 2521: 5292: 2308:

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

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is a term one typically only encounters in calculus or mathematical contexts that assume calculus. So most readers who understood this term would already know what an integral was.

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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.

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Both of these are available in more recent editions. Also,Apostol has written a two volume Calculus book that I would certainly want to check if I were teaching a course. --

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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

3440:. This approach also helps provide a criterion for whether to include the proof: whether external sources actually comment on it beyond merely stating the proof itself. 5207:

As an aside: One thing people might not know about (I didn't until recently) but can be very useful when these templates inevitably break in complicated cases is using

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on my phone and the proof at the bottom of that section (intended to be collapsable and collapsed by default) shows up inline in the content not possible to collapse.

2618: 2586: 2268:(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 2048: 5099:

in notes and convert them to CS2 in references, or change all of them with no inline citations? My apologies for asking this, because I honestly was perplexed with

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First concepts of geometry as well as their basic properties, are introduced as idealizations of the corresponding common notions and everyday experiences.

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I can't imagine trying to discuss this subject with someone who suffers from this degree of misunderstanding about technicality, complexity, and simplicity.

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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.

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first so a consensus can be reached on whether this belongs in the history section, or in another section, or should not be in the article at all.

4726: 2039:"In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and other ways of measuring shapes." 4451:

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

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has been nominated for a good article reassessment. If you are interested in the discussion, please participate by adding your comments to the

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It's only automatic if the page has been set up for auto archiving. If you think there are talk pages that need archiving manually please see

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I think this is an extremely difficult question; hence the labeling of my comments as non-constructive, the small font, and the apologies. --

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Your edit has been reverted by multiple people now. If you think there are good reasons for it, please open a discussion on the talk page of

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and construct an elementary proof out of whole cloth. The elementary proofs can be added to other sites such as Wikibooks, ProofWiki, etc.

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In this case there is neither definition nor link for what 'figure' means, though the term is used throughout the article. Then we have

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of infinitely many quantities that are each infinitely small. For example, a surface in a plane can be divided into narrow strips whose

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functions, that's a totally artificial framework that happens (miraculously!) to extend to allow one to compute interesting things. --

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in the angle article is not defined or wiki-linked, and it may not be immediately obvious to all readers what it means. Similarly, in

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It’s also sometimes possible to take a couple of swings at definitions within the same article lead, aimed at different audiences. –

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If that meaning of "under the graph of the function" already makes sense, you're not learning what an integral is from Knowledge.

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Putting long proofs in footnotes is not a good solution in practice. They are then detached from the content and hard to read. –

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The Ackermann coding is already discussed in the history section. It is clearly not off-topic. Where else would such content go?

4580:(The numbers for all of the above names are not entirely reliable, as these terms are also sometimes used for something else.) 4414: 3268: 3247:. 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). 1404:, but I don't think this article meets the criteria for a stub. I thought about moving this article to the draft space, but 3157: 3052: 3012: 2940: 2867:, other physical quantities, and more abstract physical or mathematical entities. It can be thought of non-rigorously the 1637: 1490: 1486: 1889:

the word is so generic its distracting, it makes me thing 'Am I working with functions and numbers or more general data?'

4694:. Hopefully we can still expand this over time, add some more figures, etc. Can anyone find a clear source where one of 4634:

I suppose with ChatGPT it won't be long before mathematicians are scammed uysing messages mentioning Gregory series ;-)

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But my basic point is that there’s not currently any strong consensus in the literature about what the name should be. –

4039:, linguistically speaking. Maybe the shape article should be renamed as a figure? A figure seems a bit more general. —- 3396: 1704: 1696: 1412:, so it seems necessary to discuss it first. If someone extends this article, I will withdraw this suggestion. thanks ! 5310: 5246: 5202: 5187: 5172: 5127: 5112: 5083: 5065: 5038: 5012: 4981: 4966: 4947: 4932: 4917: 4886: 4643: 4629: 4616: 4602: 4590: 4513: 4434: 4375: 4339: 4311: 4299: 4283: 4271: 4239: 4223: 4209: 4200:

You make a good point. By using these four books and other old and new books, we can expand the topics of mathematics.

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If that's the case, I'll change it to CS1. For the time being, I will keep using short citations, but some changes to

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that is the sum of the products of infinitively small time intervals by the instantaneous speed during each interval.

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quotes "Madhava's own words" but from what I can tell these are not Madhava's words, but those of a later follower. –

4035:

If I understand right, it does seem weird to speak of a figure consisting of one circle and one triangle as a single

3410:

which states that "using subpages for permanent content that is meant to be part of the encyclopedia" is disallowed.

2527:

process of “integrating” is to enable us to calculate totals that otherwise we should be unable to estimate directly.

3976: 3796: 4896:. When the power is not a positive integer, there are infinitely many terms in the expansion and it is called the 4366:. If concerns are not addressed during the review period, the good article status may be removed from the article. 4079: 1731: 1633: 1618: 1538:

is not ready to have its own. It has lack context and many things. Most of the texts, as I glanced at, especially

4723:

I proceed according to the example This method is obtained in the form of Khayyam's triangle and Newton's union.

4418: 4386: 4259: 2918: 1909:

What a terrible first sentence. Surely it is not hard to come up with something much better. Just as an example:

1217: 5198: 5123: 4962: 4473: 3817:. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. 3538: 3491: 3415: 3381:

I've seen texts with proofs in an appendix. How about putting proof for foo in foo/proofs and linking to them?

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I see several reasons for providing proofs that are not included in the flow of the text, which are related to

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feels like we are cramming too many applications in for a first sentence, we will get to all of these in a bit.

1707:

is something else) and the omnitruncate? Are they also degenerate? It would be good to note that somewhere. —

1356: 1266: 3424:

If the proof itself is notable, a self-contained topic, and would overload the main page on the theorem, then

3276:

It is my understanding that collapsible proofs do not actually break accessibility. The relevant guideline is

2248:, merely means “the sum of,” or “the sum of all such quantities as.” It therefore resembles that other symbol 2497: 2130:

as the integral of velocity for some duration or total mass as the integral of mass density in some region. –

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mentions that one should avoid such words. Because of these problems, would it be possible to merge it into

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level topics are discussed in journals, books, etc. included in citation indices such as Google scholar. –

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What is the point in doing a Google scholar search for this? It is secondary or high school mathematics.

5300: 5008: 3934: 3715: 3682: 2987: 2897: 2614: 2582: 2044: 1727: 1653: 1517: 1470: 1417: 4563:

Then we also have (combining e.g. "arctan series", "series for arctant", and "series for the arctan"):

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A set of points, lines, surfaces, or solids positioned in a certain way in space is generally called a

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This does not seem like a correct/adequate definition for this purpose. In my understanding the word

3900: 3384: 3256: 3235: 2176: 1555: 5262: 4520:("Gregory's series" OR "Gregory series") -"Madhava-Gregory" -"Leibniz-Gregory" -"Nilakantha-gregory" 5243: 5194: 5184: 5119: 5061: 4958: 4954: 4913: 4706: 4626: 4599: 4587: 4480: 4308: 4280: 4219: 4064: 4024: 3879: 3652: 3568: 3534: 3523: 3516: 3411: 3342: 3302: 3239: 3135: 3091: 3077: 3036: 2975: 2838: 2717: 2600: 2568: 2554: 2538: 2448: 2205: 2180: 2149: 2134: 2105: 2031: 2012: 1994: 1978: 1941: 1899: 1877:

if we are jumping to the hole infinitesimal thing, is there a reason not to at least say its a sum?

