Talk:Pi/Archive 13

This is an archive of past discussions about Pi. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

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Convergence series needs citation

To whomever add the 3rd series ("Another that converges even more rapidly is the arcsine series" ) into the "Rate of Convergence" section. I don't think a 3rd series is needed to demonstrate the convergence principle: there are hundreds of series for pi; it takes only 2 to illustrate the point to lay readers. Why stop at 3? why not 4? 5? But, in any case, that 3rd series needs a citation or it should be removed. --Noleander (talk) 03:00, 8 January 2013 (UTC)

Any thoughts on this? I propose to remove the 3rd example, unless there is a good reason put forth as to why 3 is better than 2 for the readers. --Noleander (talk) 15:57, 8 January 2013 (UTC)

Because the arcsine series is simple and highly convergent. -- cheers, Michael C. Price ^talk 00:16, 23 February 2013 (UTC)

I agree to a certain extent, but I think the simplicity of the arcsine series isn't well emphasized in the current edit (what's the general term? not clear) nor why it's an improvement over the other two methods. As presently written, I agree this is not suitable for the article. However, I do support a rewrite that might assuage these objections. Sławomir Biały (talk) 01:08, 23 February 2013 (UTC)

My concerns are the following:

1) There is no citation given to demonstrate the validity of the series ... for an FA status article, a cite is needed

2) This is an article on pi, not an article on convergence. Two examples are ample. More is just showing-off.

3) The pattern of the first two series are plain to the lay readers. The pattern of the new series will be a mystery to them.

4) The first two series were picked because they met two very important criteria: (a) the could be presented without using fancy notations (sigma; factorial, etc); and (b) the number pattern was clear to lay readers. The arcsin series does not meet those criteria.

That said, if anyone can find a series that has a clear pattern, and is supporte by a cite, and can be presented without notations, I have no objection to replacing one of the two original series. --Noleander (talk) 02:58, 23 February 2013 (UTC)

As I suspected, it was a waste of time. Thanks Nolander, your comment "This is an article on pi, not an article on convergence." has finally convinced me to retire from WP for good; the utility of a simple, rapidly convergent formula for the general reader should be obvious. FYI, Sławomir, the article used to include the general formula, along with a link to arcsine for interested readers. But that has been removed with time, as being just too helpful, evidently. -- cheers, Michael C. Price ^talk 18:07, 23 February 2013 (UTC)

The article Convergent series is in pretty bad shape, and has no discussion of rate-of-convergence - none at all. That article could definitely use a new section on that topic, with a large number of examples. It could also include a discussion of quantitatively measuring the rate of convergence. The "Speed of Convergence" section in this article on pi links to Convergent series, so readers of pi article could follow that link to get more examples. It would be great if someone would improve Convergent series. (PS: the pi article did include, about a year ago, lots of material that was not supported by citations. During the processing of upgrading the article to Featured Article status, some of that material was removed because it was already present in subarticles ... but in all cases several editors reviewed the changes as they were made.) Cheers. --Noleander (talk) 22:17, 23 February 2013 (UTC)

Seeing no comments, I've made that change. --Noleander (talk) 16:15, 25 January 2013 (UTC)

It is time to move Tau out of the In popular culture section

There is currently an RfC underway at User_talk:Tazerdadog/Tau_(Proposed_mathematical_constant) over whether to have a full Wikipedia article about tau. (You may want to read through it if you haven't already.) Among other new sightings of tau listed there is that the UC San Diego math department has begun teaching tau in one of its Calculus courses. There's plenty of other evidence, but when an accredited math department at a major university has begun using tau instead of pi in one of its courses, you can no longer claim tau is just "popular culture". I'm not asking for tau to be given more lines in the pi article. Just that it be moved to a more appropriate section. --Joseph Lindenberg (talk) 23:16, 28 February 2013 (UTC)

I'd like to suggest that Tau be removed from 'In Popular Culture', since by no stretch of the imagination can it be considered a feature of popular culture at all. But I propose that we don't reinstate it anywhere else instead. It's a fringe position, and attempts to represent it as otherwise are misleading. AlexTiefling (talk) 23:22, 28 February 2013 (UTC)

Professors have pretty wide latitude in their courses. We do many stranger things than that. But I doubt that this is some sort of official department decision; the book they use is the standard Hughes-Hallet text that is all in terms of π. I think that having τ in the "pop culture" section is a reasonable compromise as it is primarily a pop culture phenomenon to the extent it is a phenomenon at all. — Carl (CBM · talk) 23:24, 28 February 2013 (UTC)

I can't imagine he's doing it without the department's consent. I'm not suggesting the UCSD math department has decided to en masse switch all their courses over to tau, but I highly doubt this is a case of a rogue instructor (and his cabal of T.A.'s) trying to get away with doing it in secret. --Joseph Lindenberg (talk) 22:03, 1 March 2013 (UTC)

I can't imagine why you think this -- do you suppose that lecturers have to ask for departmental approval for every detail of their notation? You keep saying things like "They are teaching tau at [some university]", but what does it mean to "teach tau"? There isn't anything to teach which is distinct from "teaching pi" (as it were; no-one says "teach pi" either). It would help if we had some specific details of what is in these courses that involves tau. Imaginatorium (talk) 15:37, 2 March 2013 (UTC)

The UC San Diego material is linked to and discussed over in the RfC. If you look through it, you should see why I don't believe the instructor would be doing it without the department's consent. Especially on a foundational course like Calculus III. (Not saying he had to somehow officially apply for approval.) Tau displaces pi in the course, even to the extent that only tau appears on the exams. The instructor's course formula sheet handout is in terms of tau only. As are the instructor's homework exercises. So it's a pretty safe bet the lectures are too. --Joseph Lindenberg (talk) 19:38, 2 March 2013 (UTC)

They're also teaching tau in some courses at Queen Mary University of London. I haven't had time to sift through their website yet and determine the full extent of it, though. --Joseph Lindenberg (talk) 22:13, 1 March 2013 (UTC)

My recommendation would be to leave the pi article alone until the tau article issue is resolved. RfCs normally run for 30 days, so that is another few weeks for the tau RfC. Then, I predict, an AfD will happen (which is the appropriate process for the question being asked in the RfC) which will take a week or two. After that, we could revisit the pi article and see how it is impacted by all that activity. --Noleander (talk) 23:19, 1 March 2013 (UTC)

Regardless of the outcome over there, tau is clearly not a "popular culture" topic like room decorations, baked desserts, football cheers, fiction novels, pop songs, politicians, and TV shows. We really should at least begin thinking about where to fit it somewhere else in the article. Are we really providing an accurate, truthful article by knowingly miscategorizing tau, instead of just telling readers that as of the present, it isn't being widely used? --Joseph Lindenberg (talk) 00:18, 2 March 2013 (UTC)

There are no reliable mathematical sources for it. So if it's not to go in popular culture based on the 'trivia of the day' news coverage it should be removed entirely, until the day there are reliable academic sources for it.--JohnBlackburne^words_deeds 00:24, 2 March 2013 (UTC)

Fine, we'll play your Wikilawyer games, John. They're more important than providing readers with honest information. In any case, Noleander, you might want to begin thinking about where tau could be moved in the article once those sources do show up. Because it's clear that they will soon. I also want to repeat that I'm not looking to expand tau's coverage in the Pi article. But this stick-a-dunce-cap-on-it game of putting tau in the popular culture section is just plain childish. --Joseph Lindenberg (talk) 00:47, 2 March 2013 (UTC)

'Wikilawyer' ? I was expressing my opinion as you were yours. You've provided no reliable academic sources for your suggested changes, just that it's been spotted in some lecture notes. That shows nothing: in my experience individual lecturers can teach what and how they want.--JohnBlackburne^words_deeds 14:09, 2 March 2013 (UTC)

Yes, 'Wikilawyer'. You missed his second part of that statement: "They're more important than providing readers with honest information." Now, will you stop fighting to keep good, honest articles FROM existing and help instead to fight to have them to exist? Or, are you going to keep ignoring this and keep 'Wikilawyering'? John W. Nicholson (talk) 22:29, 2 March 2013 (UTC)

No. See Wikipedia:Wikilawyering#Misuse of the term. Using it without explaining it is simply pejorative. And when editors start using pejorative language it is usually as they've run out of reasoned arguments. Please bring new arguments and take the offensive language elsewhere.--JohnBlackburne^words_deeds 22:47, 2 March 2013 (UTC)

I can't believe he just defended himself from accusations of Wikilawyering by quoting a WP: Policies and Guidelines page. Priceless. --Joseph Lindenberg (talk) 22:57, 2 March 2013 (UTC)

And, which in effect is proving your point that he cares not about the reader and wants to talk about the rule of Wikipedia. John, you asked a question about if what you are doing is "'Wikilawyer'?", I gave an opinion too. Just being honest for you. John W. Nicholson (talk) 00:40, 3 March 2013 (UTC)

