text:
Talk:Port Arthur massacre (Australia)

Semi-protected edit request on 21 January 2022
In the Attacks section, under Port Arthur Historic Site, the term 'wasps' links to the insect, rather than identifying this term to mean White Anglo Saxon Protestants W.A.S.P

At around 1:10 p.m., Bryant paid the entry fee for the site and proceeded to park near the Broad Arrow Café, near the water's edge. The site security manager told him to park with the other cars because that area was reserved for camper-vans and the car park was busy that day. Bryant moved his car to another area and sat in his car for a few minutes. He then moved his car back near the water, outside the café. The security manager saw him go up to the café carrying a "sports-type bag" and a video camera, but ignored him. Bryant went into the café and purchased a meal, which he ate on the deck outside. He attempted to start conversations with people about the lack of wasps in the area and there not being as many Japanese tourists as usual. He appeared nervous and "quite regularly" looked back to the car-park and into the café.[1] 220.253.229.26 (talk) 20:41, 21 January 2022 (UTC)
 * ✅ ScottishFinnishRadish (talk) 20:51, 21 January 2022 (UTC)

Missing murder of the Martins
Reading the section titled "Attacks" I notice the only mention of the deaths of the Martins at their property was at the beginning of the article. Why are they not mentioned and why does the timeline start at the arrival of the couple to the Seascape? 47.151.213.85 (talk) 06:48, 27 September 2022 (UTC)

Requested move 27 November 2022

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: not moved. Favonian (talk) 14:45, 4 December 2022 (UTC)

Port Arthur massacre (Australia) → Port Arthur massacre (Tasmania) – per WP:NCAUST – as this is an Australian article, this article should use the relevant jurisdiction as its disambiguator. SHB2000 (talk) 12:00, 27 November 2022 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
 * Oppose This is a global encyclopaedia, with a global audience. There are two articles in Wikipedia about Port Arthur massacres, this one and Port Arthur massacre (China). They are disambiguated by use of their country names. That works fine, and would be clear to the vast majority of our readers. Changing Australia to Tasmania would actually be slightly less clear to our global audience, some of whom I know from experience sadly don't understand Tasmania's geopolitical relationship with the rest of Australia. The proposed change would be equivalent to changing the title of the other article to Port Arthur massacre (Liaoning), obviously not as useful a title to most readers. HiLo48 (talk) 22:53, 27 November 2022 (UTC)
 * What you and are claiming contradict the MoS page I linked. --SHB2000 (talk) 10:05, 29 November 2022 (UTC)
 * The policy you have linked clearly applies to disambiguation of geographic place names, not for disambiguation of events (who happen to have a location chosen as a distinguishing feature). It is clearly meant for articles like Madison, Wisconsin. Applying WP:NCAUST here is inappropriate, and if you are claiming that it should apply here, perhaps it would be a good idea to show that there is a consensus for treating such cases with the broader, geography-only policy that you have linked. Acebulf  (talk | contribs)  17:52, 29 November 2022 (UTC)
 * Oppose. Using the country rather that a subdivision for the parenthetical disambiguation is preferable. Rreagan007 (talk) 22:22, 28 November 2022 (UTC)
 * Oppose There is no need to disambiguate further than country-level distinction. HiLo48 also raises some strong arguments about discoverability, which favor keeping the title as-is. Acebulf  (talk | contribs)  03:57, 29 November 2022 (UTC)
 * Weak Oppose. Almost, but oppose for two reasons: (1) WP:TITLECHANGES. The difference is to small to be worth the costs, had’ve it been Tasmanian on creation I’d support leaving it, but it is not important enough to change title. (2) The significant impacts, consequences, legally and culturally, were nationwide, not statewide.  —SmokeyJoe (talk) 07:17, 30 November 2022 (UTC)
 * Comment The usual practice for labelling incidents whose monikers don't qualify for WP:NOYEAR is to use the year in the title, no? — Ceso femmuin mbolgaig mbung, mellohi! (投稿) 08:48, 4 December 2022 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 20:38, 22 March 2023 (UTC)
 * Broad Arrow Forensic Diagram.jpg

"Port Arthur massacre (Australia" listed at Redirects for discussion
The redirect [//en.wikipedia.org/w/index.php?title=Port_Arthur_massacre_(Australia&redirect=no Port Arthur massacre (Australia] 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  until a consensus is reached. Utopes (talk / cont) 01:00, 8 April 2024 (UTC)

title: Talk:Port Arthur massacre (Australia)


text:
Wikipedia talk:Explain jargon

Old talk
Supporters of this rule include: Larry Sanger, JerryMuelver, Tim Shell, Pinkunicorn, AyeSpy (fervently), Janet Davis, drj, GWO, tbc, AxelBoldt, Koyaanis Qatsi, Enchanter, Rotem Dan, Bensaccount Nu Aeon, Narkstraws

Discussion:

Of course jargon should be explained. Unfortunately, the technique suggested (making links to pages where unfamiliar terms would be explained) will inevitably result in the deletion of the explanation when it's moved to wiktionary as a "dictionary definition". -- Nunh-huh 21:04, 26 Mar 2004 (UTC)

Is there any other way? Bensaccount 21:39, 26 Mar 2004 (UTC)

 * Persuade people not to delete things from Wikipedia when they grab them for Wiktionary. - Nunh-huh 22:10, 26 Mar 2004 (UTC)
 * Rather: link to Wiktionary. Septentrionalis PMAnderson 14:13, 20 September 2008 (UTC)

 * -Shouldn't this be a no brainer? I would think that deleting any entry would be a negative. Nu Aeon

Opponents include: 24

24 - it sounds good, but really, you should be avoiding jargon in most articles - where it's impossible to avoid, of course, I support this rule. But remember, much jargon overlaps between fields and someone clicking down may well find that a "term of art" has become fuzzed out by many definitions. Imagine ontology, for instance, a branch of metaphysics, or a practice of knowledge representation? The article written for one will be incomprehensible to the person who is expecting the other.

Can this be modified to include trying to be reasonable about one's use of jargon? If I have to look up six words in the first sentence, and for half of them I have to look up another two words just to understand the explanations, I could end up reading twelve articles just to form a basic understanding of one sentence. The goal is to make communication easier, not more difficult. It's okay to use a specific technical term if it means exactly what you want it to mean, but if every other word has to be linked to an explanation, that's probably excessive. [[User:Aranel|Aranel ("Sarah")]] 21:20, 28 Sep 2004 (UTC)

I think you can have some common-sense expectations about the audience of particular articles. If someone is reading cell (biology), they well may not be aware of protein as anything but something-or-other that's in food. I haven't looked, but I'm confident the word protein is a link in that article. If they're reading CD133, they can reasonably be assumed to have a pretty good idea what a protein is. If I write an entry for CD133, I may not make the word protein a link. --dsws 19:11, 14 July 2005 (UTC)

Proposal to consolidate advice on writing better articles
At present there are many articles in the Wikipedia namespace that seek to give guidance on how to write better articles. I propose consolidating these into a much smaller number. On User:Jongarrettuk/Better writing guide I propose how these could be consolidated. The proposal is not to change advice, just to consolidate it. If I have inadvertently moved what you consider to be good advice that is currently in the Wikipedia namespace, please re-add it. I'm hope that the proposal to merge all these articles, in principle, will be welcomed. Of course, it may be preferred to have 2, 3 or 4 inter-connected articles than just one and would welcome advice on how this could be done. (In particular, perhaps all the guidance on layout should be spun off into one consolidated article on layout.) I'm also aware that putting lots of different bits of advice together may throw up anomalies or bits that people now disagree with (including bits that I myself disagree with:) ). I ask for support for the consolidation. Once the consolidation has happened, the advice can be changed in the normal way. Please feel free to improve on the current draft consolidation, but don't remove or add advice that is not currently on the Wikipedia namespace. If all goes well, I'll add a new Guide to writing better articles page on the 19th, though maybe some bits of the new article will need to be phased in over a longer period. I'll also take care to preserve all the archived discussion in one place. vjguk 19:44, 11 Nov 2004 (UTC)

Template
Is there a template which can be added to articles asking for an explanation of jargon? If not there should be.--naryathegreat | (talk) 05:02, Jun 15, 2005 (UTC)
 * I would say you should probably just raise the issue on the talk page. That kind of thing needs more specifics than, say, "wikify" does. --Dmcdevit 05:37, 15 Jun 2005 (UTC)

Yes, the template is known as Template:Technical. Add it a talk page using --DavidCary 07:13, 20 November 2005 (UTC)

Rule weakness
I think this rule needs to be changed to discourage editors from using wikilinks as an excuse not to explain jargon.