1606: 1574: 1502: 1377: 1365: 1334: 1317: 1278: 1262: 1258: 5163:). Please revert it if I did a mistake there. Will discuss later if someone wants to change them. 4146: 2399: 5288: 4988: 4905: 4681: 4639: 4612: 4509: 4430: 3669: 3357: 3264: 2821: 2213: 1786: 1598: 1586: 1456: 1433: 1405: 1223: 3548:

any other such thing. (Though those are all worthy questions which should probably be discussed

3243:

requires verifiability, and I do not know any source that does not requires a good knowledge of

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It's been more than half a century since I looked at them, but I was impressed at the time by

4040: 3983: 3688: 3365: 3323: 3223: 3201: 3193: 3189: 3160: 3105: 3055: 3015: 2955: 2943: 1958: 1750: 1712: 1671: 1400:

I suggest moving this article to the drafts space. I think the subject of this article meets

5296: 5156: 5026: 5019: 5004: 4893: 4190: 4160: 3846: 3591:. Geometric figures can move through space without change. Two geometric figures are called 3507: 3496: 3445: 3392: 3318: 2878: 2699: 2610: 2578: 2184: 2094: 2040: 1649: 1513: 1466: 1413: 1221: 1219: 39: 4595:

While we are at it, "Gregory series" seems somewhat more popular than "Gregory's series". –

3779: 2343: 2311: 5164: 5104: 5075: 5030: 4897: 4359: 4353: 4253: 4087: 3942: 3891: 3425: 3353: 3277: 3244: 3185: 2893:

Hello, a common method of organising mathematical proofs seems to be to place them inside

2288:

is generally used to indicate the sum of a number of finite quantities, the integral sign

1551: 1494: 1394: 3188:. In many articles, properties or formulas are presented as bulleted lists (for example, 2563:

Clearly the answer is that the integral computes the area under the graph of a function?

1936:

Now that you have alerted WP:MATH to this, the discussion can be moved to the talk page.

1351:

Multiple, as in more than one: David Eppstein and Russ Woodroofe have both reverted you.

4020:

somewhere, because in my opinion no current Knowledge article adequately handles this. –

2428: 5240: 5223: 5181: 5103:, and seek consensus first before changing them. Any explanation would be appreciated. 5057: 4909: 4703: 4623: 4596: 4584: 4477: 4468: 4305: 4277: 4215: 4142: 4075: 4060: 4021: 3677: 3649: 3565: 3520: 3338: 3132: 3088: 3073: 3045: 3033: 2972: 2713: 2596: 2564: 2550: 2535: 2379: 2291: 2271: 2251: 2227: 2202: 2145: 2131: 2028: 2008: 1990: 1974: 1937: 1930: 1895: 1835: 1602: 1547: 1498: 1374: 1328: 1313: 3641:

Geometry is the study of the properties of figures and of the relations between them.

3204:, where I have added such footnotes because I was too lazy for searching the sources. 5318: 5146: 5093: 4677: 4635: 4608: 4505: 4426: 3260: 3231: 3147: 2932: 2817: 1782: 1645: 1582: 1452: 1429: 1401: 1309: 1287: 1257:, we have an IP editor who seems intent on cramming as much off-topic notation-heavy 1254: 4272:

https://archive.org/details/n.-piskunov-differential-and-integral-calculus-mir-1969/

5233: 5136: 4403: 4002: 3886: 3735: 3407: 3298: 3285: 3227: 3213: 3209: 3154: 3049: 3025: 3009: 2937: 2801: 1746: 1708: 1410:

articles older than 90 days should not be draftified without prior consensus at AfD

1291: 2591:

The whole disk is under the graph of the function f(x,y)=1 restricted to the disk.

1261:

detail as possible into the history section. More eyes on this would be helpful. —

5215:, which can be wrapped around plain-text citations (or other cite templates with 4892:

In English, the formula for expanding powers of a sum of two terms is called the

4289:

According to the sources mentioned by Mr. Jacobolus, the best sources are ebooks.

1771:. This proposes support for quality assessment at the article level, recorded in 4265: 4186: 3814: 3441: 3388: 2928: 2874: 2844: 2749: 2695: 2090: 2064: 1913: 1565:

I have cleaned the lead up to understand the real content of the article. IMO,

4690:

Sounds like nobody else thinks there is any issue, so I’ll leave the title at

4525:

Leibniz: 401 results (some sources mean specifically the series for arctan(1))

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https://archive.org/details/ost-math-courant-differentialintegralcalculusvoli/

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So this discussion is a bit more concrete, here are definitions from Kisilev (

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An integral should be described off the bat as a continuous analog of a sum. –

1925:

for regular shapes does not apply), and so integration uses the techniques of

5118:

pick a single consistent style and reformat everything to be in that style. —

4871:{\textstyle (a+b)^{5}=a^{5}+5a^{4}b+10a^{3}b^{2}+10a^{2}b^{3}+5ab^{4}+b^{5}} 2868: 2852: 2757: 2072: 4112:› filesPDF Essential calculus with applications / by Richard A. Silverman. 2216: 1769:

Knowledge:Village pump (proposals)#Project-independent quality assessments

1485:

Just popping in to say that there is another notion of delta invariant in

3960: 3946: 3930: 3836: 3745: 3723: 3511: 2864: 2789: 2595:

or "The integral sums up an infinite number of infinitesimal quantities"

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Knowledge:Redirects for discussion/Log/2023 February 26 § Improper point

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set on them) and then highlight/pop up everything inside when used with

3024:

I don't ever read Knowledge on a mobile device, but I just navigated to

1973:

Separately, "the area under a function" is a no-go for many reasons. --

3828: 2797: 2793: 2224:

The great secret has already been revealed that this mysterious symbol

1543: 4953:

By its generalization, you mean maybe the article we already have at

4900:. And of course there is lots of related content in the articles on 3994: 3990: 3903:, the bounding circuit, or the two together, may be called a polygon. 3802: 3785: 3768: 2860: 2080: 2687:{\textstyle \iiint _{D}\mathbf {r} \times \mathbf {p} \,dx\,dy\,dz.} 5070:

Thank you. I knew that the footnote Bracewell must be connected to

4518:

If I do a Google scholar search of papers since 1980, of the form:

3631:

Any collection of points, lines, surfaces, and volumes is called a

2837:, loaned by a Jr. High teacher for me to read in class, which used 5291:. Readers of this page are welcome to comment on this redirect at 4382: 4116: 3998: 3986: 3938: 3914: 3882: 3731: 3661: 3556: 3500: 3486: 3625:

A region of space which is bounded in all directions is called a

2919:

Knowledge:Manual of Style#Scrolling lists and collapsible content

2871:

of infinitely many quantities that are each infinitely small. ...

2057:

It looks much better after your changes. Thanks for dealing with

1961:, a very technical and complex subject in music. ... Now look at 1512:

so create a Dab page at that time I agree that there is a need.--

4923:

I can write an article about this topic Just wants a references

2856: 2761: 2159:

I agree with you that in articles with topics as fundamental as

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Talk:e (mathematical constant)#Requested move 14 February 2023

3360:; the theorem is discussed there but without a full proof. We 1224: 33: 4148:

Mathematical Analysis: A Modern Approach to Advanced Calculus

5074:, but I cannot find the accurate one. I'll go add it later. 4109: 3933:

of an object or its external boundary, outline, or external

3660:

As an example of the kind of wiki-link I am thinking of, in

3600:

A theory studying properties of geometric figures is called

2708:

Touché -- the difficult question is not a definition, but a

1955:

was introduced as an example in that discussion as follows:

1855:

displacement, isn't displacement a vector and not a number."