@JL - Yes, placement of tau in the pi article is an independent question from existence of the tau article. My point is one of editing efficiency: WP only has so many volunteers, and there is lots of work to be done all over the place. Beginning a discussion here will cause two major discussions to be happening at once: the RfC, and a discussion here about WP:FRINGE. We don't need two discussions going at once. Your contributions log shows that you are essentially a single purpose account. The rest of us are spread thin working on a variety of things. I'm just suggesting that we have one major tao discussion going at a time. There is no rush. --Noleander (talk) 00:34, 2 March 2013 (UTC)

That's fine, and I agree there is no hurry. I'm completely sympathetic to being too busy to deal with everything. --Joseph Lindenberg (talk) 00:50, 2 March 2013 (UTC)

My own view: Move Tau out into its own article with a link to it perhaps from here, where it can sit and fester independently and no longer clutter up this page with its bletheringly pointless existence. Tau-fetishists can then go and play their silly games somewhere else. --Matt Westwood 09:13, 3 March 2013 (UTC)

I very much agree. Personally I find the subject of "tau" rather less interesting than, oh, say Honeycomb toffee, but there are easily enough pointers to the existence of "tauism" for it to be considered notable. Given a topic about it, it would be much easier to trim the special pleading; since it is an issue of notation alone (pace the seminar in Oxford, and I'm not going to pay sixty quid, not to mention the airfare, just to find out they can't really support their wilder claims, even if some of the history might be very interesting), and the WP article should have no mathematical content as such at all. Imaginatorium (talk) 09:59, 3 March 2013 (UTC)

Tau is a very silly choice for 2π anyway. Just look at it, it's more like half a π, or like a π with one leg missing, so it would have been a good choice for π/2 or perhaps π/3, but 2π? No, definitely not. - DVdm (talk) 14:16, 3 March 2013 (UTC)

The legs are in the denominator. --Joseph Lindenberg (talk) 21:38, 3 March 2013 (UTC)

Interesting idea, letting tau be π/2. A collaborative WPM venture entitled "A tau semifesto" could argue that π should be replaced by τ=π/2. The argument in favor is that the right angle is a meaningful geometric angle that can be readily illustrated in a drawing and accessible to a student, unlike the degenerate angle of π, a vestige of Greek Antiquity. One could conclude that π is way too much; in fact, twice as much as we are willing to take. Tkuvho (talk) 15:43, 3 March 2013 (UTC)

Nah... pi isn't way too much. Why, some of us Americans eat so much that we even want to super-size our circle constant. --Joseph Lindenberg (talk) 22:22, 3 March 2013 (UTC)

(Back to the main theme...) Perhaps the article should be on tauism (2&pi);, with tau (2π) still redirecting here. I can see no reason for there to be an article on "tau", but tauism might be appropriate. In other words, no reason to change this article at all, except possibly to shrink the section slightly, and add {{main}}. — Arthur Rubin (talk) 16:00, 3 March 2013 (UTC)

I think I understand (and agree with) your second sentence, namely that the article would be about the push/arguments to have tau replace pi, rather than just an almost-carbon-copy of the pi article with all the formulas adjusted to use tau. I'm not sure that "tauism" is the best title to use, for reasons I can explain later. But why would you still want tau (2π) to redirect here? --Joseph Lindenberg (talk) 07:14, 4 March 2013 (UTC)

That sort of article would make a mountain out of a molehill. There is no huge debate going about about whether τ should replace π - what is being presented are mostly blog posts and cherry-picked comments about τ. It would be like writing an article on the calculus reform movement in 1988. There are simply not enough reliable third-party sources for us to write a sensible article about τ at the moment, and it is better to keep the "he said / she said" text to a minimum rather than treating it as a giant soap opera. In five years, it will be clear whether τ made any headway. At the moment, it is too early to say anything much beyond what is already in this article. — Carl (CBM · talk) 03:11, 12 March 2013 (UTC)

Proponents

I removed a "who" tag. A sentence that says "proponents" and then has two references by different people is perfectly clear about "who" is making the claims: the people being referenced.

However, I am mildly troubled by labeling people who write or say anything in favor of τ as "proponents". I find it too dualistic; I don't see an need to divide people into "proponents" and "opponents" when actual opinions will be more nuanced. — Carl (CBM · talk) 13:44, 12 March 2013 (UTC)

Pi Pie Image

Implying that there is only a link between pies and pi puns because of the shape of a pie is ridiculous as pies come in any such shape they are made in, and plenty are not circular. Whether a pie is baked round or square, it's almost certainly the name association that leads people to make jokes regarding the two, not the shape. Most people aren't so mathematically enthused as to make the effort to make a math-enthusiast-only-audience joke. — Preceding unsigned comment added by 121.215.129.230 (talk) 09:08, 14 March 2013 (UTC)

This was briefly discussed here. --Joseph Lindenberg (talk) 10:22, 14 March 2013 (UTC)

The Anti-Pi Song

This is actually pretty good. (Not tau propaganda, though it does mention tau at one point.) www.youtube.com/watch?v=wCEhvenbfYM --Joseph Lindenberg (talk) 10:27, 15 March 2013 (UTC)

Pi Day (3/14) at Tau Time (6:28pm). Cartoon or not, MIT wasn't kidding.

It really is a new MIT tradition. They've announced that again this year, admissions decisions for the fall freshman class will be posted online on Pi Day (3/14) at Tau Time (6:28pm). For anyone who missed it last year, here is a link to the formal proclamation, written in official MIT crayon: mitadmissions.org/blogs/entry/i-have-smashing-news --Joseph Lindenberg (talk) 02:53, 8 March 2013 (UTC)

This item does not seem to be mentioned in the "popular culture" section. It can be added if other editors agree. Tkuvho (talk) 09:00, 8 March 2013 (UTC)

From an anonymous (I assume 'Sir Nigel Blogberry' is not a real person) blog of cartoons? That's not a reliable source and requires a significant amount of interpretation, i.e. original research, to extract the information about π and τ (they are only mentioned in the cartoon – the announcement just gives the date and time).--JohnBlackburne^words_deeds 09:38, 8 March 2013 (UTC)

Here is this years: http://mitadmissions.org/blogs/entry/breaking-news John W. Nicholson (talk) 13:12, 8 March 2013 (UTC)

Boston Globe article mentioning MIT's Tau Time, quoting Dean of Admissions Stuart Schmill, and saying that MIT plans to continue the tradition next year.
Similar Boston Globe article from last year.

--Joseph Lindenberg (talk) 04:01, 16 March 2013 (UTC)

Edit request on 19 March 2013

This edit request has been answered. Set the |answered= parameter to no to reactivate your request.

Samiwala78652 (talk) 17:50, 19 March 2013 (UTC)mention that 22/7 is a rational number which is a approximation of pi and pi by itself is a irrational number.If you divide 22/7 you will get 3.1428571 and then it will just keep on repeating.Also because of pi we can do solve many math problems like area of circle,cone,cylinder,many geometrical figures volumes,etc.

Hi Samiwala. The article already includes 22/7 and other fractional approximations to pi, plus details that pi is irrational and transcendental. The article also contains a few geometric-related formulae involving pi. Hence I am not quite sure what changes you are requesting. For a semi-protected request, you should be very specific about the changes you would like to make, e.g. replace text 'xxx' by text 'yyy'. Murray Langton (talk) 19:47, 19 March 2013 (UTC)

They had shirts made up and everything

www.youtube.com/watch?v=nnZk_YuIYkA (This is apparently a follow-up to www.youtube.com/watch?v=G2lFfH6Rknk, in case you haven't seen that video. It includes an actual serious teacher's lecture starting about 5 minutes in.)--Joseph Lindenberg (talk) 22:13, 20 March 2013 (UTC)

The real WTF is of course pronouncing it to rhyme with "now" rather than "nor".

I still can't believe people actually have sufficient time to waste on this trivial non-entity of an argument. (My excuse is that I'm procrastinating.) --Matt Westwood 08:47, 21 March 2013 (UTC)

sin 18 and cos 72

sin 18=1÷(1+sqrt5) and in radian asin(1÷(1+sqrt5))=π÷10 Twentythreethousand (talk) 21:10, 28 February 2013 (UTC)

18° is the arc of one side of a regular decagon inscribed within a circle. It's related to sqrt(5) and phi. — Loadmaster (talk) 23:39, 21 March 2013 (UTC)

the difference from 180 to 18 is 162 as for pi to pi/10=162*1radian,why is this not correct?Twentythreethousand (talk) 22:31, 23 March 2013 (UTC)

That one's true. It as little to do with this article, though. — Arthur Rubin (talk) 05:26, 24 March 2013 (UTC)

The use of fraction

Take any rational or irrational numbers under 180,divide those numbers by 180 and take the sine of those digits in radian mode or by the use of Taylor series.Invert the sine in degree mode and divide the numbers that were divided by 180 using the answers that were given by Taylor series or in radian mode reverted to degree mode(the dividend), and you obtain pi. — Preceding unsigned comment added by Twentythreethousand (talk • contribs) 20:40, 28 February 2013 (UTC)

That's because π rad = 180°. By converting between degrees and radians, your procedure multiplies or divides the intermediate values by 180/π, so everything cancels out except π. Simple algebra, nothing deep or mysterious here. — Loadmaster (talk) 21:22, 25 March 2013 (UTC)

It's not simple algebra,it's trigonometry and there is a unique constant that can relate to π, a perfect number.