The current rule does the opposite. It seems to discourage defining terms in the text:

"You can simply make your jargon terms links to articles explaining them; you can then link to that same explanation from many places. Alternatively, you may introduce the jargon term the first time you use it; beware, though, that technical terms often have a very precise meaning and that short explanations of their meaning may introduce some inaccuracies."

There are two problems with simply wikilinking words rather than explaining them. The first is that it makes understanding an article a time-intensive procedure, since the reader has to look up all the different terms on the page.

The other problem is that the articles on the jargon words are often more difficult to understand than the original article. Take the article on lightning. It begins as follows:

"Lightning is a powerful natural electrostatic discharge produced during a thunderstorm. This abrupt electric discharge is accompanied by the emission of visible light and other forms of electromagnetic radiation. The electric current passing through the discharge channels rapidly heats and expands the air into plasma, producing acoustic shock waves (thunder) in the atmosphere."

Now, it's unlikely the average reader is going to know what electrostatic discharge or plasma is. But if the reader can't understand the lightning page, he or she certainly isn't going to understand the page on electrostatic discharge.

In this case, electrostatic discharge begins by saying "Electrostatic discharge (ESD) is the sudden and momentary electric current that flows when an excess of electric charge, stored on an electrically insulated object, finds a path to an object at a different electrical potential (such as ground)." The reader now has to click on electrical potential, which is the most-complicated article yet encountered, full of mathematical equations. And so on -- he or she could go on clicking all day without understanding the lightning article.

I believe wikilinks should be used to provide extra information on a topic if the reader chooses to seek it. They should not be used instead of defining terms the reader is unlikely to know.

I'm not saying every wikilinked term needs to be defined in the text. If it's a word the likely reader of the article probably knows, such as weather, it need not be defined (unless it's the weather article, of course). Also, if the reader does not need to understand the term to understand the article, and defining the term would be unwieldy, it could be excluded. For example, the article on Silesia says most of it was taken by Prussia in 1742 in the War of the Austrian Succession, but does not define that war. There is no need to say the war was a conflict between Prussia and allies on the one hand and Austria and allies on the other resulting from Maria Theresa's succession to the throne, because the reader does not need to know that to understand that Prussia took Silesia from Austria in 1742.

On the other hand, the reader of the lightning article does need to know what electrostatic discharge and plasma are in order to understand the opening paragraph. If I were to rewrite the lightning article, I would change "electrostatic discharge" to "discharge of static electricity," since most people know what static electricity is. I would also refrain from mentioning plasma until later in the article -- perhaps a "thunder" section -- when I would have room to explain that it is a form of matter in which atoms have been stripped of their electrons. (Or so I understand; I can't really understand the plasma article).

I think editors, when they write articles, should ask themselves whether the article can be understood by a likely reader without the wikilinks. If it can't be understood without the wikilinks, it should be improved to be easier to understand -- Mwalcoff 03:59, 16 May 2006 (UTC)
 * I fully agree, a reader only somewhat familiar with a topic should not be required to click through half a dozen wikilinks to get a basic understanding of what is being talked about. Another reason also is that if Wikipedia is put in print, the articles will not be understandable. —Centrx→talk • 03:32, 22 June 2006 (UTC)

 * Science and mathematics It makes sense to include terms like electrostatic discharge or plasma (the state of matter, of course), as science has developed a necessary jargon to discuss topics that are otherwise unintelligible. The thing that's really irritating is when neologisms are inserted into social studies articles or pop culture topics for no reason. Why can't you just put backwards acronym or compound word ? Is that so hard? For instance, I'm changing Thomas Jefferson from miscegenation to <nowikimarriage between blacks and whites, so people can click on the link and learn more if they want, but they aren't compelled because they're reading an unintelligible articel.  It's distracting and not helpful to the reader to include jargon where it is unnecessary (unlike, say, articles on quantum physics.) It also turns Wikipedia into Wiktionary, since people are constantly learning frivolous new terms. -[[User:Koavf|Justin (koavf)·T·C·M 01:29, 8 August 2006 (UTC)

 * There is absolutely nothing wrong with using terms like "plasma" or even "miscegenation." But they should be explained if some readers are likely not to know them. -- Mwalcoff 22:34, 13 September 2006 (UTC)

Merge
I think this should be merged with Technical terms and definitions and Make technical articles accessible.--Piotr Konieczny aka Prokonsul Piotrus 00:17, 29 July 2006 (UTC)
 * This page applies to any jargon, whereas those appear only to scientific and similar terms, with specific recommendations. This style guide is general and simple. Perhaps the recently added Mathematics section here should be merged into Technical terms and definitions. —Centrx→talk • 04:58, 30 July 2006 (UTC)

 * I've removed the merge tags because they've been there for nine months without further discussion. --Tony Sidaway 02:00, 30 April 2007 (UTC)

 * I agree with the merge suggestion. This is very confusing. -- Quiddity (talk) 18:01, 18 May 2008 (UTC)

Wikipedia jargon
Wikipedia has become somewhat bureaucratic, and more bureaucracy than is absolutely necessary is bad for the project. In particular, bureaucratic use of jargon excludes people who don't yet know it, because it makes quite simple discussions impossible to understand. It tends to create an artificial division between those who use the jargon because they're familiar with it, and those who tend to stay away from policy discussions because they seem to be written in some weird code (and they often are!)

I've been a regular Wikipedia editor now for two-and-a-half years, which in Wikipedia terms makes me something of a grizzled old-timer, but even I do not find it easy to navigate though policy discussions when they're bristling with capitalized gibberish such as BLP, BRD, CN, ANI. For a relative newcomer, this is a very serious and quite unnecessary hurdle to involvement in Wikipedia's processes. It tends to alienate often quite good Wikipedians from the decision-making process, and thus it tends to split the community in two.

I suggest that we add a section specifically about Wikipedia jargon. My suggested wording is as follows:

 * Wikipedia jargon
 * Avoid using Wikipedia jargon on Wikipedia. All policy documents have English names that relate to their content, and these names should always be used the first time they are mentioned in any discussion or talk page section.  For instance, don't write WP:BRD, write BOLD, revert, discuss cycle (WP:BRD), so that people scanning the page will understand what you're talking about.  Repeated use in a discussion may use the shortcut identifier (BRD) or the shortcut itself (WP:BRD).  It is best not to initiate a discussion about policy solely by referring to it by its shortcut.
 * Avoid using Wikipedia jargon on Wikipedia. All policy documents have English names that relate to their content, and these names should always be used the first time they are mentioned in any discussion or talk page section.  For instance, don't write WP:BRD, write BOLD, revert, discuss cycle (WP:BRD), so that people scanning the page will understand what you're talking about.  Repeated use in a discussion may use the shortcut identifier (BRD) or the shortcut itself (WP:BRD).  It is best not to initiate a discussion about policy solely by referring to it by its shortcut.

--Tony Sidaway 22:19, 28 April 2007 (UTC)
 * WP:GOOD WP:IDEA, WP:TONY. —Signed, your friendly neighborhood MessedRocker. 01:42, 30 April 2007 (UTC)
 * I agree. Too many new proceses have came up to know what everything is. V could be vandalism or verification, so we should be clear on what we are discussing. User:Zscout370 (Return Fire) 01:43, 30 April 2007 (UTC)
 * Too many edit conflicts for my message to be anything other than "I agree". Sean William  01:44, 30 April 2007 (UTC)

 * WP:CSN - Community Sanction Noticeboard or Crosby, Stills and Nash ?
 * Even worse, what about WP:3RR, a shortcut referring to a confusing and complicated policy. What new users knows what the 3 Revert Rule is, or what a Revert is, for that matter. We should be using broad, easy to understand terms such as WP:Edit War for 3RR, WP:Vandalism for Vandals and Vandalism, and we need to kill all ambiguous shortcuts. WP:V is confusing for experienced users, christ knows what it's like for newbies.