1634:

Help talk:Citation Style 1§ Proposal: Add parameter |eudml=

2627:

That is a special case and wont cast much light on, e.g.,

2061:

properly. I'd make the first sentence more general, e.g.,

1577:

must be merged in a single article, which could be called

3250:

In summary, for a guideline, I recommend something like

5279: 4398: 4254:

https://archive.org/details/courseinmathemat01gouruoft/

4119:

Stewart Calculus Textbooks and Online Course Materials

3734:

and size, or if one has the same shape and size as the

2792:, and is widely used in all mathematics, as well as in 4729: 3982:'pertaining to drawing, painting, writing, etc.') are 2633: 2502: 2500: 2480: 2453: 2451: 2404: 2402: 2346: 2314: 2294: 2274: 2254: 2230: 2167:

I think it's potentially fine to wiki-link terms like

1497:

was to return it could even be a disambiguation page.

3434:

Proof of Fermat's Last Theorem for specific exponents

3216:. In particular, in the latter section, the sentence 2917:. However, this conflicts with two broader guidances 2784:

is the process of computing an integral. It is, with

2431: 2382: 1596:

would it be possible to merge it into Roots of unity?

5287:

to determine whether its use and function meets the

4555:

Madhava–Gregory–Leibniz: 19 (including other orders)

4537:

Gregory–Leibniz: 159 (also counting Leibniz–Gregory)

3686:

of the angle, sharing a common endpoint, called the

3503:

which doesn’t seem like it really covers the topic.

1619:

Help talk:Citation Style 1§ Proposal: Add parameter

5044:Just guessing but it seems plausible that they are 3849: 3480:

should we have an article for a 'geometric figure'?