(180/pi)^{2}+(180/pi)^{2}=6561

1^{2}+1^{2}=2

sqrt2/(pi/180)=81

— Preceding unsigned comment added by Twentythreethousand (talk • contribs) 02:07, 26 March 2013 (UTC)

Well, you're wrong, he's right; the first bit is simple arithmetic jiggling. Your following contributions: well,

1^{2}+1^{2}=2

is true. The other two are obviously false, because they imply pi is algebraic. The first one works out to a supposed value of 3.14269... for "pi", which is well-known to be wrong. I respectfully suggest that you are out of your depth here. Imaginatorium (talk) 04:55, 27 March 2013 (UTC)

Take the value 3.14269..,and then divided into 180 which I implied in the title "the use of fraction".The result is 3.1426.../pi which is a significant number to be recognized.:

1/(sqrt((((pi-pi/10)/4)^{2})*2))\,

if it is well-known it should be revised.

pi in degree and radian taking the inverse trigonometric function.In radian it would be pi/sqrt8 and in degree 180/sqrt8

45^{2}+45^{2}=4050

File:Boxgraph7jourscer.jpg

acos(cos x)

Twentythreethousand (talk) 22:38, 27 March 2013 (UTC)

That doesn't even make sense. This is about the article Pi. What are you suggesting needs to be done in or to the article? Your arithmetical investigations, whether right or wrong, are far too obscure to include in this or any article.--JohnBlackburne^words_deeds 22:51, 27 March 2013 (UTC)

thank you.Twentythreethousand (talk) 23:17, 27 March 2013 (UTC)

Tau needs attention

Editors (both from , meat puppets?) appear to be trying to recreate Tau_(2π) contrary to prior discussions. Can some others keep an eye? IRWolfie- (talk) 23:59, 11 March 2013 (UTC)

Don't look at me. I don't know anyone from Sweden. Why do you suspect they are "meat puppets", rather than just people interested in tau but not interested in following the rules? (Serious question, not rhetorical) --Joseph Lindenberg (talk) 00:29, 12 March 2013 (UTC)

Is there anything controversial about the following removed sentence? "Salman Khan, named in Time's 2012 annual list of the 100 most influential people in the world,[149] advocated the use of τ before π in one of his educational videos at Khan Academy.[150]" –St.nerol (talk) 01:47, 12 March 2013 (UTC)

It's implicitly making the argument that, because Khan was named by Time, his opinion is particularly noteworthy to the issue of τ. That is an example of what is sometimes called "synthesis" in the original research policy. In fact, it is not at all clear whether Khan's opinion about mathematics is important to the mathematical community. I am not sure that Khan Academy is particularly well regarded. — Carl (CBM · talk) 01:54, 12 March 2013 (UTC)

Might do better describing his importance in math education. A VERY LARGE number of people do learn math from Salman Khan, so while the "mathematical community" may look down their nose at his math expertise, he's an undeniably important figure in math education. By the way, where you wrote "τ before π", I think you meant "τ instead of π". --Joseph Lindenberg (talk) 02:03, 12 March 2013 (UTC)

It's not clear whether Khan has credibility in the mathematics education community, e.g. http://chronicle.com/blognetwork/castingoutnines/2013/02/05/khan-academy-redux/ as a starting point into the discussion. I would wager there has been much more discussion of Khan Academy in the mathematics education community than in the mathematics research community. — Carl (CBM · talk) 02:15, 12 March 2013 (UTC)

Just because he has critics in the math education community doesn't mean that the community in general sees him in a negative light. That's true with any expert community. --Joseph Lindenberg (talk) 02:27, 12 March 2013 (UTC)

In any case, the point about the sentence is that it is making two separate arguments: (1) that the Time mention indicates Khan's opinion about τ is valuable and (2) Khan has expressed support for &tau. Point (1) is far from clear to me - why would inclusion on Time's list indicate any particular expertise about τ? Moreover, even if it did, why would Khan's opinion be more valuable than the actual mathematicians whom we already know have written things supporting τ? Khan seems like a particularly odd choice for an example of someone who speaks for the consensus of the mathematics or mathematics education communities, given that he is not really part of either of those communities. — Carl (CBM · talk) 02:34, 12 March 2013 (UTC)

Who said we could only quote people who speak for the consensus of an entire expert community? Salman Khan's opinion matters in math education. He's head of a very large (in terms of numbers of students) educational organization. So much so that I don't think you need to explain at length who he is. "Salman Khan, founder and CEO of the online learning resource Khan Academy, advocated the use of...". Everyone knows Khan Academy. Wikilink Salman Khan (educator) and Khan Academy for people who don't. --Joseph Lindenberg (talk) 02:54, 12 March 2013 (UTC)

"Salman Khan's opinion matters in math education." - that is exactly the claim I am disputing. The sentence in question tries to argue that his opinion matters because the Time list mentions him. But, much as is the case with τ, it is too soon to see what influence Khan will have on mathematics education, and there is no reason apart from faith to think that τ will become widely accepted or that Khan will have a lasting influence. — Carl (CBM · talk) 03:06, 12 March 2013 (UTC)

Yeah, I agree citing Time isn't the way to go. But just because a man hasn't completely transformed how everyone learns math in this country doesn't mean we can't quote him in the article. The stats in the Khan Academy article make clear just how big they are, and Salman Khan steers (and built) that ship. Just by virtue of what he chooses to do at Khan Academy alone, his opinion matters in math education. After saying all this though, if you and St.nerol decided that mentioning Stephen Abbott's endorsement would be more agreeable to everyone, that's fine too. I'm going to bed. --Joseph Lindenberg (talk) 03:37, 12 March 2013 (UTC)

The problem is that adding any more material on tau - regardless of how outstanding the source is - would violate the WP UNDUE policy, because it would give readers the impression that tau is more important that it is. Tau already has about 1% of the pi article (just a rough guess) ... yet in the math literature, tau has about 0.00001% as much weight as pi. Increasing the text in the article above 1% would give readers the erroneous impression. Any more details about tau can go into an article dedicated to tau, not here. --Noleander (talk) 03:48, 12 March 2013 (UTC)

That's why a separate article for tau would in doubt be appropriate. Personally I would support such an article alone to get rid of the neverending and somewhat naueating discussions here. Tau has cenrtainly seen enough media attention to warrant its own article, even if it just seen as popular science/cultural phenomenon.--Kmhkmh (talk) 17:42, 20 March 2013 (UTC)

The solution to the "nauseating discussions" is to create a separate "arguments" page, as at 0.999.... Actually, the media attention has died down since the initial sensationalist burst two years ago. Wikitalkpage verbiage is not a valid reason for creating a page. Tkuvho (talk) 17:46, 20 March 2013 (UTC)

I think you misread my (sarcastic) comment somewhat. Avoiding nauseating discussion is of course no proper reason to create articles and I have no objections against the arguments page. I do believe however tau is as (pop or internet) phenomenon well known enough to have its own article, which as consequence then also solves the problem of edits here (on the article) and the WP:UNDUE issue (within the the article). Meaning a more detailed description of tau is certainly inappropriate (undue) within the pi article, but obviously not when having an article on its own.--Kmhkmh (talk) 12:16, 22 March 2013 (UTC)

When I started editing Wikipedia I was taught that sentences should not just state stuff, but exemplify why it is relevant. It seems to me that was what the deleted sentence tried to do. Does naming a notable proponent gives tau undue wheight? Well, then that'd be because the rest of the article is too short. With your reasoning we should also go straight ahead and e.g. remove the three sections about creationism from the article of evolution. –St.nerol (talk) 11:04, 12 March 2013 (UTC)

The problems with the sentence are (1) it is not clear how "strongly" he is a proponent; all I see is that he made a video about τ. Has he done a lecture tour on it? Has he written a textbook that uses it? The sentence mentions his name but there is no way, at the moment, to tell exactly what his contribution is. (2) If the goal was simply to mention that Khan supports τ (whatever that means, cf. 1), then there is no need to mention the Time article. Really, the problem is that there is not enough reliably sourced material about τ which is what makes it tempting to look for anything at all related just to have something to say. But the solution to that is to wait until there are enough good sources before trying to write much. — Carl (CBM · talk) 11:51, 12 March 2013 (UTC)

It appears that Salman Khan (educator) has his own page (if this is the same person as discussed above). If so, providing the link to his page is sufficient. Any additional adjectives should be removed as WP:PEACOCK terms. Tkuvho (talk) 15:01, 12 March 2013 (UTC)

WP:PEACOCK says that one shouldn't use terms like legendary, great, etc; but just describe the facts. The non-peacock example given is: "Dylan was included in Time's 100: The Most Important People of the Century, where he was called "master poet..." –St.nerol (talk) 19:14, 12 March 2013 (UTC)

John Machin inaccurate

The John Machin method is inaccurate past the 16th digit. See WolframAlpha. --72.219.142.167 (talk) 20:29, 6 April 2013 (UTC)

That is showing the limits of wolframalpha, not John Machin's formula. Try it on something else, say Pari/GP, which can handle multiprecision values. John W. Nicholson (talk) 01:51, 7 April 2013 (UTC)

The fallacy of Point, Line and the Death of Pi

Please review WP:NOTFORUM as articles talk pages are not a place to discuss new ideas that are not based on reliable sources. Johnuniq (talk) 07:02, 12 April 2013 (UTC)

The following discussion has been closed. Please do not modify it.