-- Nick  t  01:47, 30 April 2007 (UTC)

 * I'll take that as a loud "aye". Let's try whopping it into the policy. --Tony Sidaway 01:50, 30 April 2007 (UTC)

 * I don't know who suggested "wiki" is "wikipedia jargon", but the problem is just the opposite; there are too many people in the world who think that "wiki" refers to "wikipedia" when the reality is the other way around.
 * And on that topic -- wikipedia doesn't need 90% less acronyms for processes, it just needs 90% less processes. —Preceding unsigned comment added by 71.201.204.149 (talk) 07:43, 13 October 2008 (UTC)

Problem with this rule
My big problem with this rule is that it is completely open-ended. What criteria should an editor use to judge how much terminology to explain? What level of education should be assumed? What is or is not jargon depends entirely on who is doing the reading. At some point a technical article needs to assume a certain level of knowledge on the part of the reader or the text gets bogged down in pedantic explanation. — RJH (talk) 19:33, 31 May 2007 (UTC)

Not everyone likes this style
...but I prefer to be very terse in style guidelines. Since WP:Words to avoid linked to jargon rather than this page until today, I imported the stuff I thought people might have actually read at jargon, mixed it with what was on this page, and then pared away everything that I thought people already knew or could deduce. Feel free to rewrite or revert. - Dan Dank55 (send/receive) 03:34, 19 September 2008 (UTC)

 * The page had one paragraph devoted to WP-space. Style guidelines concern articles only, and the distinction is important because people mistakenly apply style guideline recommendations to WP-space and userspace all the time, so this material needs to find a new home: "Avoid using Wikipedia jargon on Wikipedia.  All policy documents have English names that relate to their content, and these names should always be used the first time they are mentioned in any discussion or talk page section.  For instance, don't write WP:BRD, write BOLD, revert, discuss cycle (WP:BRD), so that people scanning the page will understand what you're talking about.  Repeated use in a discussion may use the shortcut identifier (BRD) or the shortcut itself (WP:BRD).  It is best not to initiate a discussion about policy solely by referring to it by its shortcut." - Dan Dank55 (send/receive) 12:51, 19 September 2008 (UTC)
 * People who are looking for help with math units and symbols aren't going to come to this page, they'll be looking at the style guidelines pages WP:MOSNUM and/or the math MOS. I've proposed at WT:MOSNUM that we move this material there.  I don't think we can cover this with any justice with just a few sentences here.  Perhaps this would be better: "Mathematical units and symbols can be jargon; they should sometimes be avoided, written out in words, or explained and given pronunciation; see [proper section of WP:MOSNUM]." "Mathematical symbols can sometimes be jargon, to be avoided, written out in words, or explained and given pronunciation; see [proper section of WP:Manual of Style (mathematics)]."   Thoughts? - Dan Dank55 (send/receive) 14:01, 19 September 2008 (UTC)
 * Just what are "mathematical units"? As a mathematician, I don't know what that term means.  Obviously in some contexts mathematical terms and symbols need to get explained; in others they must necessarily be assumed.  That is a simple and obvious truism. Michael Hardy (talk) 02:21, 20 September 2008 (UTC)
 * How about that? - Dan Dank55 (send/receive) 02:24, 20 September 2008 (UTC)

Mathematics
This section gives the reader reason to doubt that the person who wrote it knows what the word "equation" means. I wonder if that person would consider the expression
 * $$ \int_0^1 \psi(x)\,dx$$
 * $$ \int_0^1 \psi(x)\,dx$$

to be an "equation". Michael Hardy (talk) 01:55, 20 September 2008 (UTC)

What to do with this page
[Sept's comment moved here...hope that's okay Sept!] It is fairly clear, in fact, that this page is an extreme opinion in the abstruseness discussion. It is rather old, and has not been modified or looked at recently; it would, taken literally, prohibit use of the mathematical senses of group, field, algebra, and probably class and set. It should be an essay, and warnings to consider avoiding technical terms, when feasible, inserted in useful places. Septentrionalis PMAnderson 03:56, 20 September 2008 (UTC)

 * I've been working on it for a couple days; let me know if it's getting better or worse. It's gotten shorter, and it might make sense for it to become a section in WP:Words to avoid.  On the other hand, there are some kinds of words and phrases, listed at WP:WORDS, that you don't want to have in article-space in front of any readership; I think it might help to distinguish these from words and phrases that make sense to some readers but not others, and function as jargon. - Dan Dank55 (send/receive) 04:31, 20 September 2008 (UTC)

 * Okay, I made the edit based on what I've heard so far. Feel free to revert.  I erred on the side of including material that was in this guideline and at jargon, which is the page WP:Words to avoid used to point to, but I aimed to delete all clearly redundant material, and also the sections that aren't getting wide support.  We could delete a few more sentences without any harm, probably, but let's take one step at a time. - Dan Dank55 (send/receive) 13:47, 20 September 2008 (UTC)
 * I've kicked it along a little further. A presumption that every article should define things is a bad idea. Septentrionalis PMAnderson 14:43, 20 September 2008 (UTC)
 * Great work, more soon. - Dan Dank55 (send/receive) 15:04, 20 September 2008 (UTC)

Removed sentence

 * Except for a very few technical and narrowly targeted articles, articles should use words whose meaning will be approximately the same for the casual reader as for the expert.

This sentence contains a reasonable thought, but this is bad guidance; unless half of mathematics is accounted a very few technical and narrowly targeted articles. If someone else can think what would be reasonable to say here, please do so. Septentrionalis PMAnderson 15:35, 20 September 2008 (UTC) ←Okay, you took out "misunderstand". I was hoping if we left that in, we wouldn't need a separate sentence covering the case where people understand the wrong thing. Would you prefer a separate sentence, or adding "misunderstand"? - Dan Dank55 (send/receive) 19:55, 21 September 2008 (UTC)
 * Right, that's a good point. I'm fine with just leaving the sentence out, if you prefer; people don't need to be told every little thing.  The point is clear enough.
 * You deleted the sentence on subject areas; I'm fine with that. I'm still happy I had that version in there, because if someone wants to revert, that gives them a version to revert to that is closer to what was there before.
 * How about this for cramming down 6 sentences (3 of mine, 3 of yours) into one? "If you retain jargon that the typical reader of that article might not understand or misunderstand, introduce the term with a short (but accurate) explanation, and link it if there is an explanatory article on Wikipedia, or perhaps on Wiktionary." - Dan Dank55 (send/receive) 19:36, 20 September 2008 (UTC)
 * That's not what I would advise. If there is a wikilink, we may not need the explanation. Septentrionalis PMAnderson 17:46, 21 September 2008 (UTC)
 * I'm not sure what you're saying. Could you make a change to that sentence that reflects what you want? - Dan Dank55 (send/receive) 18:50, 21 September 2008 (UTC)
 * If you retain terms that the typical reader of that article might not understand, explain the term briefly or link it if there is an explanatory article on Wikipedia, or on Wiktionary if they explain enough to make the distinction clear. The substantive change is the bolded or; we don't want articles filled with explanations; although your introduction typical will prevent the worst exaggerations. Septentrionalis PMAnderson 19:24, 21 September 2008 (UTC)
 * Isn't misunderstanding a form of not understanding? Do we need to say both, at the cost of cluttering the sentence? Try reading your draft cold, and see what it looks like. Septentrionalis PMAnderson 02:11, 22 September 2008 (UTC)

 * I'm assuming "they have other resources, not vulnerable to vandalism." is intended as humor. "Those who do not know the subject should still be able to read the Wikipedia article." is okay, but can't that be deduced from the rest of it? - Dan Dank55 (send/receive) 19:55, 20 September 2008 (UTC)
 * No, it was quite serious, even though it alliterates. At any given time, some of the statements in WP will be the jokes of bored middle-school students; which ones will change. This is one reason why scholars will never rely on us - and why, therefore, we need not use the jargon their sources do. (But it is a purple patch, so I won't revert.)
 * Shading towards ultraviolet. And, I never rely on Wikipedia.  I use Wikipedia to find sources that I rely on.  Wait, I take that back; I've gotten to know the habits of a lot of the editors well enough that I'll rely on something if I see it's their work. - Dan Dank55 (send/receive) 18:52, 21 September 2008 (UTC)

Generally I leave people's stuff alone if it seems good enough to do the job, but a major goal of mine is to get the WIAGA pages just as short and tight as possible. Does this get everything into the first section that you're looking for? "Some articles may never become accessible to a wide readership, but most articles using academic or professional jargon should contain more explanation at a more basic level than would be available in the typical academic paper or textbook. On the other hand, an article which defines every term, or every symbol, may not be readable by anybody. It is often helpful to  wikilink terms not obvious to most readers; sometimes links to Wiktionary may serve the reader as well as links to other Wikipedia articles.  Pay particular attention to terms having meanings different from the common meaning." - Dan Dank55 (send/receive) 03:22, 22 September 2008 (UTC)
 * done (with a couple of tweaks). Septentrionalis PMAnderson 15:58, 22 September 2008 (UTC)

Next cut

 * ''Encyclopedias should either restate these terms in words that will be understood by as wide a readership as possible, or explain the terms at their first occurrence if the terms themselves are notable and relevant.