4870: 2744:I suggests the following for the firat paragraph: 2686: 2515: 2486: 2466: 2437: 2417: 2388: 2364: 2332: 2300: 2280: 2260: 2236: 3885:that is described by a finite number of straight 1333:What do you mean by "multiple people"? Also, see 5162:for multiple short citations in one <ref: --> 3190:List of integrals#Integrals of simple functions 2746: 5025:I have updated some references in the article 2577:What part of a circle is under its perimeter? 2189:list of continuity-related mathematical topics 1869:displacement, area, volume, and other concepts 4459:, since this was discovered independently by 4266:https://archive.org/details/calculus0000apos/ 1951:This is not constructive, but: I notice that 1491:K-stability_of_Fano_varieties#Delta_invariant 1232:This page has archives. Sections older than 57: 8: 4700:Madhava series § Madhava's arctangent series 3202:Heronian triangle#Properties of side lengths 3194:Heronian triangle#Properties of side lengths 1542:, use many second-person pronouns; however, 4439: 2889:Collapsed proofs: WP:ACCESSIBILITY concerns 1804:concerning the target of the redirect page 1722:This type of thread is better reserved for 5213:|ref={{harvid|Name|Year}} |reference=...}} 4999:You are invited to join the discussion at 3867: 3855: 3382: 3254: 3177:value if a reference for it is provided. 1632:You are invited to join the discussion at 64: 50: 4862: 4849: 4830: 4820: 4804: 4794: 4775: 4759: 4746: 4728: 4197:-- Revised 15:52, 15 February 2023 (UTC) 3937:, as opposed to other properties such as 3864: 3861: 2710:first sentence of an encyclopedia article 2652: 2644: 2638: 2632: 2501: 2499: 2479: 2452: 2450: 2430: 2403: 2401: 2381: 2345: 2313: 2293: 2273: 2253: 2229: 1965:, which is a very basic concept in maths. 4715:Khayyam-Newton expansion in math Ittihad 4304:These are all scans of physical books. – 4187:Shmuel (Seymour J.) Metz Username:Chatul 3294:Knowledge:WikiProject_Mathematics/Proofs 2915:Knowledge:WikiProject Mathematics/Proofs 2875:Shmuel (Seymour J.) Metz Username:Chatul 2696:Shmuel (Seymour J.) Metz Username:Chatul 2694:The first sentence should be general. -- 2516:{\textstyle {\tfrac {1}{1{,}000{,}000}}} 2091:Shmuel (Seymour J.) Metz Username:Chatul 1663:what is a cantellated great icosahedron? 3823:Again, no explanation anywhere of what 3464: 3406:That has been determined to go against 3282:in the absence of JavaScript and/or CSS 2673: 2665: 2657: 1861:I legitimately do know this means. Is 1763:Project-independent quality assessments 88: 5001:Talk:Algebraic variety#Merger proposal 4657:This discussion shows a redirect from 4531:Madhava: 43 (many for the sine series) 4519: 3966: 3920: 3834: 3751: 3721: 3706:) which more explicitly uses the term 3667: 3621: 3583: 3438:Wiles's proof of Fermat's Last Theorem 3251: 3217: 2842: 2546: 2222: 2062: 1956: 1689:truncated great stellated dodecahedron 1595: 1409: 1370: 18:Knowledge talk:WikiProject Mathematics 5325:WikiProject Mathematics archives/2023 4522:and likewise for other names, I get: 3870: 1296:2601:547:501:8F90:6D91:586F:CC4B:73D2 7: 3858: 3852: 3337:Very well said. I agree with this. 1724:Knowledge:Reference desk/Mathematics 1638:European Digital Mathematics Library 2144:jargon, sadly), not a position. -- 1339:2601:547:501:8F90:75EF:C82F:5D9:1C9 4328:We can search in this,book address 45:WikiProject Mathematics archives ( 32: 4168:Addison-Wesley Publishing Company 4153:Addison-Wesley Publishing Company 3993:on some surface, such as a wall, 3352:There is actually one more case: 2812:Feel free to improve this draft. 2712:with the requested properties. -- 2244:, which is after all only a long 1236:may be automatically archived by 5295:until a consensus is reached. — 5272: 4994: 4667: 3845: 3813:, one of the oldest branches of 3479: 3292:Now as far as actual style, the 2653: 2645: 2120:cumulative distribution function 1627: 1443: 38: 4117:https://www.stewartcalculus.com 4743: 4730: 4488:I can agree with what he said 4352:Good article reassessment for 4164:Calculus and Analytic Geometry 3560:definition about these topics. 2851:is the continuous analog of a 2835:Calculus and Analytic Geometry 2467:{\textstyle {\tfrac {1}{100}}} 2087:and other physical quantities. 2071:is the continuous analog of a 1933:to compute areas and volumes." 1852:Assigning numbers to functions 1703:But where are the cantellate ( 1: 5311:21:54, 26 February 2023 (UTC) 5247:22:32, 24 February 2023 (UTC) 5203:21:59, 24 February 2023 (UTC) 5188:21:53, 24 February 2023 (UTC) 5173:09:44, 25 February 2023 (UTC) 5128:17:33, 24 February 2023 (UTC) 5113:16:56, 24 February 2023 (UTC) 5084:02:24, 24 February 2023 (UTC) 5066:18:12, 23 February 2023 (UTC) 5039:12:44, 23 February 2023 (UTC) 5013:23:00, 20 February 2023 (UTC) 4982:11:12, 20 February 2023 (UTC) 4967:20:44, 19 February 2023 (UTC) 4948:10:01, 19 February 2023 (UTC) 4933:18:55, 17 February 2023 (UTC) 4918:17:38, 17 February 2023 (UTC) 4887:09:57, 17 February 2023 (UTC) 4710:23:48, 19 February 2023 (UTC) 4686:12:42, 18 February 2023 (UTC) 4644:20:33, 19 February 2023 (UTC) 4630:01:05, 18 February 2023 (UTC) 4617:23:51, 17 February 2023 (UTC) 4603:19:11, 17 February 2023 (UTC) 4591:18:18, 17 February 2023 (UTC) 4558:Nilakantha–Gregory–Leibniz: 3 4514:11:44, 17 February 2023 (UTC) 4498:09:45, 17 February 2023 (UTC) 4484:06:55, 17 February 2023 (UTC) 4435:12:24, 18 February 2023 (UTC) 4376:18:06, 17 February 2023 (UTC) 4340:07:40, 16 February 2023 (UTC) 4312:17:06, 15 February 2023 (UTC) 4300:16:31, 15 February 2023 (UTC) 4284:15:12, 15 February 2023 (UTC) 4240:16:31, 15 February 2023 (UTC) 4224:16:00, 15 February 2023 (UTC) 4210:13:36, 15 February 2023 (UTC) 4195:11:25, 15 February 2023 (UTC) 4131:09:33, 15 February 2023 (UTC) 4092:16:35, 15 February 2023 (UTC) 4069:15:58, 15 February 2023 (UTC) 4049:18:35, 14 February 2023 (UTC) 4028:04:24, 14 February 2023 (UTC) 3726:, two figures or objects are 3656:03:35, 14 February 2023 (UTC) 3572:01:48, 14 February 2023 (UTC) 3555:My claim is that the article 3543:01:20, 14 February 2023 (UTC) 3527:01:08, 14 February 2023 (UTC) 3450:04:50, 14 February 2023 (UTC) 3420:00:48, 14 February 2023 (UTC) 3401:06:08, 13 February 2023 (UTC) 3374:09:29, 13 February 2023 (UTC) 3347:21:26, 13 February 2023 (UTC) 3332:09:12, 11 February 2023 (UTC) 3311:18:07, 10 February 2023 (UTC) 