1. Any point in 2-dimension or 3-dimension is not a point, unless below described exceptions Consider the points below: .... Which of the above is a point – fourth dot or fifth dot (so small, that it can not be seen with the naked eye)? If we enlarge the fourth point and the fifth point with a lens or a microscope, we will see it as big as probably the first dot, if not bigger. Thus, the fourth and fifth points are spheres (or something else) and they are not points. However small and accurately we describe the position of the point, it will still have a left, right, above and below to it, besides the sides / diagonals. The position of a point can be defined only if the coordinates are in multiples of 1 or other exceptions below. Also, it will not be possible to represent the point diagrammatically, even if all its coordinates are in multiples of 1. If we put a point in that coordinate, then, some part of the point will be above the coordinate, some part below and so on. Even here, it is only a hypothetical point and any attempted representation of the point will only be an approximation, with the spreading across of the minute point (when enlarged through a lens, as described above). Exclusions: The fact of the matter is that there is no point in 2-D or 3-D, excluding certain exceptions. Let us take 2-D for starters. If we have coordinates of (1, 2), then 1 and 2 being whole numbers, this will exactly represent a point in 2-D with respect to origin i.e. (0,0). A point with the coordinates in 2-D of (3.23, 4.69) cannot be a point. This is because, 0.23 lies between 0 and 1 or between 0.22 and 0.24. What it means is that if it is not in multiples of 1 or an equally divided proportion of 1 and its multiples, then it cannot be a point. If we take 1m as the length of a line, then the line can be divided into exactly equal and measurable parts only by 2, 5 and multiples and powers and other combination of products and powers of these two numbers; of parts. This is so, because 1 cannot be divided into exactly 3 equal parts; nor 6; nor 7; nor 9. But, it can be divided into 2, 4, 5, 8 equal parts. It can also be divided into 1000 equal parts or 25 equal parts. This is so because; the division of 1 by the other numbers does not have a finite number of decimal places. So, how much ever precision we go to, we can never represent any point accurately, with the other decimal representations. So, (1, 1.1) can be represented for a point and similarly, (1, 1.25) can also be represented. But not (1, 1.35).

2. Any line is not a line; except the hypothetical line measuring in length as above

Consider below lines (assume of varying widths): ________ ________ ________ ________

Similar to a point, a line, too, cannot be represented as a line. For, which of the above 4 lines is a line and which are combination of multiple parallel lines? Same as above, if we expand the third and fourth (so small, that it is not visible to the naked eye) lines under a microscope, we will see it as big, if not bigger that the first line. Obviously, the first one is not a line and similarly, other 3 are also not lines. Any straight line drawn is as good as a rectangular thin rod (or something else), as we will have points on the line, which will be like other geometrical objects like sphere, etc. So, a straight line is only a hypothetical line, joining two points that can be defined as above. In reality, it would not exist. When it comes to the length of a line, again, it has to be as described in the previous point (point no. 1). Otherwise, it will have a range of length. Let us see how? If we have a length of a line of 1 m, then it is exactly measurable. However, if we have the length of a line which is not in multiples of 1 or multiples of parts of 1 divisible by any combination product / power of 2 and 5; then, it is never a line. In those cases (e.g. 2.53 m), the line is not a line, it is a function of numbers, whose size falls between 2.5 m and 2.625 m (which are multiples of 1 + numeric multiples of equally divisible parts of 1 i.e. divisible by 4 and multiples of 8 and hence exactly measurable). Thus, any line is hypothetical, like points. And any two points in space (even if defined as per point no.1) will never be able to form a line, unless the length of the line joining the two points (shortest distance between the two points) is as described in this section. And, if they don’t follow this principle, then the distance between the two points can never be measured accurately.

3. A circle can have diameters only as defined above in point no.2 Any line (even if hypothetical) will have a measurable and constant length, only if the previously stated conditions hold for the length of the line. Thus, this holds for even the diameter of a circle. Thus, any diameter other than of length as described in point no. 2 is neither measurable, nor constant. And, if the diameter is neither constant nor measurable, then, it cannot form a perfect circle. Thus, you can have a diameter of 1 m or 1.5 m; but not a diameter of 1.59 m. Or maybe, you can also have a diameter of 1.59 (= 1 + ½ +1/25 + 1/20); which the mathematicians should ascertain. In this case, by rotating the diametrical line by 360 degrees, we will get a circle – or we thought so! Let see more surprise below.

4. The circumference of a circle can never be determined Assume that the diameter of a circle is 1 m. Then the circumference of the circle = π x d = π. The circumference of a circle is nothing but a straight line of same length as the circumference, turned into a circle. Thus, the length of the line representing the circumference is π, in this case. However, π is not a number that can be represented in any of the manner mentioned in the previous point nos. 2 and 3. That is, it is not a finite number, which can measure a line accurately and precisely. It is represented by an infinite series. So, definitely, it cannot be a measurable and constant length, as should define a line or the length of the circumference of this circle. Thus, if we were to split the circle at any point and then stretch the two ends to form a line, then, if the length of this line is π or any multiples thereof, then it is definitely not going to be measurable or constant or finite. Anything finite (circumference of a circle) cannot be represented by and infinite number / series. Although π is termed to be a constant; since it does not follow the above rules, it is not a measurable constant for a line; and, hence for the circumference. Thus, there are two options:

a. Either π x d is not the circumference of a circle or

b. The circumference of a circle can never be determined accurately, despite an accurate and measurable diameter. And a circle can be formed only by a measurable diameter, as described above. E.g. 1/3 meters can never be the diameter of a circle, as it is not finite. Likewise, 1/6 or 1/7 or 1/9 meters also cannot be the diameter of a circle, as the resulting fractional number is not finite and the length of the line is not an exact equal divisor of 1.

In case (a), mathematicians have to determine the new circumference of a circle, if it is exactly measurable from point to point.

In case (b), what it means is that the so calculated circumference of the circle is either less or more than the point to same point distance traversed through the circumference of the circle. What this means is that, a circle as defined generally as traversing from one point to the same point around a 360 degree arc, around a center, with the same diameter, is never possible in reality to draw. Thus, we always draw somewhat lesser or somewhat more of a circle. In other words, a circle can only be defined as an infinite loop, with no beginning or no end, with every point in the circle being exactly the same distance from a central point. Of course, the distance of each point from the center should follow the above description of a proper line (point nos. 2 and 3).

Conclusion: It is thus, for the mathematicians to define the exact laws and review formulaes again. For, this article can sound the death knell for the most vouched for and most wowed constant π! I am sure the above theories will apply to all geometrical figures, their lengths, their circumferences, their areas, their volumes and so on.

--Annienaras (talk) 14:48, 11 April 2013 (UTC)

No. You are wrong. You're taking elements like construction errors and line thickness, and pretending they're part of the geometry. They aren't; they're just noise. Points have a good, clear definition as 0-dimensional entities in n-dimensional space, and circles, spheres, etc, are similarly clearly defined. Also, some of your diagrams are missing. AlexTiefling (talk) 14:53, 11 April 2013 (UTC)

I don't think it's even wrong -- just incoherent crank nonsense, of a fairly usual type. Can't contributions like this simply be deleted? Imaginatorium (talk) 19:34, 11 April 2013 (UTC)

We need a Talk:Pi/Arguments page (similar to Talk:0.999.../Arguments) where opinions and discussions about

π

should go. They don't belong here in the Talk page, since this is reserved for discussions about improving the article, and not about

π

itself. — Loadmaster (talk) 02:16, 12 April 2013 (UTC)

Just hat it and the replies instead: it takes up no more space, should not distract other editors (except the few that check the contents) and is easily found by the original poster if they want to revisit the discussion (if it's moved they may think we delete such comments). If we get more maybe add an edit note with suggestions.--JohnBlackburne^words_deeds 03:12, 12 April 2013 (UTC)

Why PI x D cannot represent the circumference of a circle?

Gentlemen, I accept your comments; however, please look at the below logic, which explains my rationale better:

When the circumference of a circle is straightened (by stretching the two ends), it becomes a line or vice-versa.