Do we need this? It is largely subsumed into the text just introduced; it's measurably stronger, but I'm not sure I agree with the strengthening. Septentrionalis PMAnderson 16:04, 22 September 2008 (UTC)
 * Really nice. I did a minor copyedit that I don't think changed the meanings. - Dan Dank55 (send/receive) 16:51, 22 September 2008 (UTC)

Keeping an eye on edits
As style guidelines pages get better, people start reading them more and adding things. If you see something you do or don't like, please speak up; if I see comments from a couple of people whose work I'm familiar with, I probably won't bother to check it myself.

Today's edit by 68.0.124.33, adding a see-also link to a section of WP:BETTER, looks great to me. - Dan Dank55 (send/receive)

Just passing this along
I had to give a quick summary of this page over at WT:ACCESS. This was what came to mind; does this sound right?
 * When a "term" (word, phrase, abbreviation, symbol, etc.) isn't understood by a significant number of readers, or differently by different readers, then usually, either define it in the text or replace it with a term everyone will understand. If you keep it, wikilink the first occurrence.  (The exceptions are in articles that aren't going to be understood by everyone no matter how hard you try ... defining every term would clutter the text.)

- Dan Dank55 (send/receive) 17:45, 29 September 2008 (UTC)

1037C terms
I reverted. I'm not opposed to including more detail on some page (although this kind of detail probably belongs in one of the pages linked at See also instead of here), but first, I'd like to see an explanation of why this old list of US government technical terms is superior to general and specialized dictionaries, and why we should mention lists from the US and not from other countries, and why the implication that we prefer some terms over others belongs in a WP:GA? guideline. - Dan Dank55 (send/receive) 13:46, 31 October 2008 (UTC)

Dictionary
A dictionary would be a good thing. It is inevitable that a jargon is developing as a means to express efficiently: it is in the human nature. However, the rule to avoid jargon is a good one, unless we wish to scare away new editors, so a dictionary could be used by:
 * 1) jargony editors who wish to make themselves understood and therefore wish to learn a common language translation,
 * 2) newbies who need (they should be encouraged) to correct the language of too-jargony editors. F.ex. despite being a long-timer, it wasn't until last thursday that I realized that "speedy keep" is a technical term, not a pun.
 * 3) link entries to use when WP:jargon is unavoidable, f.ex. speedy keep ... said: Rursus (bork²) 11:03, 8 February 2009 (UTC)
 * WP:Glossary, WP:SELFREF and of course Wiktionary might be relevant. - Dan Dank55 (push to talk) 17:47, 8 February 2009 (UTC)
 * WP:Glossary was what I was out for! Thanks. ... said: Rursus (bork²) 19:08, 1 March 2009 (UTC)

Defenitions
As a animal editor I sometimes run aground on this rule. At what point is a word "jargon"? Example, in Featured article candidates/Ruff/archive1 an editor objected to the term "wintering ground" in the context of annual migration as jargon. At what point do we start writing all these articles in simple English? Sabine's Sunbird  talk  06:04, 1 July 2009 (UTC)

Explain & link
Should there be internal links to terms and expinations of their meanings in articles? Hyacinth (talk) 18:20, 1 August 2009 (UTC)

What does Jargon mean?
I thought this article was supposed to "explain jargon" but I still don't know what jargon means. 174.18.15.106 (talk) 04:39, 13 August 2009 (UTC)

Consolidation?
Please note that this page has been nominated to be consolidated with the primary Manual of Style page. Please join the discussion at the MOS talk page in order to discus the possibility of merging this page with the MOS. Thank you. — V = IR (Talk • Contribs) 15:21, 27 March 2010 (UTC)

To follow Ohms's point here, I've scrutinised the page as part of the WP Styleguide Taskforce audit program. I wonder whether any editor would mind discussing what is substantive in this page; I do believe it's message(s) could easily be added in a few sentences to the main MoS page instead of standing alone on this one. Please let us know what you think. Tony  (talk)  10:38, 1 April 2010 (UTC)
 * Please provide your few sentences here so I can review Gnevin (talk) 12:11, 1 April 2010 (UTC)
 * Well, I'm not sure this statement is useful, since it seems to have a bet each way: "most articles using academic or professional terms should contain more explanation at a more basic level than would be available in the typical academic paper or textbook. On the other hand, an article that defines every term, or every symbol, may be so cluttered that no one can read it." It doesn't really give editors much to go by in terms of knowing the balance. You'd hope that that balance would work itself out in the normal collaborative environment.
 * The stuff about wikilinking is already at WP:LINK, and Wiktionary is also mentioned elsewhere in the style guides.
 * The point about mathematical symbols is at MOS (mathematics).

Gnevin, I think a few summary sentences at MoS main could be written that encompass the messages at "Avoid jargon" and "Make technical articles accessible. What about this, under its own subsection in the "Miscellaneous" section?

"While some topics are intrinsically technical, editors should take every opportunity to make them accessible to an audience wider than the specialists in the field, and to a general audience where possible. Technical Technical words and phrases and jargon should be either avoided or explained. Cleanup-jargon or Jargon-statement can be used to tag articles with jargon problems."

There could be a link to what would then be an essay, "Make technical articles accessible", although I've suggested on the talk page at MTAA that it would be a good idea to tweak or remove a few of the points, whatever its status becomes. Tony  (talk)  13:11, 1 April 2010 (UTC)

 * Do we get a Guide to the Jargon used in the "Guide to Jargon"? Very little of this makes any sense  --Jubilee♫ clipman  15:44, 1 April 2010 (UTC)

When I posted above I thought I was at WP:Technical terms and definitions. I agree this should be merged WP:Make_technical_articles_accessible in fact I'm going to be bold Gnevin (talk) 17:38, 1 April 2010 (UTC)

Revisit
I need this page! And the redirect is an essay, not really what I need. I am going to be (equally) bold and redirect this to WP:NOTTEXTBOOK. Forgive me. CharlesGillingham (talk) 18:44, 2 November 2010 (UTC)

 * That kinda screws up attribution though.. cuz the content from this page was merged to WP:Make_technical_articles_accessible so technically the redirect should point to where it was merged. -- œ ™ 21:25, 2 November 2010 (UTC)

 * I have two problems with that. (1) The information on "jargon" (i.e., technical language) is buried in that essay. (I've done a little work over there to "unbury" it.) (2) It's been downgraded from a guideline to an essay, so WP:JARGON doesn't have the same force any more, even though it's still a part of the manual of style. So how about this? I'm redirecting it to "Technical language" in the MOS. There's a "see also" link which leads directly back to this article. Sound good? CharlesGillingham (talk) 18:09, 3 November 2010 (UTC)

 * Yup! -- œ ™ 15:13, 4 November 2010 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Wikipedia talk:Explain jargon


text:
Pascal's triangle

In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, India, China, Germany, and Italy.

The rows of Pascal's triangle are conventionally enumerated starting with row $$n = 0$$ at the top (the 0th row). The entries in each row are numbered from the left beginning with $$k = 0$$ and are usually staggered relative to the numbers in the adjacent rows. The triangle may be constructed in the following manner: In row 0 (the topmost row), there is a unique nonzero entry 1. Each entry of each subsequent row is constructed by adding the number above and to the left with the number above and to the right, treating blank entries as 0. For example, the initial number of row 1 (or any other row) is 1 (the sum of 0 and 1), whereas the numbers 1 and 3 in row 3 are added to produce the number 4 in row 4.

Formula
In the $$n$$th row of Pascal's triangle, the $$k$$th entry is denoted $$\tbinom nk$$, pronounced "$n$ choose $k$". For example, the topmost entry is $$\tbinom 00 = 1$$. With this notation, the construction of the previous paragraph may be written as $$ {n \choose k} = {n-1 \choose k-1} + {n-1 \choose k}$$ for any positive integer $$n$$ and any integer $$0 \le k \le n$$. This recurrence for the binomial coefficients is known as Pascal's rule.

History

The pattern of numbers that forms Pascal's triangle was known well before Pascal's time. The Persian mathematician Al-Karaji (953–1029) wrote a now-lost book which contained the first formulation of the binomial coefficients and the first description of Pascal's triangle. It was later repeated by Omar Khayyám (1048–1131), another Persian mathematician; thus the triangle is also referred to as Khayyam's triangle in Iran. Several theorems related to the triangle were known, including the binomial theorem. Khayyam used a method of finding nth roots based on the binomial expansion, and therefore on the binomial coefficients.