3238:(see below for a proof), and 3165:11:27, 10 February 2023 (UTC) 3139:06:27, 10 February 2023 (UTC) 3114:05:53, 10 February 2023 (UTC) 3095:02:30, 10 February 2023 (UTC) 3060:01:50, 11 February 2023 (UTC) 3040:18:54, 10 February 2023 (UTC) 3020:11:34, 10 February 2023 (UTC) 2979:02:25, 10 February 2023 (UTC) 2883:22:02, 12 February 2023 (UTC) 2855:, which is used to calculate 2826:16:02, 12 February 2023 (UTC) 2788:, a fundamental operation of 2722:19:40, 13 February 2023 (UTC) 2704:22:02, 12 February 2023 (UTC) 2619:14:36, 13 February 2023 (UTC) 2605:20:33, 12 February 2023 (UTC) 2587:14:39, 12 February 2023 (UTC) 2573:23:17, 11 February 2023 (UTC) 2559:22:52, 11 February 2023 (UTC) 2542:21:59, 10 February 2023 (UTC) 2418:{\textstyle {\tfrac {1}{10}}} 2209:21:47, 10 February 2023 (UTC) 2154:20:30, 10 February 2023 (UTC) 2138:19:15, 10 February 2023 (UTC) 2114:17:44, 10 February 2023 (UTC) 2099:17:08, 10 February 2023 (UTC) 2075:, which is used to calculate 2049:12:37, 10 February 2023 (UTC) 2035:02:36, 10 February 2023 (UTC) 2017:18:09, 10 February 2023 (UTC) 1999:00:51, 10 February 2023 (UTC) 1865:a reference way to linearity? 1636:. Need advice on whether the 1487:K-stability of Fano varieties 4402:should remain a redirect to 3676:is the figure formed by two 3432:, we have splitoff articles 3082:21:57, 9 February 2023 (UTC) 2964:07:49, 9 February 2023 (UTC) 2948:04:54, 9 February 2023 (UTC) 1983:23:37, 9 February 2023 (UTC) 1946:21:56, 9 February 2023 (UTC) 1904:21:55, 9 February 2023 (UTC) 1818:01:13, 8 February 2023 (UTC) 1791:20:23, 6 February 2023 (UTC) 1755:06:28, 5 February 2023 (UTC) 1736:05:42, 5 February 2023 (UTC) 1717:05:39, 5 February 2023 (UTC) 1705:great rhombicosidodecahedron 1697:great stellated dodecahedron 1658:07:06, 4 February 2023 (UTC) 1611:22:29, 3 February 2023 (UTC) 1591:17:10, 3 February 2023 (UTC) 1560:15:14, 3 February 2023 (UTC) 1522:03:42, 1 February 2023 (UTC) 1507:01:37, 1 February 2023 (UTC) 1475:13:30, 31 January 2023 (UTC) 1461:12:34, 31 January 2023 (UTC) 1438:12:06, 31 January 2023 (UTC) 1422:11:22, 31 January 2023 (UTC) 1381:02:26, 1 February 2023 (UTC) 1361:16:12, 30 January 2023 (UTC) 1347:23:20, 29 January 2023 (UTC) 1322:16:13, 29 January 2023 (UTC) 1304:21:59, 28 January 2023 (UTC) 1271:21:50, 28 January 2023 (UTC) 4467:We already have an article 4394:Talk:Prime (disambiguation) 3889:connected to form a closed 3704:Encyclopedia of Mathematics 3519:could use a lot of help.) – 3143:So, suggestion: When using 1678:truncated great icosahedron 5341: 5018:References in the article 4417:, it is discussed whether 4396:, it is discussed whether 4161:Thomas, George Brinton Jr. 4098:great books about calculus 4080:Help:Archiving a talk page 3795: 3778: 2756:is, roughly speaking, the 2487:{\textstyle 1{,}000{,}000} 2118:For a concrete example, a 5072:The Fourier transforms... 4419:e (mathematical constant) 4387:e (mathematical constant) 4110:https://aetemad.iut.ac.ir 3775:'land measurement'; from 3761: 3698:This definition of angle 3210:Homomorphism#Monomorphism 2863:, their generalizations, 2083:, their generalizations, 5285:redirects for discussion 5267:Redirects for discussion 4987:Merge discussions about 4474:Knowledge:Article titles 3957:graphical representation 3931:graphical representation 3492:configuration (geometry) 3280:, and it is simply that 3214:Homomorphism#Epimorphism 3026:Homomorphism#Epimorphism 2494:parts, each of which is 2193:Continuity (mathematics) 1776:WikiProject banner shell 4720:the other is European. 4696:Madhava of Sangamagrama 4381:Move discussions about 4082:for suggested methods. 4001:, or stone, to inform, 3700:originated with Sidorov 3510:currently redirects to 3499:currently redirects to 3356:currently redirects to 3218:the two definitions of 2923:Knowledge:Accessibility 2913:. This is specified in 2474:of an inch long; or of 2445:parts, each part being 2425:of an inch long; or of 2173:displacement (geometry) 1859:in a way that describes 1830:I randomly came across 1683:great icosidodecahedron 1571:Primitive root modulo n 1465:I agree. Thank you ! -- 4974:Mohammad.Hosein.J.Shia 4940:Mohammad.Hosein.J.Shia 4925:Mohammad.Hosein.J.Shia 4879:Mohammad.Hosein.J.Shia 4872: 4490:Mohammad.Hosein.J.Shia 4408:Prime (disambiguation) 4406:or should be moved to 4332:Mohammad.Hosein.J.Shia 4292:Mohammad.Hosein.J.Shia 4232:Mohammad.Hosein.J.Shia 4202:Mohammad.Hosein.J.Shia 4123:Mohammad.Hosein.J.Shia 3809:'a measure') is, with 3730:if they have the same 2806: 2688: 2517: 2488: 2468: 2439: 2419: 2390: 2366: 2365:{\textstyle \int dx=x} 2334: 2333:{\textstyle \int dy=y} 2302: 2282: 2262: 2238: 1800:Input is requested at 1579:Root of unity modulo n 1567:Root of unity modulo n 1530:Root of unity modulo n 1239:Lowercase sigmabot III 4902:binomial coefficients 4873: 4552:Madhava–Nilakantha: 6 4549:Nilakantha-Gregory: 4 4546:Nilakantha–Leibniz: 2 3899:). The bounded plane 3716:congruence (geometry) 3585:1. Geometric figures. 3430:Fermat's Last Theorem 3196:). In this case, per 2804:that use mathematics. 2689: 2518: 2489: 2469: 2440: 2420: 2391: 2367: 2335: 2303: 2283: 2263: 2239: 2191:which redirects from 1957:For example, look at 4727: 4572:inverse tangent: 135 4214:Don't forget Spivak 4115:stewartcalculus.com 2983:But putting them in 2631: 2498: 2478: 2449: 2429: 2400: 2380: 2344: 2312: 2292: 2272: 2252: 2228: 2177:domain of a function 1923:area = base x height 5289:redirect guidelines 5283:has been listed at 4955:multinomial theorem 4543:Madhava–Gregory: 40 4540:Madhava–Leibniz: 49 4252:Try Goursat (1904) 3616:Lessons in Geometry 3517:mathematical object 3501:Shape § In geometry 3222:are equivalent for 2438:{\displaystyle 100} 2181:continuous function 1847:Here are my issues 1796:RfD requiring input 1575:Carmichael function 1534:I am not sure that 4989:algebraic manifold 4868: 4108:aetemad.iut.ac.ir 3913:is wiki-linked to 3792:'earth, land' and 3670:Euclidean geometry 3512:Geometry § Objects 3358:de Rham cohomology 2954:the footnotes. -- 2684: 2674: 2666: 2658: 2513: 2511: 2484: 2464: 2462: 2435: 2415: 2413: 2389:{\displaystyle 10} 2386: 2362: 2330: 2301:{\textstyle \int } 2298: 2281:{\textstyle \sum } 2278: 2261:{\textstyle \sum } 2258: 2237:{\textstyle \int } 2234: 4906:Pascal's triangle 4659:Arctangent series 4457:arctangent series 4446:arctangent series 4364:reassessment page 3963:, which defines: 3917:, which defines: 3909:But in this case 3897:polygonal circuit 3403: 3387:comment added by 3272: 3259:comment added by 2510: 2461: 2412: 2214:Silvanus Thompson 2156: 1985: 1969: 1959:Mensural notation 1832:this village pump 1823:Lead Sentence to 1672:great icosahedron 1246: 1245: 95:Nov 2002–Dec 2003 5332: 5282: 5276: 5238: 5232: 5228: 5222: 5218: 5214: 5161: 5155: 5151: 5145: 5141: 5135: 5098: 5092: 5027:Point (geometry) 5020:Point (geometry) 4998: 4997: 4894:binomial theorem 4877: 4875: 4874: 4869: 4867: 4866: 4854: 4853: 4835: 4834: 4825: 4824: 4809: 4808: 4799: 4798: 4780: 4779: 4764: 4763: 4751: 4750: 4692:Gregory's series 4675: 4671: 4670: 4663:Gregory's series 4504:series article. 