Length of a line has to be always finite. You cannot have an infinite representation as length of a line e.g. 1 1/3 metres. 1/3 is not an exactly and equally divisible part of 1. It is 0.3333333....... So, we can have length of a line as only say 1.33, which can be represented as 1+1/4+1/25+1/25. Thus, a line of 1 meter can be divided into exact equal parts of 2, 4, 5, 8, 10 and so on. Any infinite decimal cannot represent exactly a line of finite length. It will only be an approximation; it can never be exact. Such lines are just hypothetical; in reality they are undefinable / non-existing.

Anything that has a finite length (circumference of a circle) cannot have an infinite measurement of the same. Thus, for a diameter of 1, circumference = Pi = 3.14159.... If we approximate to 3.14, then it is less than the exact circumference. If we approximate to 3.1416, it is more than the exact circumference.

For diameter = 1, circumference = Pi. Pi is not an exact finite number. We cannot have lengths in fractions, of a line, which are not finite. So, if Pi x D is the circumference of a circle; then it is always indeterminate, exactly. So, we can never determine the circumference of a circle exactly; which means that a circle can never be drawn as starting at one point and ending at same point, with all points equi-distant from the center.

What it also means is that, the current formula of determining the circumference of a circle is not appropriate. If at all it is possible to determine the circumference of a circle exactly, then a new formula needs to be devised and it should have a finite result (in terms of number of decimal places). Otherwise, you cannot define a circumference of a circle exactly. You will be something more or something less than the exact circumference, always.

What we draw is just a continuous loop. So, a circle has no beginning or end. It is just an infinite loop.

Annienaras (talk) 04:22, 12 April 2013 (UTC)

Why does Π redirect here?

I don't think I've ever seen Π used for the circle constant, ever. It's production, just about always, isn't it? Twin Bird (talk) 18:16, 24 April 2013 (UTC)

(Aside...) I think you mean "product" for Π. I do not think "production" means "multiplication"! Imaginatorium (talk) 17:13, 25 April 2013 (UTC)

Mediawiki does not distinguish between having the first letter of an article capitalized or uncapitalized. So Π and π are the same article, which is a redirect to this page. — Carl (CBM · talk) 18:32, 24 April 2013 (UTC)

I've long felt that the first-letter-case-insensitivity should apply only to letters from the Latin alphabet (with or without diacritics). But Brion is exquisitely uninterested in making such a change. --Trovatore (talk) 20:11, 24 April 2013 (UTC)

Physics/engineering

I think Simple Harmonic Motion rates a mention. Pi crops up whenever we are discussing things that oscillate or wobble. — Preceding unsigned comment added by Paul Murray (talk • contribs) 05:14, 1 May 2013 (UTC)

Pi#Physics isn't good enough for you? --Izno (talk) 12:38, 1 May 2013 (UTC)

Archimedes approximation

The actual method of approximation for pi with 96 gons within a circle of 1 diameter is sin(180/96)*96=3.141031950890509638111352....,correct to 3 digits to the decimal places.Twentythreethousand (talk) 20:18, 11 May 2013 (UTC)

Calculation of Pi with Excel

We propose here to set up and run, on a spreadsheet, the calculation of Pi using the idea of Archimedes to inscribe in a circle the regular polygon with 6 sides (regular hexagon), then (by halving the central angles) one with 12 sides, then 24, 48 and 96 sides, calculating for this a perimeter equal to: " three times the diameter plus a certain portion of it that is smaller than a seventh and largest of 10/71 of the same diameter " which is the approximate value of Pi suggested by Archimedes.

Draw a circle of unit diameter and inscribe in it the regular hexagon. Divide by half the angle AOB through OC, then the angle AOC through OE and continue indefinitely, resulting in the succession of regular polygons of 12, 24, 48, ... etc.. sides, inscribed in the circumference, which associate with positive integers n (n = 1 is associated with the hexagon, n = 2 with the dodecagon, etc..).

The arrow CD of the arc AB, denoted by f, is:

CD = OB-(OB²-DB²)^1/2 cioè:

f₁ = r-(r²-(l₁/2)²)^1/2

where r is the radius of the circle and l₁ the side of the hexagon (r = l₁ = 0,5). It has, in general:

f_n = r-(r²-(l_n/2)²)^1/2

and the lengths of the sides of the polygons are calculated in succession:

l_n+1 = (f_n²+(l_n/2)²)^1/2

Entering formulas in a spreadsheet, as shown in figure (Inserting formulas):

you get the table (Calculation):

The last column of the table contains the succession of values of p_n, the perimeter of the regular polygon of n sides inscribed in the circle of unit diameter. By induction will be lim p_n = Pi as n tends to infinity. — Preceding unsigned comment added by Ancora Luciano (talk • contribs) 16:56, 24 May 2013 (UTC)

This serves no purpose that I can see, rather than using Excel's Pi() or 4*Atan(1) — Arthur Rubin (talk) 19:04, 24 May 2013 (UTC)

The purpose was not to trivially calculate Pi with Excel, but to show an inductive method to get the value of Pi, following the idea of Archimedes. The use of Excel lends itself for this purpose, since the program contains the characteristic automatism of mathematical induction.--Ancora Luciano (talk) 19:55, 24 May 2013 (UTC)

At the risk of irritating Tkuvho, here's a "helpful YouTube video" on this. It does make for a really neat demonstration, in that students with very elementary math knowledge can actually calculate pi for themselves. Not sure how well it could be adapted to the format of an encyclopedia article though. --Joseph Lindenberg (talk) 04:24, 25 May 2013 (UTC)

It would probably fit better in the article Approximations of π, in either the "Approximation with a regular polygon" section or the "Software for calculating π" section. --Joseph Lindenberg (talk) 20:57, 25 May 2013 (UTC)

Eventually it has to end

In theory, pi has to conclude. It is the ratio of a circles diameter to its circumference, and it has to be a rational number. — Preceding unsigned comment added by Dakoolst (talk • contribs) 22:11, 28 May 2013 (UTC)

Hi Dakoolst, you are (falsely) assuming that both the diameter and the circumference can be expressed as rational numbers. Bear in mind that pi has been proven to be both irrational and transcendental. Murray Langton (talk) 07:36, 29 May 2013 (UTC)

This has nothing to do with rational or irrational. The result of division of 1 by 3 is already an unending decimal. Tkuvho (talk) 08:11, 29 May 2013 (UTC)

I think what Tkuvho's saying is that even if Dakoolst proves that

π

is a rational number (by virtue of it being the ratio ⁠circumferencediameter⁠), it might still never end, since many rational numbers like ⁠13⁠ never end. --Joseph Lindenberg (talk) 23:44, 29 May 2013 (UTC)

This is decidedly not what I am saying. Tkuvho (talk) 07:18, 30 May 2013 (UTC)

Sorry, could you elaborate then? (And please realize I wasn't saying that

π

actually is a rational number because it equals the ratio ⁠circumferencediameter⁠. Just saying that even if we accept that flawed logic and say

π

is rational, we still haven't proved that

π

ends. I thought that was your point.) --Joseph Lindenberg (talk) 23:20, 30 May 2013 (UTC)

Since pi has been proven to be irrational, by definition it never concludes. Murray Langton (talk) 06:29, 30 May 2013 (UTC)

Can I remind everyone that this page is for discussing improvements to the content of the article, not showcasing our mathematical skills (or in some cases, ignorance)? AlexTiefling (talk) 07:20, 30 May 2013 (UTC)

π is known to us as irrational, however it must have to end. Whatever a circles circumference/diameter is, that is π. We just haven't fount the ending yet. -Dakoolst 6:19 pacific standard time

Closed RFC on Tau (2pi)

Tau material

I removed two things from the tau section: (1) an illustration; and (2) a sentence about Albert Eagle. The illustration was a bit UNDUE, considering that tau is not used seriously, and an illustration is very suggestive - and also there is a lot of info about pi that is not in this article. The sentence about Eagle was perhaps okay, but was not supported by a cite (at least, I could find no mention of Eagle in the cites). --Noleander (talk) 11:51, 11 May 2013 (UTC)

Eagle's 𝜏=

π

/2 is mentioned on his page which is linked here. There appears to be consensus at WPM in favor of keeping this. Tkuvho (talk) 07:39, 12 May 2013 (UTC)

Uh-oh Noleander. You're an uncooperative tauist now too, for asking that a reference be provided. Neither of the two references on Eagle's page mention it. While I don't see where Tkuvho's reported consensus for keeping it in the Pi article formed, I don't object to having it. But more rabid tauists like Noleander tend to ask that the work of finding a source be done by the person adding the sentence. ;-) Joseph Lindenberg (talk) 11:07, 12 May 2013 (UTC)

@User:Joseph Lindenberg: You are in error. The 1958 book does mention it. One of the relevant pages is given at Albert Eagle. Tkuvho (talk) 11:18, 12 May 2013 (UTC)

If Eagle's own book is the only available source, and that's OK, well then just add that as the reference at the end of your sentence, and we can be done here. Noleander and I are busy people. We've got lots of nefarious tauist plots we need to work on. --Joseph Lindenberg (talk) 11:47, 12 May 2013 (UTC)