Pascal's triangle was known in China during the early 11th century through the work of the Chinese mathematician Jia Xian (1010–1070). During the 13th century, Yang Hui (1238–1298) defined the triangle, and it is known as Yang Hui's triangle in China.

In Europe, Pascal's triangle appeared for the first time in the Arithmetic of Jordanus de Nemore (13th century). The binomial coefficients were calculated by Gersonides during the early 14th century, using the multiplicative formula for them. Petrus Apianus (1495–1552) published the full triangle on the frontispiece of his book on business calculations in 1527. Michael Stifel published a portion of the triangle (from the second to the middle column in each row) in 1544, describing it as a table of figurate numbers. In Italy, Pascal's triangle is referred to as Tartaglia's triangle, named for the Italian algebraist Niccolò Fontana Tartaglia (1500–1577), who published six rows of the triangle in 1556. Gerolamo Cardano also published the triangle as well as the additive and multiplicative rules for constructing it in 1570.

Pascal's Traité du triangle arithmétique (Treatise on Arithmetical Triangle) was published posthumously in 1665. In this, Pascal collected several results then known about the triangle, and employed them to solve problems in probability theory. The triangle was later named for Pascal by Pierre Raymond de Montmort (1708) who called it table de M. Pascal pour les combinaisons (French: Mr. Pascal's table for combinations) and Abraham de Moivre (1730) who called it Triangulum Arithmeticum PASCALIANUM (Latin: Pascal's Arithmetic Triangle), which became the basis of the modern Western name.

Binomial expansions

Pascal's triangle determines the coefficients which arise in binomial expansions. For example, in the expansion $$(x + y)^2 = x^2 + 2xy + y^2 = \mathbf{1} x^2 y^0 + \mathbf{2} x^1 y^1 + \mathbf{1} x^0 y^2,$$ the coefficients are the entries in the second row of Pascal's triangle: $$\tbinom 20 = 1$$, $$\tbinom 21 = 2$$, $$\tbinom 22 = 1$$.

In general, the binomial theorem states that when a binomial like $$x + y$$ is raised to a positive integer power $$n$$, the expression expands as $$(x + y)^n = \sum_{k=0}^{n} a_{k} x^{n-k} y^{k} = a_{0} x^n + a_{1} x^{n - 1} y + a_{2} x^{n - 2} y^{2} + \ldots + a_{n - 1} x y^{n-1} + a_{n} y^{n}, $$ where the coefficients $$a_{k} $$ are precisely the numbers in row $$n $$ of Pascal's triangle: $$a_k = {n \choose k}.$$

The entire left diagonal of Pascal's triangle corresponds to the coefficient of $$x^n $$ in these binomial expansions, while the next left diagonal corresponds to the coefficient of $$x^{n-1} y $$, and so on.

To see how the binomial theorem relates to the simple construction of Pascal's triangle, consider the problem of calculating the coefficients of the expansion of $$(x + y)^{n + 1} $$ in terms of the corresponding coefficients of $$(x + 1)^{n} $$, where we sett $$y = 1 $$ for simplicity. Suppose then that $$ (x + 1)^{n} = \sum_{k = 0}^{n} a_{k} x^{k}. $$ Now $$ (x+1)^{n+1} = (x+1)(x+1)^n = x(x+1)^n + (x+1)^n = \sum_{i=0}^n a_i x^{i+1} + \sum_{k=0}^n a_k x^k.$$

The two summations can be reindexed with $$k=i+1 $$ and combined to yield $$ \begin{align} \sum_{i=0}^{n} a_{i} x^{i+1} + \sum_{k=0}^n a_k x^k &= \sum_{k=1}^{n+1} a_{k-1} x^{k} + \sum_{k=0}^n a_k x^k \\ [4pt] &= \sum_{k=1}^{n} a_{k-1} x^{k} + a_{n}x^{n+1} + a_0x^0 + \sum_{k=1}^n a_k x^k \\[4pt] &= a_0x^0 + \sum_{k=1}^{n} (a_{k-1} + a_k)x^{k} + a_{n}x^{n+1} \\[4pt] &= x^0 + \sum_{k=1}^{n} (a_{k-1} + a_k)x^{k} + x^{n+1}. \end{align} $$

Thus the extreme left and right coefficients remain as 1, and for any given $$0 < k < n + 1 $$, the coefficient of the $$x^{k} $$ term in the polynomial $$(x + 1)^{n + 1} $$ is equal to $$a_{k-1} + a_{k} $$, the sum of the $$x^{k-1} $$ and $$x^{k} $$ coefficients in the previous power $$(x + 1)^n $$. This is indeed the downward-addition rule for constructing Pascal's triangle.

It is not difficult to turn this argument into a proof (by mathematical induction) of the binomial theorem.

Since $$(a + b)^{n} = b^{n}(\tfrac{a}{b} + 1 )^{n} $$, the coefficients are identical in the expansion of the general case.

An interesting consequence of the binomial theorem is obtained by setting both variables $$x = y = 1 $$, so that $$ \sum_{k = 0}^{n} {n \choose k} = {n \choose 0} + {n \choose 1} + \cdots + {n \choose n-1} + {n \choose n} = (1+1)^n = 2^{n}. $$

In other words, the sum of the entries in the $$n$$th row of Pascal's triangle is the $$n$$th power of 2. This is equivalent to the statement that the number of subsets of an $$n$$-element set is $$2^n$$, as can be seen by observing that each of the $$n$$ elements may be independently included or excluded from a given subset.

Combinations
A second useful application of Pascal's triangle is in the calculation of combinations. The number of combinations of $$n$$ items taken $$k$$ at a time, i.e. the number of subsets of $$k$$ elements from among $$n$$ elements, can be found by the equation

 * $$ \mathbf{C}(n, k) = \mathbf{C}_{k}^{n}= {_{n}C_{k}} = {n \choose k} = \frac{n!}{k!(n-k)!}$$.

This is equal to entry $$k$$ in row of $$n$$ Pascal's triangle. Rather than performing the multiplicative calculation, one can simply look up the appropriate entry in the triangle (constructed by additions). For example, suppose 3 workers need to be hired from among 7 candidates; then the number of possible hiring choices is 7 choose 3, the entry 3 in row 7 of the above table, which is $$ \tbinom{7}{3}=35 $$.

Relation to binomial distribution and convolutions
When divided by $$ 2^n$$, the $$ n$$th row of Pascal's triangle becomes the binomial distribution in the symmetric case where $$ p = \tfrac{1}{2}$$. By the central limit theorem, this distribution approaches the normal distribution as $$ n$$ increases. This can also be seen by applying Stirling's formula to the factorials involved in the formula for combinations.

This is related to the operation of discrete convolution in two ways. First, polynomial multiplication corresponds exactly to discrete convolution, so that repeatedly convolving the sequence $$ \{ \ldots, 0, 0, 1, 1, 0, 0, \ldots \}$$ with itself corresponds to taking powers of $$ x + 1$$, and hence to generating the rows of the triangle. Second, repeatedly convolving the distribution function for a random variable with itself corresponds to calculating the distribution function for a sum of n independent copies of that variable; this is exactly the situation to which the central limit theorem applies, and hence results in the normal distribution in the limit. (The operation of repeatedly taking a convolution of something with itself is called the convolution power.)

Patterns and properties
Pascal's triangle has many properties and contains many patterns of numbers.