4453:Gregory's series 4442:Gregory's series 4421:should moved to 4401: 4270:Piskunov (1969) 4180: 4156: 4018:geometric figure 3877: 3876: 3873: 3872: 3869: 3866: 3863: 3860: 3857: 3854: 3851: 3806: 3799: 3789: 3782: 3772: 3765: 3708:geometric figure 3589:geometric figure 3508:geometric object 3497:Geometric figure 3472: 3471:This is a proof. 3469: 3319:Bounded operator 3198:WP:Verifiability 3182:WP:Verifiability 3152: 3146: 3002: 2996: 2992: 2986: 2936: 2912: 2906: 2902: 2896: 2693: 2691: 2690: 2685: 2656: 2648: 2643: 2642: 2522: 2520: 2519: 2514: 2512: 2503: 2493: 2491: 2490: 2485: 2473: 2471: 2470: 2465: 2463: 2454: 2444: 2442: 2441: 2436: 2424: 2422: 2421: 2416: 2414: 2405: 2395: 2393: 2392: 2387: 2371: 2369: 2368: 2363: 2339: 2337: 2336: 2331: 2307: 2305: 2304: 2299: 2287: 2285: 2284: 2279: 2267: 2265: 2264: 2259: 2243: 2241: 2240: 2235: 2185:linear continuum 2142: 1972: 1950: 1780: 1774: 1728:Partofthemachine 1643: 1631: 1630: 1622: 1451: 1447: 1446: 1332: 1282: 1241: 1225: 66: 59: 52: 42: 34: 5340: 5339: 5335: 5334: 5333: 5331: 5330: 5329: 5315: 5314: 5278: 5270: 5236: 5230: 5226: 5220: 5216: 5208: 5159: 5153: 5149: 5143: 5139: 5133: 5096: 5090: 5023: 4995: 4992: 4898:binomial series 4858: 4845: 4826: 4816: 4800: 4790: 4771: 4755: 4742: 4725: 4724: 4717: 4668: 4666: 4566:arctangent: 205 4449: 4440:Proposal: move 4397: 4390: 4360:Albert Einstein 4357: 4354:Albert Einstein 4264:Apostol (1967) 4258:Courant (1937) 4177: 4159: 4143:Apostol, Tom M. 4141: 4100: 4056: 4005:, or entertain. 3892:polygonal chain 3848: 3844: 3710:. But the word 3482: 3477: 3476: 3475: 3470: 3466: 3354:de Rham theorem 3278:MOS:PRECOLLAPSE 3245:category theory 3150: 3144: 3000: 2998:collapse bottom 2994: 2990: 2984: 2926: 2910: 2908:collapse bottom 2904: 2900: 2894: 2891: 2786:differentiation 2634: 2629: 2628: 2496: 2495: 2476: 2475: 2447: 2446: 2427: 2426: 2398: 2397: 2378: 2377: 2342: 2341: 2310: 2309: 2290: 2289: 2270: 2269: 2250: 2249: 2226: 2225: 2129: 2126: 1828: 1798: 1778: 1772: 1765: 1665: 1641: 1628: 1625: 1620: 1532: 1495:Delta invariant 1444: 1442: 1398: 1395:Delta invariant 1326: 1276: 1251: 1237: 1226: 1220: 1211: 1097: 87: 86: 73: 70: 30: 29: 28: 12: 11: 5: 5338: 5336: 5328: 5327: 5317: 5316: 5280:Improper point 5269: 5263:Improper point 5259: 5258: 5257: 5256: 5255: 5254: 5253: 5252: 5251: 5250: 5249: 5205: 5195:David Eppstein 5177: 5176: 5175: 5120:David Eppstein 5054: 5053: 5052: 5049: 5022: 5016: 4991: 4985: 4970: 4969: 4959:David Eppstein 4921: 4920: 4865: 4861: 4857: 4852: 4848: 4844: 4841: 4838: 4833: 4829: 4823: 4819: 4815: 4812: 4807: 4803: 4797: 4793: 4789: 4786: 4783: 4778: 4774: 4770: 4767: 4762: 4758: 4754: 4749: 4745: 4741: 4738: 4735: 4732: 4716: 4713: 4655: 4654: 4653: 4652: 4651: 4650: 4649: 4648: 4647: 4646: 4593: 4581: 4578: 4577: 4576: 4575:inverse tan: 4 4573: 4570: 4567: 4561: 4560: 4559: 4556: 4553: 4550: 4547: 4544: 4541: 4538: 4535: 4534:Nilakantha: 12 4532: 4529: 4526: 4469:Madhava series 4448: 4438: 4389: 4379: 4356: 4350: 4349: 4348: 4347: 4346: 4345: 4344: 4343: 4342: 4319: 4318: 4317: 4316: 4315: 4314: 4274: 4268: 4262: 4256: 4249: 4248: 4247: 4246: 4245: 4244: 4243: 4242: 4229: 4183: 4182: 4181: 4176:978-0201162905 4175: 4157: 4136: 4099: 4096: 4095: 4094: 4055: 4054:Basic Question 4052: 4033: 4032: 4031: 4030: 4009: 4008: 4007: 3953: 3952: 3951: 3907: 3906: 3905: 3821: 3820: 3819: 3742: 3741: 3740: 3696: 3695: 3694: 3658: 3646: 3645: 3644: 3614:And Hadamard ( 3612: 3611: 3610: 3574: 3561: 3553: 3552:on Knowledge.) 3535:David Eppstein 3481: 3478: 3474: 3473: 3463: 3462: 3458: 3457: 3456: 3455: 3454: 3453: 3452: 3412:Mathnerd314159 3379: 3350: 3349: 3314: 3313: 3303:Mathnerd314159 3290: 3232:abelian groups 3174: 3173: 3172: 3171: 3170: 3169: 3168: 3167: 3128: 3124: 3120: 3098: 3097: 3084: 3070: 3069: 3068: 3067: 3066: 3065: 3064: 3063: 3062: 3029: 2969: 2890: 2887: 2886: 2885: 2831: 2769:areas form an 2741: 2739: 2738: 2737: 2736: 2735: 2734: 2733: 2732: 2731: 2730: 2729: 2728: 2727: 2726: 2725: 2724: 2706: 2683: 2680: 2677: 2672: 2669: 2664: 2661: 2655: 2651: 2647: 2641: 2637: 2625: 2624: 2623: 2622: 2621: 2592: 2532: 2509: 2506: 2483: 2460: 2457: 2434: 2411: 2408: 2385: 2361: 2358: 2355: 2352: 2349: 2329: 2326: 2323: 2320: 2317: 2297: 2277: 2257: 2233: 2220: 2211: 2199: 2196: 2165: 2127: 2124: 2106:David Eppstein 2055: 2053: 2052: 2051: 2025: 2024: 2023: 2022: 2021: 2020: 2019: 1970: 1968: 1934: 1931:infinitesimals 1910: 1891: 1890: 1884: 1878: 1872: 1866: 1856: 1827: 1821: 1797: 1794: 1764: 1761: 1760: 1759: 1758: 1757: 1739: 1738: 1701: 1700: 1694: 1686: 1680: 1675: 1664: 1661: 1624: 1617:Discussion at 1615: 1614: 1613: 1593: 1548:Roots of unity 1531: 1528: 1527: 1526: 1525: 1524: 1482: 1481: 1480: 1479: 1478: 1477: 1397: 1391: 1390: 1389: 1388: 1387: 1386: 1385: 1384: 1383: 1363: 1353:128.164.177.55 1284: 1279:David Eppstein 1263:David Eppstein 1250: 1247: 1244: 1243: 1231: 1228: 1227: 1222: 1218: 1216: 1213: 1212: 1210: 1209: 1154: 1098: 1096: 1095: 1040: 985: 930: 875: 820: 765: 710: 655: 600: 545: 490: 435: 380: 325: 270: 215: 160: 105: 84: 83: 82: 79: 78: 75: 74: 69: 68: 61: 54: 46: 43: 37: 31: 15: 14: 13: 10: 9: 6: 4: 3: 2: 5337: 5326: 5323: 5322: 5320: 5313: 5312: 5308: 5305: 5302: 5298: 5294: 5290: 5286: 5281: 5277:The redirect 5275: 5268: 5264: 5260: 5248: 5245: 5242: 5235: 5225: 5212: 5206: 5204: 5200: 5196: 5191: 5190: 5189: 5186: 5183: 5178: 5174: 5170: 5166: 5158: 5148: 5138: 5131: 5130: 5129: 5125: 5121: 5116: 5115: 5114: 5110: 5106: 5102: 5095: 5087: 5086: 5085: 5081: 5077: 5073: 5069: 5068: 5067: 5063: 5059: 5055: 5050: 