Zentralblatt review of Eagle's book also mentions 𝜏=

π

/2. Tkuvho (talk) 12:05, 12 May 2013 (UTC)

I've looked thru the sources and still cannot find where Eagle is mentioned. Can someone provide the source (and quote from the source) here in the talk page? At a minimum, the source needs to be a 2ndary source (not Eagle's own writings); and also the source must connect Eagles tau to the newer 2pi tau (because the text in this article is making that connection, so it would violate WP:SYNTH if sources do not also make that connection). --Noleander (talk) 12:22, 14 May 2013 (UTC)

It may be of interest to record that Oxford University hosted a day school (June 2013) on Tau and Pi. The proceedings are here.Robinwhitty (talk) 21:52, 3 June 2013 (UTC)

Popular culture addition

Edited mention of Euclidean geometry in first paragraph of body

Ref 153

Electronics

Added ref/source and will continue to do so in Electronics section. Many issues in this field NOT covered in physics. Please add references rather than just deleting whole section because of "unsourced"!! I will continue to add sources as I expand. Thanks. Pdecalculus (talk) 01:14, 3 August 2013 (UTC)

It being unsourced was the least of the problems. The main is there is already a section on physics which it largely overlaps with. E.g. the fact that many physics formulae include π because of the circles [and spheres] that occur in physics is the very first mentioned in that section. Coulomb's law is not only mentioned but given, as well as many other examples. The others you mention, Gauss's law and Ampère's circuital law, don't include π. Finally 'outside the scope of this article' should not be used in any article, per WP:SELF. That can easily be fixed, and references can I'm sure be found, but the duplication means it's redundant even if the other problems are addressed. So it needs to be removed. New content could be added to the physics section but I think it is long enough already and does not need more examples.

And please don't describe any other editor, or their actions, as malicious. There is no need to justify every edit with a talk page summary. Per WP:BRD it's normal practice to revert first, and only after go on to discuss it to try and come to consensus.--JohnBlackburne^words_deeds 02:01, 3 August 2013 (UTC)

You're simply wrong on the last two-- pi is prominent in Gauss and Ampere, I did my doctoral dissertation on it 15 years ago, and have numerous cites if you want them. And "that's the least of the problems" is sarcastic, you too can keep it civil. I'm happy to provide 10 pages of specific formula examples in circuits, going back to trade secret uses by HP of voltage signals using pi for numerical methods in CAS. Your argument that it is easier just to delete errors (your correct "self" referential point) also sounds like you're saying our attitude should be not to improve with (in this case, easy) edits, but to delete instead -- is that because it takes more work than just deleting? Or do you have a better reason for not wanting to contribute to the apps topic itself? See the top new "uses" section, in case you want to take the time to write an entire section on many of the missing apps instead of just deleting, you might want to consider the unresolved balance questions in this article before judging. The argument that "there are many apps that aren't covered here" as a reason not to cover them (not necessarily made by you, wonder if you agree) doesn't mean they shouldn't be-- compared to pop culture and "finding more digits" topics, for example. Pdecalculus (talk) 14:18, 4 August 2013 (UTC)

Would it make sense to move the "Physics" section down next to the "Engineering and geology" section, rather than having them separated by the nonphysical "Probability and statistics" section? Perhaps then a combined section title could be considered. Saying that one formula is physics, but another formula is engineering, and a third is electricity, seems absurd to me. Lump them into one section with a title like "Science/Describing the physical world". --Joseph Lindenberg (talk) 02:59, 3 August 2013 (UTC)

OK, I implemented this. Title tweaks are welcome. Maybe "Describing the physical world".

Also, some reordering of the topics might make sense. I'd be inclined to move Coulomb's Law ahead of Heisenberg's Uncertainty Principle, since it's introduced to more students earlier (and is presumably easier to understand). Of course, if a lot more stuff is to be added, then maybe we'd need a different organizational scheme. However, I agree with JohnBlackburne that it's sufficiently long already. Perhaps Pdecalculus could rely heavily on wikilinks to articles like Simple harmonic motion, Fourier analysis, Alternating current, etc. to offer the reader more information without bloating the article. As JohnBlackburne also pointed out though, most of the

π

's in this section are just various byproducts of the area and volume formulas for circles and spheres. Without fleshing out that fact more emphatically, we may just be contributing to readers' inappropriate amazement that the same number magically appears, by coincidence, in so many different physics/engineering/physicalworld formulas. --Joseph Lindenberg (talk) 04:00, 4 August 2013 (UTC)

The example of Heisenberg's uncertainty principle isn't very compelling because the π appears alongside Planck's constant. Its sole function in that formula is to convert the units of h (in Planck's equation) from Hertz to radians/sec. (The real reason π would need to appear in such a formula necessarily involves the Fourier transform. This is what should be emphasized; see my post below.) Likewise in the example of Einstein's equation, it is present to convert G (which is the gravitational flux across a sphere) into a density. So the presence of π in these formulae is not mysterious but ultimately comes down to the system of measurement. (I suspect it's the same story with the statics and fluid dynamics formulae, but these lie outside my own areas of expertise.) I would suggest that all of these applications be condensed into a brief description, with links, possibly describing the role that π plays in them along these lines.

Remarkably, all of these questionable physical applications have been developed seemingly at the expense of a more detailed discussion of the Fourier transform. This is important enough to warrant an independent subsection in the Uses section. Sławomir Biały (talk) 12:08, 4 August 2013 (UTC)

Split the History section just before the computer era?

Fourier transform

Broader "Use" (Applications) Coverage? Need your Opinions!

Please see the electronics discussion also. I added a section on electronics, and had intended to expand it, then add sections on molecular biology and physical chemistry, but an editor kept deleting with "already covered" (not true) as a strategic explanation for deletion, instead of contribution to the section or discussion of the bigger issue of balance.

My general problem with this article is the paucity of "use" coverage and the overbearing corpus of information on finding additional digits! Can we look at the whole article from a 30,000 foot view of balance? If you Google pi in electronics or physics, bio, chemistry, etc. you will find a real opportunity for Wiki to contribute here. I've checked 6 current texts in computational electronics alone, and there are over 33 pages of very important material on pi in that "use" (which probably should be called "applications") alone. This is a subset of the broader, and changing, field of pure vs. applied math, which of course have converged. Instead of a 50/50 balance, the article relegates "use" to a small section, and one which seems the subject of a trend to compress and defeature rather than expand. I'm hoping we have an attitude of supporting STEM in addition to gleefully adding a bunch of pop culture facts that admittedly will help us win at trivia at our favorite pub (not a small benefit), but not ignore topics (like electronics) that themselves make this site itself possible.

Whoever had the idea to add "outside mathematics" had a good idea. That would be the section I'd add apps in chem, bio, physics, electronics, as "outside" probably is intended to mean "outside pure math." I mean, some of the examples of algorithms in the article get beyond math (AND their intended topic of adding digits) and into computational complexity; unless you want to lump the whole field (big O etc.) under "discrete math" (meaning, all the material relevant to IT that high schools no longer teach in the US), or regroup that under an outside math topic of "computing," which it actually is. The distinction is subtle: as soon as I start using pi, even in a compiler equation in Scheme, to produce a model of a molecule, I've transitioned "into" rather than outside of math!! — Preceding unsigned comment added by Pdecalculus (talk • contribs) 15:36, 4 August 2013 (UTC)

I'm happy to put in the work to expand applications in chemistry, biology, physics and electronics if anyone thinks that this would be of value, but with a busy semester of teaching coming up I don't want to do so just to have global deletion if there is no agreement on the need in GENERAL for expanded applications (forget the specifics, they can be built). Pdecalculus (talk) 13:55, 4 August 2013 (UTC)

That π appears in many formulas is not under question. I think the issue is rather how an encyclopedia article on the subject should approach the question of how the number appears in the sciences. An exhaustive (or even vaguely representative) listing of formulas involving π is clearly outside the scope of this article (and probably outside the scope of any reasonable collection of encyclopedia articles). I find the current section on physical applications overly specific at the moment, conveying the formulas without explaining why π appears in those formulas. I think the section needs more of the why, and less of the specifics. Sławomir Biały (talk) 17:08, 4 August 2013 (UTC)

I definitely agree with the thrust of Slawomir's last two sentences here. While I'm not so bothered by having lots of formulas and details and specifics in that section, I think the formulas should indeed be grouped by how they got their

π

. This would be WP:OR until someone finds a source to cite, and my physics is very rusty, but as I recall, there would be just a few groups. For one group of equations, the

π

traces back to plugging in SURFACE AREA OF A SPHERE = 4

π

r² (e.g. Coulomb's Law). For another group of equations, the

π

traces back to PERIOD OF A SINE WAVE = 2

π

(e.g. almost every equation in the undergraduate electrical engineering curriculum).