Rows
\frac{ \displaystyle (n+1)!^{n+2} \prod_{k = 0}^{n + 1} \frac{1}{k!^2}}{\displaystyle n!^{n+1}\prod_{k=0}^{n}{\frac{1}{k!^2}}} = \frac{(n + 1)^n}{n!}$$ and the ratio of these ratios is $$\frac{s_{n + 1} \cdot s_{n - 1}}{s_{n}^{2}} = \left( \frac{n + 1}{n} \right)^n, ~ n\ge 1.$$ The right-hand side of the above equation takes the form of the limit definition of $e$ $$e =\lim_{n \to \infty} \left( 1 + \frac{1}{n} \right)^{n}$$.
 * The sum of the elements of a single row is twice the sum of the row preceding it. For example, row 0 (the topmost row) has a value of 1, row 1 has a value of 2, row 2 has a value of 4, and so forth. This is because every item in a row produces two items in the next row: one left and one right. The sum of the elements of row $$ n$$ equals to $$ 2^n$$.
 * Taking the product of the elements in each row, the sequence of products is related to the base of the natural logarithm, e.  Specifically, define the sequence $$ s_{n}$$  for all  $$n \ge 0$$ as follows: $$s_{n} = \prod_{k = 0}^{n} {n \choose k} = \prod_{k = 0}^{n} \frac{n!}{k!(n-k)!}$$  Then, the ratio of successive row products is $$\frac{s_{n+1}}{s_{n}} =
 * $\pi$ can be found in Pascal's triangle by use of the Nilakantha infinite series. $$\pi = 3 + \sum_{n = 1}^{\infty} (-1)^{n + 1} \frac$$
 * Some of the numbers in Pascal's triangle correlate to numbers in Lozanić's triangle.
 * The sum of the squares of the elements of row $n$ equals the middle element of row $2n$. For example, $1^{2} + 4^{2} + 6^{2} + 4^{2} + 1^{2} = 70$. In general form, $$\sum_{k=0}^n {n \choose k}^2 = {2n \choose n}.$$
 * In any even row $$n=2m$$, the middle term minus the term two spots to the left equals a Catalan number, specifically $$C_{m-1} = \tbinom{2m}{m} - \tbinom{2m}{m-2}$$. For example, in row 4, which is 1, 4, 6, 4, 1, we get the 3rd Catalan number $$C_3 = 6-1 = 5 $$.
 * In a row $p$, where $p$ is a prime number, all the terms in that row except the 1s are divisible by $p$. This can be proven easily, from the multiplicative formula $$\tbinom pk = \tfrac{p!}{k!(p-k)!} $$. Since the denominator $$p!(p-k)!$$ can have no prime factors equal to $p$, so $p$ remains in the numerator after integer division, making the entire entry a multiple of $p$.
 * Parity: To count odd terms in row $n$, convert $n$ to binary. Let $x$ be the number of 1s in the binary representation. Then the number of odd terms will be $2^{x}$. These numbers are the values in Gould's sequence.
 * Every entry in row 2n − 1, n ≥ 0, is odd.
 * Polarity: When the elements of a row of Pascal's triangle are alternately added and subtracted together, the result is 0. For example, row 6 is 1, 6, 15, 20, 15, 6, 1, so the formula is 1 − 6 + 15 − 20 + 15 − 6 + 1 = 0.

Diagonals
The diagonals of Pascal's triangle contain the figurate numbers of simplices:
 * The diagonals going along the left and right edges contain only 1's.
 * The diagonals next to the edge diagonals contain the natural numbers in order. The 1-dimensional simplex numbers increment by 1 as the line segments extend to the next whole number along the number line.
 * Moving inwards, the next pair of diagonals contain the triangular numbers in order.
 * The next pair of diagonals contain the tetrahedral numbers in order, and the next pair give pentatope numbers.

 * $$\begin{align}

P_0(n) &= P_d(0) = 1, \\ P_d(n) &= P_d(n-1) + P_{d-1}(n) \\ &= \sum_{i=0}^n P_{d-1}(i) = \sum_{i=0}^d P_i(n-1). \end{align}$$

The symmetry of the triangle implies that the nth d-dimensional number is equal to the dth n-dimensional number.

An alternative formula that does not involve recursion is $$P_d(n)=\frac{1}{d!}\prod_{k=0}^{d-1} (n+k) = {n^{(d)}\over d!} = \binom{n+d-1}{d},$$ where n(d) is the rising factorial.

The geometric meaning of a function Pd is: Pd(1) = 1 for all d. Construct a d-dimensional triangle (a 3-dimensional triangle is a tetrahedron) by placing additional dots below an initial dot, corresponding to Pd(1) = 1. Place these dots in a manner analogous to the placement of numbers in Pascal's triangle. To find Pd(x), have a total of x dots composing the target shape. Pd(x) then equals the total number of dots in the shape. A 0-dimensional triangle is a point and a 1-dimensional triangle is simply a line, and therefore P0(x) = 1 and P1(x) = x, which is the sequence of natural numbers. The number of dots in each layer corresponds to Pd − 1(x).

Calculating a row or diagonal by itself
There are simple algorithms to compute all the elements in a row or diagonal without computing other elements or factorials.

To compute row $$n$$ with the elements $$\tbinom{n}{0}, \tbinom{n}{1}, \ldots, \tbinom{n}{n}$$, begin with $$\tbinom{n}{0}=1$$. For each subsequent element, the value is determined by multiplying the previous value by a fraction with slowly changing numerator and denominator:

 * $$ {n\choose k}= {n\choose k-1}\times \frac{n+1-k}{k}.$$

For example, to calculate row 5, the fractions are $$\tfrac{5}{1}$$,  $$\tfrac{4}{2}$$,  $$\tfrac{3}{3}$$,  $$\tfrac{2}{4}$$ and $$\tfrac{1}{5}$$, and hence the elements are  $$\tbinom{5}{0}=1$$,   $$\tbinom{5}{1}=1\times\tfrac{5}{1}=5$$,   $$\tbinom{5}{2}=5\times\tfrac{4}{2}=10$$, etc. (The remaining elements are most easily obtained by symmetry.)

To compute the diagonal containing the elements $$\tbinom{n}{0}, \tbinom{n+1}{1}, \tbinom{n+2}{2},\ldots,$$ begin again with $$\tbinom{n}{0} = 1$$ and obtain subsequent elements by multiplication by certain fractions:

 * $$ {n+k\choose k}= {n+k-1\choose k-1}\times \frac{n+k}{k}.$$

For example, to calculate the diagonal beginning at $$\tbinom{5}{0}$$, the fractions are $$\tfrac{6}{1}, \tfrac{7}{2}, \tfrac{8}{3}, \ldots$$, and the elements are $$\tbinom{5}{0}=1, \tbinom{6}{1}=1 \times \tfrac{6}{1}=6, \tbinom{7}{2}=6\times\tfrac{7}{2}=21$$, etc. By symmetry, these elements are equal to $$\tbinom{5}{5}, \tbinom{6}{5}, \tbinom{7}{5}$$, etc.

Overall patterns and properties

 * The pattern obtained by coloring only the odd numbers in Pascal's triangle closely resembles the fractal known as the Sierpinski triangle. This resemblance becomes increasingly accurate as more rows are considered; in the limit, as the number of rows approaches infinity, the resulting pattern is the Sierpinski triangle, assuming a fixed perimeter. More generally, numbers could be colored differently according to whether or not they are multiples of 3, 4, etc.; this results in other similar patterns.
 * As the proportion of black numbers tends to zero with increasing n, a corollary is that the proportion of odd binomial coefficients tends to zero as n tends to infinity.

Pascal's triangle overlaid on a grid gives the number of distinct paths to each square, assuming only rightward and downward movements are considered.

 * In a triangular portion of a grid (as in the images below), the number of shortest grid paths from a given node to the top node of the triangle is the corresponding entry in Pascal's triangle. On a Plinko game board shaped like a triangle, this distribution should give the probabilities of winning the various prizes.

 * If the rows of Pascal's triangle are left-justified, the diagonal bands (colour-coded below) sum to the Fibonacci numbers.
 * {| style="align:center;"

 * - align=center
 * bgcolor=red|1
 * - align=center
 * style="background:orange;"|1
 * style="background:yellow;"|1
 * - align=center
 * style="background:yellow;"|1
 * bgcolor=lime|2
 * bgcolor=aqua|1
 * - align=center
 * bgcolor=lime|1
 * bgcolor=aqua|3
 * style="background:violet;"|3
 * bgcolor=red|1
 * - align=center
 * bgcolor=aqua|1
 * style="background:violet;"|4
 * bgcolor=red|6
 * style="background:orange;"|4
 * style="background:yellow;"|1
 * - align=center
 * style="background:violet;"|1
 * bgcolor=red|5
 * style="background:orange;"|10
 * style="background:yellow;"|10
 * bgcolor=lime|5
 * bgcolor=aqua|1
 * - align=center
 * bgcolor=red|1
 * style="background:orange;"|6
 * style="background:yellow;"|15
 * bgcolor=lime|20
 * bgcolor=aqua|15
 * style="background:violet;"|6
 * bgcolor=red|1
 * - align=center
 * style="background:orange; width:40px;"|1
 * style="background:yellow; width:40px;"|7
 * style="background:lime; width:40px;"|21
 * style="background:aqua; width:40px;"|35
 * style="background:violet; width:40px;"|35
 * style="background:red; width:40px;"|21
 * style="background:orange; width:40px;"|7
 * style="background:yellow; width:40px;"|1
 * }

Construction as matrix exponential
Due to its simple construction by factorials, a very basic representation of Pascal's triangle in terms of the matrix exponential can be given: Pascal's triangle is the exponential of the matrix which has the sequence 1, 2, 3, 4, ... on its subdiagonal and zero everywhere else.