5048:0-07-007015-6 5046: 5045: 5043: 5042: 5041: 5040: 5036: 5032: 5028: 5021: 5017: 5015: 5014: 5010: 5006: 5002: 4990: 4986: 4984: 4983: 4979: 4975: 4968: 4964: 4960: 4956: 4952: 4951: 4950: 4949: 4945: 4941: 4935: 4934: 4930: 4926: 4919: 4915: 4911: 4907: 4903: 4899: 4895: 4891: 4890: 4889: 4888: 4884: 4880: 4863: 4859: 4855: 4850: 4846: 4842: 4839: 4836: 4831: 4827: 4821: 4817: 4813: 4810: 4805: 4801: 4795: 4791: 4787: 4784: 4781: 4776: 4772: 4768: 4765: 4760: 4756: 4752: 4747: 4739: 4736: 4733: 4721: 4714: 4712: 4711: 4708: 4705: 4701: 4697: 4693: 4688: 4687: 4683: 4679: 4674: 4664: 4660: 4645: 4641: 4637: 4633: 4632: 4631: 4628: 4625: 4620: 4619: 4618: 4614: 4610: 4606: 4605: 4604: 4601: 4598: 4594: 4592: 4589: 4586: 4582: 4579: 4574: 4571: 4568: 4565: 4564: 4562: 4557: 4554: 4551: 4548: 4545: 4542: 4539: 4536: 4533: 4530: 4527: 4524: 4523: 4521: 4517: 4516: 4515: 4511: 4507: 4502: 4501: 4500: 4499: 4495: 4491: 4486: 4485: 4482: 4479: 4476:. Thoughts? – 4475: 4470: 4465: 4462: 4461:Kerala school 4458: 4454: 4447: 4443: 4437: 4436: 4432: 4428: 4424: 4420: 4416: 4411: 4409: 4405: 4400: 4395: 4388: 4384: 4380: 4378: 4377: 4373: 4369: 4365: 4361: 4355: 4351: 4341: 4337: 4333: 4330: 4327: 4326: 4325: 4324: 4323: 4322: 4321: 4320: 4313: 4310: 4307: 4303: 4302: 4301: 4297: 4293: 4290: 4287: 4286: 4285: 4282: 4279: 4275: 4273: 4269: 4267: 4263: 4261: 4257: 4255: 4251: 4250: 4241: 4237: 4233: 4230: 4227: 4226: 4225: 4221: 4217: 4213: 4212: 4211: 4207: 4203: 4199: 4198: 4196: 4192: 4188: 4184: 4178: 4173: 4169: 4165: 4162: 4158: 4154: 4150: 4149: 4144: 4140: 4139: 4137: 4135: 4134: 4133: 4132: 4128: 4124: 4120: 4118: 4113: 4111: 4106: 4103: 4097: 4093: 4089: 4085: 4081: 4077: 4073: 4072: 4071: 4070: 4066: 4062: 4053: 4051: 4050: 4046: 4042: 4038: 4029: 4026: 4023: 4019: 4014: 4010: 4006: 4004: 4000: 3996: 3992: 3988: 3985: 3981: 3978: 3975: 3973: 3972:Ancient Greek 3969: 3965: 3964: 3962: 3958: 3954: 3950: 3948: 3944: 3940: 3936: 3932: 3928: 3924: 3919: 3918: 3916: 3912: 3908: 3904: 3902: 3898: 3894: 3893: 3888: 3887:line segments 3884: 3881: 3875: 3842: 3838: 3833: 3832: 3830: 3826: 3822: 3818: 3816: 3812: 3808: 3805: 3798: 3794: 3791: 3788: 3781: 3777: 3774: 3771: 3764: 3760: 3758: 3757:Ancient Greek 3754: 3750: 3749: 3747: 3743: 3739: 3738:of the other. 3737: 3733: 3729: 3725: 3720: 3719: 3717: 3713: 3709: 3705: 3701: 3697: 3693: 3692:of the angle. 3691: 3690: 3685: 3684: 3680:, called the 3679: 3675: 3671: 3666: 3665: 3663: 3659: 3657: 3654: 3651: 3647: 3643: 3642: 3640: 3636: 3634: 3628: 3624: 3620: 3619: 3617: 3613: 3609: 3608: 3605: 3603: 3599: 3594: 3590: 3586: 3582: 3581: 3579: 3575: 3573: 3570: 3567: 3562: 3558: 3554: 3551: 3546: 3545: 3544: 3540: 3536: 3531: 3530: 3529: 3528: 3525: 3522: 3518: 3513: 3509: 3504: 3502: 3498: 3493: 3488: 3468: 3465: 3461: 3451: 3447: 3443: 3439: 3435: 3431: 3427: 3423: 3422: 3421: 3417: 3413: 3409: 3405: 3404: 3402: 3398: 3394: 3390: 3386: 3380: 3378: 3377: 3376: 3375: 3371: 3367: 3363: 3359: 3355: 3348: 3344: 3340: 3336: 3335: 3334: 3333: 3329: 3325: 3320: 3312: 3308: 3304: 3300: 3295: 3291: 3287: 3283: 3279: 3275: 3274: 3273: 3270: 3266: 3262: 3258: 3253: 3248: 3246: 3242: 3241: 3237: 3233: 3229: 3228:vector spaces 3225: 3221: 3215: 3211: 3205: 3203: 3199: 3195: 3191: 3187: 3183: 3178: 3166: 3162: 3159: 3156: 3149: 3142: 3141: 3140: 3137: 3134: 3129: 3125: 3121: 3117: 3116: 3115: 3111: 3107: 3102: 3101: 3100: 3099: 3096: 3093: 3090: 3085: 3083: 3079: 3075: 3071: 3061: 3057: 3054: 3051: 3047: 3043: 3042: 3041: 3038: 3035: 3030: 3027: 3023: 3022: 3021: 3017: 3014: 3011: 3006: 2999: 2989: 2982: 2981: 2980: 2977: 2974: 2970: 2967: 2966: 2965: 2961: 2957: 2952: 2951: 2950: 2949: 2945: 2942: 2939: 2934: 2930: 2924: 2920: 2916: 2909: 2899: 2888: 2884: 2880: 2876: 2872: 2870: 2866: 2862: 2858: 2854: 2850: 2846: 2841:. What about 2840: 2836: 2832: 2830: 2829: 2828: 2827: 2823: 2819: 2813: 2810: 2805: 2803: 2799: 2795: 2791: 2787: 2783: 2779: 2777: 2772: 2768: 2767:infinitesimal 2763: 2759: 2755: 2751: 2745: 2742: 2723: 2719: 2715: 2711: 2707: 2705: 2701: 2697: 2681: 2678: 2675: 2670: 2667: 2662: 2659: 2649: 2639: 2635: 2626: 2620: 2616: 2612: 2608: 2607: 2606: 2602: 2598: 2593: 2590: 2589: 2588: 2584: 2580: 2576: 2575: 2574: 2570: 2566: 2562: 2561: 2560: 2556: 2552: 2548: 2545: 2544: 2543: 2540: 2537: 2533: 2531: 2530: 2528: 2524: 2507: 2504: 2481: 2458: 2455: 2432: 2409: 2406: 2396:pieces, each 2383: 2373: 2359: 2356: 2353: 2350: 2347: 2327: 2324: 2321: 2318: 2315: 2295: 2275: 2255: 2247: 2231: 2221: 2218: 2215: 2212: 2210: 2207: 2204: 2200: 2197: 2194: 2190: 2186: 2182: 2178: 2174: 2170: 2166: 2162: 2158: 2157: 2155: 2151: 2147: 2141: 2140: 2139: 2136: 2133: 2121: 2117: 2116: 2115: 2111: 2107: 2102: 2101: 2100: 2096: 2092: 2088: 2086: 2082: 2078: 2074: 2070: 2066: 2060: 2059:infinitesimal 2056: 2054: 2050: 2046: 2042: 2038: 2037: 2036: 2033: 2030: 2026: 2018: 2014: 2010: 2006: 2002: 2001: 2000: 1996: 1992: 1987: 1986: 1984: 1980: 1976: 1971: 1966: 1964: 1960: 1954: 1949: 1948: 1947: 1943: 1939: 1935: 1932: 1928: 1924: 1919: 1915: 1911: 1908: 1907: 1906: 1905: 1901: 1897: 1888: 1885: 1882: 1881:infinitesimal 1879: 1876: 1873: 1870: 1867: 1864: 1860: 1857: 1853: 1850: 1849: 1848: 1845: 1844: 1840: 1837: 1833: 1826: 1822: 1820: 1819: 1815: 1811: 1807: 1803: 1795: 1793: 1792: 1788: 1784: 1777: 1770: 1762: 1756: 1752: 1748: 1743: 1742: 1741: 1740: 1737: 1733: 1729: 1725: 1721: 1720: 1719: 1718: 1714: 1710: 1706: 1698: 1695: 1693: 1690: 1687: 1684: 1681: 1679: 1676: 1673: 1670: 1669: 1668: 1662: 1660: 1659: 1655: 1651: 1647: 1639: 1635: 1623: 1616: 1612: 1608: 1604: 1600: 1597: 1594: 1592: 1588: 1584: 1580: 1576: 1572: 1568: 1564: 1563: 1562: 1561: 1557: 1553: 1549: 1545: 1541: 1537: 1529: 1523: 1519: 1515: 1510: 1509: 1508: 1504: 1500: 1496: 1492: 1488: 1484: 1483: 1476: 1472: 1468: 1464: 1463: 1462: 1458: 1454: 1450: 1441: 1440: 1439: 1435: 1431: 1426: 1425: 1424: 1423: 1419: 1415: 1411: 1407: 1403: 1396: 1392: 1382: 1379: 1376: 1372: 1367: 1364: 1362: 1358: 1354: 1350: 1349: 1348: 1344: 1340: 1336: 1330: 1325: 1324: 1323: 1319: 1315: 1311: 1310:BIT predicate 1307: 1306: 1305: 1301: 1297: 1293: 1289: 1285: 1280: 1275: 1274: 1273: 1272: 1268: 1264: 1260: 1256: 1255:BIT predicate 1249:BIT predicate 1248: 1240: 1235: 1230: 1229: 1215: 1214: 1208: 1204: 1200: 1196: 1192: 1188: 