By the way, List_of_formulae_involving_π might be a better place for someone to experiment initially with a different approach. I'm not suggesting using it as a sandbox, but there are fewer people to object to trying out a new approach on that page. --Joseph Lindenberg (talk) 18:18, 4 August 2013 (UTC)

Was unaware of list of formulas page, it is very cool! Wonder if a "list of applications of pi" would be helpful, not only for the great point JL made about sine periods, but many apps in signal processing and other fields too. Such a list could point back to each specific article that shows the why of use there. Calculations in electronics that get to frequencies can be trivial uses, but voltage/information calculations can be integral to CAS solutions to many math problems that are less trivial. The Hilbert space side is really more related to projective geometry, so the sphere info probably covers it via generalization, with a little inductive reasoning. Pi pops up ubiquitously in some fractal and bio math and p chem, but I didn't want this to become some "golden triangle" myth giving it more importance than due. Thanks for taking the time to opine on balance. Pdecalculus (talk) 00:43, 5 August 2013 (UTC)

Edit request on 19 August 2013

Comment by Freond

History section

Too big?

Incorrect number reported on page????

In the section titled: "Motivations for Computing Pi", you cite Arndt & Haenel who state that 39 digits of Pi are necessary in order to calculate the volume of the known universe to an accurracy of the volume of one hydrogen atom. Being suspicious of this number,I found their book, and they report this number without comment or proof. They cite another paper by other authors, and I have to admit that I did not researtch this paper. Instead, I and a colleague calculated this quantity ourselves, and we determined that 111 or 112 digits are required. I am cutting and pasting our analysis. What do you think?

OOOPS! This page does not support "Equation Editor" in Microsoft Word. This is my very first time I have ever commented on a Wikipedia page, and, as you can tell, I'm not that good at it yet. Is there some way I can attach a Word document? In any event, our procedure was to calculate the volume of the universe twice: Once using an exact expression for Pi, and the second: using (π-δ) where δ is the error one would need in their approximation of Pi to get the required error in the calculation of the volume of the universe. Subtract these two expressions for the volume, this difference in volumes is then set equal to the volume of a hydrogen atom. Solving for δ yields a value of approximately 5 times 10 to the negative 111.

What do you think?

Bob Michaud74.78.5.64 (talk) 13:09, 3 November 2013 (UTC)

Use the search in the archive field at the top of the page. "volume of universe" or "hydrogen" should work as search terms. And of course, it is mentioned in the ToDo list at the top (Edit: now relocated to this page as section "Comment by Freond"--22:07, 3 November 2013 (UTC)). There are relevant discussions in Archive 1, coming up with 270 decimals for volume, Archive 7, where it is discussed that to get the circumference of the universe within one hydrogen radius on needs 37 vs 39 digits, and Archive 11, where it is again pointed out that 39 digits refers to the circumference computations, not the volume.--LutzL (talk) 14:37, 3 November 2013 (UTC)

Use google with search words "pi places universe atom". The Arndt quote seems singular, otherwise it's always about the circumference (and why it is ridiculous if taken seriously, since space is not flat and space-time even less so)--LutzL (talk) 14:58, 3 November 2013 (UTC)

Pi(e) puns

Pi exists?

squaring 180 and the identical pi.

Abraham Sharp's method is directly contradicted

The article's sub-section entitled Infinite series contains the following:

"In 1699, English mathematician Abraham Sharp used the Gregory-Leibniz series to compute π to 71 digits [....]"

This is several years before John Machin's improved algorithmic variations on that series. The subsequent sub-section entitled Rate of convergence indicates that:

The Gregory-Leibniz series requires 500,000 terms to produce [just] five correct decimal digits of π.

The implication of the second statement on the first statement is that Abraham Sharp evaluated the first 50,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 terms. The world's fastest computer would take a lot more than trillions of years to directly evaluate that many terms, so Sharp as he was, I claim there's a contradiction. The second claim is easily verified "manually" by basic error bounding in Numerical Analysis, therefore the pre-Machin-like efforts of Abraham Sharp did not use the Gregory-Leibniz series to directly produce 71 decimal digits of π (or if he did, he hasn't finished yet; he won't have even really got going yet).

Both of the article's statements are cited to a source, but the former is a book I cannot afford, and the latter requires a paid subscription I do not have.

On a related but almost pedantic matter, mathematicians are usually not interested in the number of correct digits in an approximation. The resultant error of an approximation is much more important, and these metrics are not the same thing. As an example of the difference, I have a wonderful approximation for 1. It is the sum of the series of terms where the nth term is defined to be 10^(-3(n-1)) - 10^(-3n). After just three terms, the approximation is 0.999999999 with an error of very nearly one part in a billion. But the number of correct decimal digits is zero, and will stay that way no matter how many terms are taken.
With thanks from ChrisJBenson (talk) 06:32, 11 January 2014 (UTC).

Abraham Sharp used the Gregory series with

z=1/{\sqrt {3}}

, whereas the rate of convergence section discusses the rate with

z=1

. It takes about 300 terms to get 71 correct digits using Sharp's method. (Also, in your example of correct decimal digits of 1, you are ignoring the fact that there is more than one representation of 1 as a decimal. See 0.999....) Sławomir Biały (talk) 13:22, 11 January 2014 (UTC)

Latin and Greek

π as a fraction

In reviewing some of the more esoteric errors in the later sections over the last six months, I had missed a basic mathematical error featured quite prominently in the lead section. Since edit 563172535 on 6 July 2013 at 16:31 by Giraffedata, the third sentence of this article stated that no fraction can be exactly equal to $π$ (the exact wording was: "no fraction can be its exact value"). A full rigourous proof (disproof) of this needs only one counteraxample. Here's a fraction that is exactly equal to $π$ :

{\frac {\pi ^{2}}{\pi }}

I've already reverted the text in the article. This is here just in case a proof was required. With thanks from ChrisJBenson (talk) 07:43, 11 January 2014 (UTC)

The lead used the word fraction before that edit as well . From the context it was quite clear that the text referred to the basic meaning of fraction as any number of equal parts of a whole. It would be more interesting IMO to mention that convergents of continuous fractions can be used to obtain successively more accurate rational approximations of pi, the first one being 22/7, 333/106, and 355/113. Isheden (talk) 09:19, 11 January 2014 (UTC)

I agree that this was not a mathematical error, but rather an ambiguity of wording: "fraction" can either refer to a ratio of integers or a ratio of more general values, and in this context it was clear that the former meaning was intended. There is an issue of WP:TECHNICAL here: we should word things as simply as possible (while maintaining correctness) to make our articles accessible to as wide an audience as possible. "Ratio of integers" is more jargony and less accessible than "fraction". —David Eppstein (talk) 17:55, 11 January 2014 (UTC)

I do not think that a reasonable reader, who is not specifically looking to find such ambiguities in the wording, would interpret fraction as anything other than a fraction of integers given the context. Probably a bigger concern, given the wide readership that an article like this generates, is that "fraction" carries a connotation of being less than one. But since the article already lists 22/7 as an example of a fraction, I do not think there is really any ambiguity in what is intended by the term. Sławomir Biały (talk) 22:21, 11 January 2014 (UTC)

I agree with Chris Benson basically: there is a problem with saying something that is not quite correct on the grounds that everyone can see what is meant. Everyone, that is, who understands what the sentence is trying to say. I also agree that "ratio of integers" is more 'jargony'; so it should be explained, with a footnote perhaps... "ratio of integers [an "ordinary" fraction such as 22/7, or 314159/100000]". Imaginatorium (talk) 06:08, 12 January 2014 (UTC)

I disagree with the implication that it is "not quite correct". It's not really about "correct" versus "incorrect", but rather which phrasing conveys the meaning to likely readers of the article most clearly. I would argue that the former does. Sławomir Biały (talk) 14:07, 12 January 2014 (UTC)

I think it is disingenuous to call this an error, but I have no problem with making the intended meaning more clear by more explicit wording. Dicklyon (talk) 06:41, 12 January 2014 (UTC)

Perhaps Isheden (talk can review his own link. Prior to this edit, the article did not claim that "no fraction could represent $π$ exactly". General (rather than mathematical) dictionaries define a fraction as "a numerical quantity that is not a whole number" (perform a Google search for "define: fraction"). Despite that, please feel free to not call this an error, and instead call it an ambiguity as suggested. My change then has merely removed an ambiguity. With thanks for all the comments, from ChrisJBenson (talk) 22:09, 12 January 2014 (UTC).