Construction of Clifford algebra using simplices
Labelling the elements of each n-simplex matches the basis elements of Clifford algebra used as forms in Geometric Algebra rather than matrices. Recognising the geometric operations, such as rotations, allows the algebra operations to be discovered. Just as each row, $n$, starting at 0, of Pascal's triangle corresponds to an $(n-1)$-simplex, as described below, it also defines the number of named basis forms in $n$ dimensional Geometric algebra. The binomial theorem can be used to prove the geometric relationship provided by Pascal's triangle. This same proof could be applied to simplices except that the first column of all 1's must be ignored whereas in the algebra these correspond to the real numbers, $$\R$$, with basis 1.

Relation to geometry of polytopes
Pascal's triangle can be used as a lookup table for the number of elements (such as edges and corners) within a polytope (such as a triangle, a tetrahedron, a square, or a cube).

Number of elements of simplices
Let's begin by considering the 3rd line of Pascal's triangle, with values 1, 3, 3, 1. A 2-dimensional triangle has one 2-dimensional element (itself), three 1-dimensional elements (lines, or edges), and three 0-dimensional elements (vertices, or corners). The meaning of the final number (1) is more difficult to explain (but see below). Continuing with our example, a tetrahedron has one 3-dimensional element (itself), four 2-dimensional elements (faces), six 1-dimensional elements (edges), and four 0-dimensional elements (vertices). Adding the final 1 again, these values correspond to the 4th row of the triangle (1, 4, 6, 4, 1). Line 1 corresponds to a point, and Line 2 corresponds to a line segment (dyad). This pattern continues to arbitrarily high-dimensioned hyper-tetrahedrons (known as simplices).

To understand why this pattern exists, one must first understand that the process of building an n-simplex from an $(n − 1)$-simplex consists of simply adding a new vertex to the latter, positioned such that this new vertex lies outside of the space of the original simplex, and connecting it to all original vertices. As an example, consider the case of building a tetrahedron from a triangle, the latter of whose elements are enumerated by row 3 of Pascal's triangle: 1 face, 3 edges, and 3 vertices. To build a tetrahedron from a triangle, position a new vertex above the plane of the triangle and connect this vertex to all three vertices of the original triangle.

The number of a given dimensional element in the tetrahedron is now the sum of two numbers: first the number of that element found in the original triangle, plus the number of new elements, each of which is built upon elements of one fewer dimension from the original triangle. Thus, in the tetrahedron, the number of cells (polyhedral elements) is $0 + 1 = 1$; the number of faces is $1 + 3 = 4;$ the number of edges is $3 + 3 = 6;$ the number of new vertices is $3 + 1 = 4$. This process of summing the number of elements of a given dimension to those of one fewer dimension to arrive at the number of the former found in the next higher simplex is equivalent to the process of summing two adjacent numbers in a row of Pascal's triangle to yield the number below. Thus, the meaning of the final number (1) in a row of Pascal's triangle becomes understood as representing the new vertex that is to be added to the simplex represented by that row to yield the next higher simplex represented by the next row. This new vertex is joined to every element in the original simplex to yield a new element of one higher dimension in the new simplex, and this is the origin of the pattern found to be identical to that seen in Pascal's triangle.

Number of elements of hypercubes
A similar pattern is observed relating to squares, as opposed to triangles. To find the pattern, one must construct an analog to Pascal's triangle, whose entries are the coefficients of $(x + 2)^{row number}$, instead of $(x + 1)^{row number}$. There are a couple ways to do this. The simpler is to begin with row 0 = 1 and row 1 = 1, 2. Proceed to construct the analog triangles according to the following rule:

 * $$ {n \choose k} = 2\times{n-1 \choose k-1} + {n-1 \choose k}.$$

That is, choose a pair of numbers according to the rules of Pascal's triangle, but double the one on the left before adding. This results in:
 * $$\begin{matrix}

\text{ 1} \\ \text{ 1}   \quad \text{  2} \\ \text{ 1}   \quad \text{  4}   \quad \text{  4} \\ \text{ 1}   \quad\text{  6}   \quad   \text{ 12}   \quad\text{  8} \\ \text{ 1}   \quad\text{  8}   \quad   \text{ 24}   \quad  \text{ 32}   \quad  \text{ 16} \\ \text{ 1}   \quad   \text{ 10}   \quad  \text{ 40}   \quad  \text{ 80}   \quad  \text{ 80}    \quad  \text{ 32} \\ \text{ 1}   \quad  \text{ 12}   \quad  \text{ 60}   \quad  160   \quad 240  \quad  192   \quad   \text{ 64} \\ \text{ 1}   \quad  \text{ 14}   \quad  \text{ 84}   \quad  280  \quad  560  \quad  672   \quad  448   \quad   128 \end{matrix}$$ The other way of producing this triangle is to start with Pascal's triangle and multiply each entry by 2k, where k is the position in the row of the given number. For example, the 2nd value in row 4 of Pascal's triangle is 6 (the slope of 1s corresponds to the zeroth entry in each row). To get the value that resides in the corresponding position in the analog triangle, multiply 6 by $2^{position number} = 6 × 2^{2} = 6 × 4 = 24$. Now that the analog triangle has been constructed, the number of elements of any dimension that compose an arbitrarily dimensioned cube (called a hypercube) can be read from the table in a way analogous to Pascal's triangle. For example, the number of 2-dimensional elements in a 2-dimensional cube (a square) is one, the number of 1-dimensional elements (sides, or lines) is 4, and the number of 0-dimensional elements (points, or vertices) is 4. This matches the 2nd row of the table (1, 4, 4). A cube has 1 cube, 6 faces, 12 edges, and 8 vertices, which corresponds to the next line of the analog triangle (1, 6, 12, 8). This pattern continues indefinitely.

To understand why this pattern exists, first recognize that the construction of an n-cube from an $(n − 1)$-cube is done by simply duplicating the original figure and displacing it some distance (for a regular n-cube, the edge length) orthogonal to the space of the original figure, then connecting each vertex of the new figure to its corresponding vertex of the original. This initial duplication process is the reason why, to enumerate the dimensional elements of an n-cube, one must double the first of a pair of numbers in a row of this analog of Pascal's triangle before summing to yield the number below. The initial doubling thus yields the number of "original" elements to be found in the next higher n-cube and, as before, new elements are built upon those of one fewer dimension (edges upon vertices, faces upon edges, etc.). Again, the last number of a row represents the number of new vertices to be added to generate the next higher n-cube.

In this triangle, the sum of the elements of row m is equal to 3m. Again, to use the elements of row 4 as an example: $1 + 8 + 24 + 32 + 16 = 81$, which is equal to $$3^4 = 81$$.

Counting vertices in a cube by distance
Each row of Pascal's triangle gives the number of vertices at each distance from a fixed vertex in an n-dimensional cube. For example, in three dimensions, the third row (1 3 3 1) corresponds to the usual three-dimensional cube: fixing a vertex V, there is one vertex at distance 0 from V (that is, V itself), three vertices at distance 1, three vertices at distance √2 and one vertex at distance √3 (the vertex opposite V). The second row corresponds to a square, while larger-numbered rows correspond to hypercubes in each dimension.

Fourier transform of sin(x)n+1/x
As stated previously, the coefficients of (x + 1)n are the nth row of the triangle. Now the coefficients of (x − 1)n are the same, except that the sign alternates from +1 to −1 and back again. After suitable normalization, the same pattern of numbers occurs in the Fourier transform of sin(x)n+1/x. More precisely: if n is even, take the real part of the transform, and if n is odd, take the imaginary part. Then the result is a step function, whose values (suitably normalized) are given by the nth row of the triangle with alternating signs. For example, the values of the step function that results from:

 * $$\mathfrak{Re}\left(\text{Fourier} \left[ \frac{\sin(x)^5}{x}   \right]\right)$$

compose the 4th row of the triangle, with alternating signs. This is a generalization of the following basic result (often used in electrical engineering):

 * $$\mathfrak{Re}\left(\text{Fourier} \left[ \frac{\sin(x)^1}{x}\right] \right)$$

is the boxcar function. The corresponding row of the triangle is row 0, which consists of just the number 1.

If n is congruent to 2 or to 3 mod 4, then the signs start with −1. In fact, the sequence of the (normalized) first terms corresponds to the powers of i, which cycle around the intersection of the axes with the unit circle in the complex plane: $$ +i,-1,-i,+1,+i,\ldots  $$

Extensions
Pascal's triangle may be extended upwards, above the 1 at the apex, preserving the additive property, but there is more than one way to do so.