1184: 1180: 1176: 1172: 1168: 1164: 1160: 1159: 1155: 1153: 1149: 1145: 1141: 1137: 1133: 1129: 1125: 1121: 1117: 1113: 1109: 1105: 1104: 1100: 1099: 1094: 1090: 1086: 1082: 1078: 1074: 1070: 1066: 1062: 1058: 1054: 1050: 1046: 1045: 1041: 1039: 1035: 1031: 1027: 1023: 1019: 1015: 1011: 1007: 1003: 999: 995: 991: 990: 986: 984: 980: 976: 972: 968: 964: 960: 956: 952: 948: 944: 940: 936: 935: 931: 929: 925: 921: 917: 913: 909: 905: 901: 897: 893: 889: 885: 881: 880: 876: 874: 870: 866: 862: 858: 854: 850: 846: 842: 838: 834: 830: 826: 825: 821: 819: 815: 811: 807: 803: 799: 795: 791: 787: 783: 779: 775: 771: 770: 766: 764: 760: 756: 752: 748: 744: 740: 736: 732: 728: 724: 720: 716: 715: 711: 709: 705: 701: 697: 693: 689: 685: 681: 677: 673: 669: 665: 661: 660: 656: 654: 650: 646: 642: 638: 634: 630: 626: 622: 618: 614: 610: 606: 605: 601: 599: 595: 591: 587: 583: 579: 575: 571: 567: 563: 559: 555: 551: 550: 546: 544: 540: 536: 532: 528: 524: 520: 516: 512: 508: 504: 500: 496: 495: 491: 489: 485: 481: 477: 473: 469: 465: 461: 457: 453: 449: 445: 441: 440: 436: 434: 430: 426: 422: 418: 414: 410: 406: 402: 398: 394: 390: 386: 385: 381: 379: 375: 371: 367: 363: 359: 355: 351: 347: 343: 339: 335: 331: 330: 326: 324: 320: 316: 312: 308: 304: 300: 296: 292: 288: 284: 280: 276: 275: 271: 269: 265: 261: 257: 253: 249: 245: 241: 237: 233: 229: 225: 221: 220: 216: 214: 210: 206: 202: 198: 194: 190: 186: 182: 178: 174: 170: 166: 165: 161: 159: 155: 151: 147: 143: 139: 135: 131: 127: 123: 119: 115: 111: 110: 106: 104: 100: 96: 92: 89: 85:Earlier years 81: 80: 77: 76: 72: 67: 62: 60: 55: 53: 48: 47: 41: 36: 35: 27: 23: 19: 5303: 5271: 5265:" listed at 5193:to change. — 5071: 5024: 4993: 4971: 4936: 4922: 4722: 4718: 4689: 4672: 4656: 4528:Gregory: 349 4487: 4466: 4450: 4412: 4404:Prime number 4391: 4368:Onegreatjoke 4358: 4288: 4163: 4147: 4121: 4114: 4107: 4105:references: 4104: 4101: 4057: 4036: 4034: 4017: 4012: 3979: 3974: 3967: 3956: 3955:From there, 3926: 3922: 3910: 3896: 3890: 3840: 3824: 3803: 3800: 3793: 3786: 3783: 3776: 3769: 3766: 3759: 3752: 3736:mirror image 3727: 3711: 3707: 3703: 3687: 3681: 3673: 3638: 3637: 3632: 3630: 3626: 3622: 3615: 3606: 3601: 3598:2. Geometry. 3597: 3596: 3592: 3588: 3584: 3577: 3549: 3505: 3495:definition? 3483: 3467: 3459: 3426:WP:SPLITting 3383:— Preceding 3361: 3351: 3315: 3286:MOS:COLLAPSE 3281: 3255:— Preceding 3249: 3219: 3206: 3179: 3175: 3004: 2988:collapse top 2898:collapse top 2892: 2848: 2834: 2814: 2811: 2807: 2802:technologies 2781: 2780: 2775: 2770: 2766: 2753: 2747: 2743: 2740: 2709: 2529: 2525: 2374: 2245: 2223: 2128:displacement 2068: 2058: 2004: 1922: 1892: 1886: 1880: 1874: 1868: 1862: 1858: 1851: 1846: 1842: 1841: 1829: 1810:66.44.62.177 1799: 1766: 1702: 1692:(degenerate) 1691: 1666: 1626: 1540:in this part 1536:this article 1533: 1448: 1399: 1366:WP:OWNERSHIP 1335:WP:OWNERSHIP 1259:WP:TECHNICAL 1252: 1233: 1156: 1111: 1101: 1042: 987: 932: 877: 822: 767: 712: 657: 602: 547: 492: 437: 382: 327: 272: 217: 162: 107: 103:Sep–Dec 2004 99:Jan–Aug 2004 44: 5297:Mx. Granger 5005:SilverMatsu 4665:is needed. 4569:arctan: 224 4166:(6th ed.). 3980:(graphikós) 3815:mathematics 3220:epimorphism 3127:interested. 3003:makes them 2845:mathematics 2839:Epsilontics 2796:, and most 2782:Integration 2750:mathematics 2065:mathematics 1914:mathematics 1894:discussion. 1685:(rectified) 1667:Ya got yer 1650:SilverMatsu 1648:. thanks ! 1640:(Parameter 1514:SilverMatsu 1467:SilverMatsu 1414:SilverMatsu 1406:WP:DRAFTIFY 5165:Dedhert.Jr 5105:Dedhert.Jr 5101:WP:CITEVAR 5076:Dedhert.Jr 5031:Dedhert.Jr 4423:e (number) 4003:illustrate 3997:, screen, 3827:means. In 3811:arithmetic 3460:References 3289:guideline. 3005:impossible 2611:XOR'easter 2579:XOR'easter 2041:XOR'easter 1552:Dedhert.Jr 91:Motivation 5241:jacobolus 5182:jacobolus 4704:jacobolus 4624:jacobolus 4597:jacobolus 4585:jacobolus 4478:jacobolus 4306:jacobolus 4278:jacobolus 4216:Thenub314 4076:Thenub314 4061:Thenub314 4022:jacobolus 3959:links to 3831:we have: 3770:geōmetría 3763:γεωμετρία 3728:congruent 3718:we have: 3664:we have: 3650:jacobolus 3593:congruent 3566:jacobolus 3550:somewhere 3521:jacobolus 3506:Related, 3339:PatrickR2 3133:jacobolus 3089:jacobolus 3074:PatrickR2 3046:Jacobolus 3034:jacobolus 2973:jacobolus 2597:Tazerenix 2565:Tazerenix 2536:jacobolus 2508:1,000,000 2482:1,000,000 2203:jacobolus 2132:jacobolus 2029:jacobolus 2005:graphs of 1991:Tazerenix 1938:Tazerenix 1896:Thenub314 1875:combining 1806:Free term 1699:(regular) 1674:(regular) 1499:Tazerenix 1375:jacobolus 1329:PatrickR2 1314:PatrickR2 5319:Category 5307:contribs 5217:ref=none 5211:wikicite 4678:D.Lazard 4636:NadVolum 4609:NadVolum 4506:NadVolum 4427:D.Lazard 4145:(1960). 3977:γραφικός 3968:Graphics 3961:graphics 3947:material 3837:geometry 3753:Geometry 3748:itself: 3746:geometry 3724:geometry 3602:geometry 3578:Geometry 3397:contribs 3385:unsigned 3269:contribs 3261:D.Lazard 3257:unsigned 3186:WP:LEAST 2933:D.Lazard 2849:integral 2818:D.Lazard 2798:sciences 2790:calculus 2776:integral 2771:integral 2754:integral 2195:, etc.). 2169:velocity 2161:integral 2125:position 2069:integral 1963:Integral 1953:Integral 1927:calculus 1918:integral 1825:Integral 1783:Aymatth2 1644:) meets 1583:D.Lazard 1453:D.Lazard 1430:D.Lazard 1253:Over on 24:‎ | 20:‎ | 5180:YMMV. – 5157:harvtxt 3991:designs 3943:texture 3935:surface 3878:) is a 3841:polygon 3829:polygon 3236:modules 3155:Mako001 3050:Mako001 3010:Mako001 2938:Mako001 2865:momenta 2861:volumes 2794:physics 2085:momenta 2081:volumes 1836:be bold 1802:the RfD 1747:Tamfang 1709:Tamfang 1642:|eudml= 1621:|eudml= 1544:MOS:YOU 1234:15 days 22:Archive 4013:figure 3995:canvas 3987:images 3984:visual 3970:(from 3927:figure 3911:figure 3901:region 3883:figure 3825:figure 3804:métron 3797:μέτρον 3755:(from 3712:figure 3689:vertex 3633:figure 3627:volume 3442:DMacks 3389:Chatul 3240:groups 2929:DMacks 2340:, and 1646:WP:GNG 1402:WP:GNG 1393:about 1288:WP:AGF 5224:harvp 4908:. -- 4464:etc. 4399:Prime 4383:Prime 4084:Nthep 4037:shape 3999:paper 3949:type. 3945:, or 3939:color 3929:is a 3923:shape 3915:shape 3880:plane 3732:shape 3683:sides 3674:angle 3672:, an 3662:angle 3557:shape 3487:shape 3408:WP:SP 3362:could 3299:WP:OR 3163:🇺🇦 3058:🇺🇦 3018:🇺🇦 2946:🇺🇦 2873:?? 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