A correction: your change has not "merely removed an ambiguity", it has also made the article more technical. I'm not convinced the cost was worth the benefit. But perhaps we can find a wording that is both unambiguous and less jargony. —David Eppstein (talk) 04:52, 13 January 2014 (UTC)

The version before that edit read "such as 22/7 or other fractions that are commonly used to approximate

π

". From the context it was clear that "fractions" referred to the ordinary usage with integer numerator and denominator. Of course an expression such as

π

/1 is also technically a fraction since both numerator and denominator are algebraic expressions, but I agree with David Eppstein that pointing out this makes the lead more technical without any particular benefit. Isheden (talk) 13:47, 14 January 2014 (UTC)

I still believe (and have new empirical evidence locally gathered) that most people have a vague awareness that a fraction in general is not synonymous with common fraction (US) or vulgar fraction (UK), even if they can't remember the precise secondary school definition. I wonder if this is a British/American difference, or perhaps an old/young difference (I am the former in each pair). Some of the comments above seem to indicate that they believe fraction means vulgar fraction in their common parlance. This is not European usage, nor the general dictionary usage in America, nor in Google's default definition, nor in my Collins Pocket (British) English dictionary, the online Merriam-Webster (American) dictionary, nor is it the opinion of the Wikipedia article on fractions. I am sure that the reason for having the definitions common fraction (US) or vulgar fraction (UK) is that they refer to a slightly different concept (a subset) than the more general term fraction. In this csse, vulgar means its old sense of for ordinary folks, not the full mathematical spectrum of meaning. In my long long ago experience of a previous millennium, as well as each of the sources cited above, the term fraction was only restricted to a ratio of integers if explicitly stated as a vulgar fraction (kmown as a common fraction in America). Of course

π

was originally defined as the ratio of a circle's circumference (named periphery by my ancestor William Jones) to its diameter. This can be expressed as the fraction (p/d) and of course will always be an irrational fraction.

In its lead section, the Wikipedia article on fractions explicitly states:

The word fraction is also used to describe mathematical expressions that are not rational numbers.

That article then cites algebraic fractions and fractional expressions that contain irrational numbers, even giving

π

/4 as an example of a fraction.

I should have sought a common ground rewording instead of just removing the sentence. My poorly executed point was that fraction has a wider definition than the common or vulgar fraction that some suggest above. Whether the "average reader" knows this or not, I would prefer not to present a statement that is only true in an unspecified restricted subset. It really surprised me that even if mine were a minority definition of fraction (it isn't), mathematics should err by being too rigorous rather than failing to specify scope. But on to potential solutions. I noted that one commenter above considered a combined change of nothing (restoring wording to the version of 5 July 2013) still made the article more technical. I hope the following is not too complicated. I did some field work and the phrase "the ratio of two whole numbers" was not considered too technical (jargony!) by anybody I asked.

Is the following wording sufficiently non-technical? I find that the brief historical information helps to frame the sentence:

It has been known since 1761 that $π$ is not exactly equal to the ratio of any two whole numbers. Well-known common fractions such as 22/7 are merely approximations to the value of $π$ .

With thanks (and apologies for my lack of grace), from ChrisJBenson (talk) 14:57, 15 January 2014 (UTC).

I gather from your lengthy argument that the term fraction has a broader meaning in mathematics than the term common fraction, which is of course true. To avoid any risk of misunderstanding what is meant in this context, I therefore replaced "fraction" with "common fraction", which is an unambiguous term that is at the same time accessible. In case the reader is interested in the definition of the term common fraction there is a wikilink that may be clicked. One could include "ratio of two whole numbers" within parentheses as well, but that might be unnecessarily technical for the lead section. The various meanings of the term fraction in mathematics have been discussed extensively at Talk:Fraction (mathematics) in the past and the discussion above would be more appropriate to post there. Isheden (talk) 21:52, 15 January 2014 (UTC)

Thank you kindly, Isheden. I kept this comment here to document a further identical edit, as well as a similar edit. Yes I agree with the characterization of your first sentence (in common parlance too). I also like both the solution you present in your second sentence and your pending (self-reverted) edit.

The sentence I misguidedly removed from the lead section appears again with identical wording near the start of the Properties section. I took the liberty of applying your solution (common fraction) there too. Another alternative term simple fraction appears at the start of the Continued fractions section. Simple fraction is yet another synonym for common fraction, vulgar fraction, and rational number. For consistency, I added your term there too, but kept the original words. I have now officially had too much

π

.

ChrisJBenson (talk) 06:48, 16 January 2014 (UTC)

I'm not too keen on the current version of the lead. There is a dangling sentence about approximation by rational numbers that for some reason is on a separate line. I think this should be put back into the preceding paragraph somewhere. (But that might just be me: I personally don't like extremely short paragraphs.) Sławomir Biały (talk) 12:01, 22 January 2014 (UTC)

Agree. I think the dangling sentence should be introduced in the context that there are methods for producing increasingly accurate rational approximations (specifically convergents of continued fractions) of pi, along with a few examples such as 22/7. Based on the discussion above, any occurrence of the term "fraction" should be changed to "common fraction" or "simple fraction". When these plain-language terms are used, it is actually unnecessary to mention "rational number" or "ratio of two integers" since this is what they represent. Isheden (talk) 12:33, 23 January 2014 (UTC)

how to compute with fractions

Tau

Semi-protected edit request on 2 March 2014

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Please change the following text: Two verses in the Hebrew Bible (written between the 8th and 3rd centuries BC) describe a ceremonial pool in the Temple of Solomon with a diameter of tencubits and a circumference of thirty cubits; the verses imply π is about three if the pool is circular.[25][26] Rabbi Nehemiah explained the discrepancy as being due to the thickness of the vessel. His early work of geometry, Mishnat ha-Middot, was written around 150 AD and takes the value of π to be three and one seventh.[27] See Approximations of π#Imputed biblical value.

To this: Two verses in the Hebrew Bible (written between the 8th and 3rd centuries BC) describe a ceremonial pool in the Temple of Solomon with a diameter of ten cubits and a circumference of thirty cubits; the verses imply π is about three if the pool is circular.[25][26] Rabbi Nehemiah explained the discrepancy as being due to the thickness of the vessel. His early work of geometry, Mishnat ha-Middot, was written around 150 AD and takes the value of π to be three and one seventh.[27] See Approximations of π#Imputed biblical value. Rabbi Eliyahu of Vilna (The Vilna Gaon) wrote in his commentary on the Bible that the correct reading of the Biblical text indicates to apply a factor of 111/106 which results in 1.04716981 to the approximate π value of 3. This means that the value of π used in the construction of the ceremonial pool was actually 1.04716981 X 3 which equals 3.14150943. It is accurate to the 4th decimal point. This factor is derived from the extraneous word "koh" (קוה) written in the original Hebrew of 1 Kings 7:23. It is to be pronounced however "ko" (קו). Similarly, in 2 Chronicles 4:2, the original Hebrew is actually written "ko" (קו). The Hebrew letters also have numerical values. (קוה) has a value of 111 and (קו) has a numerical value of 106. 108.2.9.169 (talk) 16:42, 2 March 2014 (UTC)

The edit as suggested is definitely unsatisfactory. The convoluted argument it is trying to describe can be seen a bit more clearly here for example, but the editor's attempt doesn't get this over at all. In any event, the argument is ridiculous special-pleading. Actually I think it would be better to delete all but the first sentence of the quote above. In the Bible there is a description (in a bit about history, *not* mathematics) of a pool about 10 cubits in diameter and 30 cubits around. There is no problem whatsoever with that, because the value of pi is 3 to a first approximation. (If it said the pool was 6 cubits across and 43 cubits around, things would be different.) Imaginatorium (talk) 17:47, 2 March 2014 (UTC)

The international systems of units were not used in the time of King Solomon and it could create some conflicts because they were neither precise nor standard if it was used in today's measurements . I would still say three cubits for pi if I was living at that time.184.148.14.64 (talk) 02:17, 5 March 2014 (UTC)

Ludolphine number honourable mention?

Antiquity Section

Missing informtion

"Foreign" fonts

Edit Request

If under the section "Approximate Value" the first 100 decimal digits are defined as: 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679, then the leading 3 is not considered a decimal digit. In this case, under the section "Polygon approximation era", the sentence: "With a correct value for its seven first decimal digits, this value of 3.141592920... remained the most accurate approximation of π available for the next 800 years." should be replaced with "With a correct value for its six first decimal digits, this value of 3.141592920... remained the most accurate approximation of π available for the next 800 years." — Preceding unsigned comment added by 65.201.161.119 (talk) 15:31, 15 April 2014 (UTC)

I believe there is an issue here, but all this is modulo British/American terminology differences, which are often huge in these areas. In BrE (I was at school 1953-1966), the word for the digits after the decimal point is "decimal place", in which case this should be "six decimal places". But "digit" is a more general word, "decimal digit" is redundant, so I suggest this should be changed to "seven significant figures", which I think is universally correct. I will change it unless someone comes up with a problem. Imaginatorium (talk) 07:59, 23 April 2014 (UTC)

"Decimal digit" is redundant, because of "binary digit", "octal digit" and "hexadecimal digit" are commonly used. "Figure" is misleading: for many people "figure" is almost synonymous of "drawing". "Place" suffers for the lack of an accurate definition. "Digit" or "decimal digit" is the only word that is accurately defined, not only from a graphical point of view (a digit is a specific alphanumeric character), but also as a mathematical concept. The IP user is right, the digits before the dot must be counted. Otherwise, one would need to say that 3 and 2 are two approximations of

π

, both with zero correct digits. Thus, I disagree with Imaginatorium suggestion. Instead, I suggest to simply add "after the dot" after "100 decimal digits". D.Lazard (talk) 08:50, 23 April 2014 (UTC)

Where do we go from here?

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