To higher dimensions
Pascal's triangle has higher dimensional generalizations. The three-dimensional version is known as Pascal's pyramid or Pascal's tetrahedron, while the general versions are known as Pascal's simplices.

To complex numbers
When the factorial function is defined as $$z! = \Gamma(z + 1)$$, Pascal's triangle can be extended beyond the integers to $$\Complex$$, since $$\Gamma(z + 1)$$ is meromorphic to the entire complex plane.

To arbitrary bases
Isaac Newton once observed that the first five rows of Pascal's triangle, when read as the digits of an integer, are the corresponding powers of eleven. He claimed without proof that subsequent rows also generate powers of eleven. In 1964, Robert L. Morton presented the more generalized argument that each row $$n$$ can be read as a radix $$a$$ numeral, where $\lim_{n \to \infty} 11^{n}_{a}$ is the hypothetical terminal row, or limit, of the triangle, and the rows are its partial products. He proved the entries of row $$n$$, when interpreted directly as a place-value numeral, correspond to the binomial expansion of $$(a + 1)^n = 11^{n}_{a}$$. More rigorous proofs have since been developed. To better understand the principle behind this interpretation, here are some things to recall about binomials:
 * A radix $$a$$ numeral in positional notation (e.g. $$14641_{a}$$) is a univariate polynomial in the variable $$a$$, where the degree of the variable of the $$i$$th term (starting with $$i = 0$$) is $$i$$. For example, $$14641_{a} = 1 \cdot a^{4} + 4 \cdot a^{3} + 6 \cdot a^{2} + 4 \cdot a^{1} + 1 \cdot a^{0}$$.
 * A row corresponds to the binomial expansion of $$(a + b)^{n}$$. The variable $$b$$ can be eliminated from the expansion by setting $$b = 1$$. The expansion now typifies the expanded form of a radix $$a$$ numeral, as demonstrated above. Thus, when the entries of the row are concatenated and read in radix $$a$$ they form the numerical equivalent of $$(a + 1)^{n} = 11^{n}_{a}$$. If $$c = a + 1$$ for $$c < 0$$, then the theorem holds for $$a = \{c - 1, -(c + 1)\} \;\mathrm{mod}\; 2c$$ with odd values of $$n$$ yielding negative row products.

By setting the row's radix (the variable $$a$$) equal to one and ten, row $$n$$ becomes the product $$11^{n}_{1} = 2^{n}$$ and $$11^{n}_{10} = 11^{n}$$, respectively. To illustrate, consider $$a = n$$, which yields the row product $$n^n \left( 1 + \frac{1}{n} \right)^{n} = 11^{n}_{n}$$. The numeric representation of $11^{n}_{n}$ is formed by concatenating the entries of row $$n$$. The twelfth row denotes the product:

 * $$11^{12}_{12} = 1:10:56:164:353:560:650:560:353:164:56:10:1_{12} = 27433a9699701_{12}$$

with compound digits (delimited by ":") in radix twelve. The digits from $$k = n - 1$$ through $$k = 1$$ are compound because these row entries compute to values greater than or equal to twelve. To normalize the numeral, simply carry the first compound entry's prefix, that is, remove the prefix of the coefficient $${n \choose n - 1}$$ from its leftmost digit up to, but excluding, its rightmost digit, and use radix-twelve arithmetic to sum the removed prefix with the entry on its immediate left, then repeat this process, proceeding leftward, until the leftmost entry is reached. In this particular example, the normalized string ends with $$01$$ for all $$n$$. The leftmost digit is $$2$$ for $$n > 2$$, which is obtained by carrying the $$1$$ of $$10_{n}$$ at entry $$k = 1$$. It follows that the length of the normalized value of $$11^{n}_{n}$$ is equal to the row length, $$n + 1$$. The integral part of $$1.1^{n}_{n}$$ contains exactly one digit because $$n$$ (the number of places to the left the decimal has moved) is one less than the row length. Below is the normalized value of $$1.1^{1234}_{1234}$$. Compound digits remain in the value because they are radix $$1234$$ residues represented in radix ten:

 * $$1.1^{1234}_{1234} = 2.885:2:35:977:696:\overbrace{\ldots}^\text{1227 digits}:0:1_{1234} = 2.717181235\ldots_{10}$$

title: Pascal's triangle


text:
Wikipedia talk:Writing better articles/Integrate changes

Supporters of this rule include:
 * Larry Sanger
 * Linus Tolke
 * Pinkunicorn (strongly)
 * Koyaanis Qatsi
 * sjc
 * Janet Davis
 * drj
 * Mike Dill (hard isn't it?),
 * Damian Yerrick (who personally doesn't think it's that hard),
 * GWO
 * tbc
 * AxelBoldt, 24,
 * Enchanter I agree strongly! If the text you want to add flows logically it's so much easier to read the article
 * Karen Johnson
 * Rotem Dan (This is a significant characteristic of brilliant prose)
 * r3m0t 10:29, 13 Dec 2003 (UTC)
 * Loisel 03:37, 18 Apr 2004 (UTC)

No opponents

You can and should add disjunct comments to an article. Over time, these comments will accumulate, and eventually there will be enough so that you or some other Wikinaut can junct them into beautiful prose.

Are you really saying "Don't ever add add comments to the bottom of the article. Always integrate your comments." ?
However, comments relevent to the existing beautiful prose should be integrated into the flow of the article rather than tacked on. The rule, as presently formulated, is correct for such cases, but is harmfully restrictive with regards to comments not relevent to the prose as it currently exists.

There's nothing "harmfully restrictive" about it: if you are a good writer and you understand the subject, you will easily be able to figure out where in the article your comment fits. But this much is true: if you feel motivated to add a paragraph but you don't feel motivated to put it anywhere in particular, sure, go ahead and tack it onto the bottom. Just realize that you're creating work for other people, who will (or won't) use your contribution in updating the article properly later on. If you feel at all motivated, please do update the article properly, i.e., integrate your contribution with the existing entry. --LMS

It is harmfully restrictive, in that if the rule were consistently followed it would restrict how people comment in a way that is harmful to the growth of Wikipedia. It would prevent people from adding information that cannot be integrated into the material already written, without adding a substantial amount of new material. In cases when people do not wish to add a substantial amount of new matieral, they would leave nothing. Adding new information to the bottom of the page is preferable to adding nothing.

Well, I agree 100% with the latter paragraph. But this is consistent with what I said. I've edited the rule so you ought to be able to agree with it now, Tim. --LMS

What should I do when I find (someone else's) disjointed comments at the end ?
Perhaps we could change to something like ?
 * please place and edit your comments so that they flow seamlessly with the present text.
 * Go ahead and append comments at the end of the article. But please move and edit such comments -- even those written by others -- so that they flow seamlessly with the present text.

If this were really a hard rule -- ""Don't ever add add comments to the bottom of the article." -- then the proper thing to do would be to post to the User_talk page of the user who added that comment, telling him Don't ever do that again.

But I think "integrate changes" is a much softer rule -- sort of like the "spell correctly" rule. If I see a typo, I quietly fix it. --DavidCary 15:14, 29 Jul 2004 (UTC)

See also Tim's Refactoring as the essential Wikipedia process.

Proposal to consolidate advice on writing better articles
At present there are many articles in the Wikipedia namespace that seek to give guidance on how to write better articles. I propose consolidating these into a much smaller number. On User:Jongarrettuk/Better writing guide I propose how these could be consolidated. The proposal is not to change advice, just to consolidate it. If I have inadvertently moved what you consider to be good advice that is currently in the Wikipedia namespace, please re-add it. I'm hope that the proposal to merge all these articles, in principle, will be welcomed. Of course, it may be preferred to have 2, 3 or 4 inter-connected articles than just one and would welcome advice on how this could be done. (In particular, perhaps all the guidance on layout should be spun off into one consolidated article on layout.) I'm also aware that putting lots of different bits of advice together may throw up anomalies or bits that people now disagree with (including bits that I myself disagree with:) ). I ask for support for the consolidation. Once the consolidation has happened, the advice can be changed in the normal way. Please feel free to improve on the current draft consolidation, but don't remove or add advice that is not currently on the Wikipedia namespace. If all goes well, I'll add a new Guide to writing better articles page on the 19th, though maybe some bits of the new article will need to be phased in over a longer period. I'll also take care to preserve all the archived discussion in one place. jguk 19:47, 11 Nov 2004 (UTC)