Talk:Pi/Archive 12

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why the common '59' ending?

i don't see why the last 2 digits, commonly given as 59, were not rounded up to 60. in other words, 3.1416.

sure the number can be stopped at any given point, but to stop it at a high 9 is quite odd. — Preceding unsigned comment added by 75.84.95.229 (talk) 06:55, 8 December 2012 (UTC)

Given all the effort put into memorizing the digits of pi, I think people don't want to cut it off at a point where they'd have to round up, and thus write a digit that doesn't actually belong to pi. You can do that at 3, 3.1, 3.14, 3.14159, 3.14159265, 3.14159265358979, etc. In most daily applications, the 6 significant digits of 3.14159 is plenty, while the 9 significant digits of 3.14159265 is more than necessary, and the 3 significant digits of 3.14 is often not enough. --Joseph Lindenberg (talk) 12:35, 11 December 2012 (UTC)

Also, this article is not the place to explain that rounding may be different of truncating. Therefore to give an approximation of π, it is less confusing to choose a number of digits such that rounding is the same as truncating, like 3.1, 3.14, 3.14159, ... (that is the first digit that is not written is less than 5). On the other hand, choosing five digits, one should have to explain that 3.1416 is the best approximation, and that the last digit 6 does not belong to π (truncating to five digits gives 3.1415). D.Lazard (talk) 13:13, 11 December 2012 (UTC)

interesting replies, nonetheless "approximation" is not the same as accurate digits. in this regard, 3.1416 is clearly better than 3.14159 — Preceding unsigned comment added by 75.84.95.229 (talk) 07:59, 15 December 2012 (UTC)

Sorry, could you define or explain 'clearly better'? I agree with Lazard and Lindenburg that a good choice is a cutoff point which uses an actual digit in the expansion of pi. Murray Langton (talk) 08:46, 15 December 2012 (UTC)

3.14159 lends itself to a rhythmical delivery which allows a poetic treatment: "Let me lay pi on the line: 3.14159" with greater facility than the plonkingly unmusical 3.1416. --Matt Westwood 00:32, 16 December 2012 (UTC)

Yes, but bad poetry is fairly easy to write:

Towards a rhyme we strive
How 'ere we dare contrive
Lest digits we deprive
In short, we will derive
3.1415

(I hereby place this into the public domain.) With that being said, I think "approximately equal to 3.14159" is the best choice for the lede. — Loadmaster (talk) 22:12, 18 December 2012 (UTC)

Rule of seven? Six digits and a decimal point makes seven pieces of information -- and also seven syllables, in English. But perhaps this whole conversation is a bit too much like chatter? It's not like any of this will affect the article -- it's original research all the way! -- Perey (talk) 11:08, 17 December 2012 (UTC)

It wasn't meant to be authoritative and encyclopedic, it was merely another comment adding a little weight into why 3.14159 was better than 3.1416. I hadn't realised how seriously life on twitipedia was supposed to be taken. --Matt Westwood 21:43, 17 December 2012 (UTC)

In this video, Vi Hart is implying that that WP is in violation of of copyright law if Matt Westwood is right: http://www.youtube.com/watch?v=XJtLSLCJKHE . Weird I know, but it might need to be checked out. — Preceding unsigned comment added by Reddwarf2956 (talk • contribs) 13:01, 17 December 2012 (UTC)

Thought I'd made it up off the top of my head on the spur of the moment. Sorry guys. Copyright law sucks. --Matt Westwood 21:43, 17 December 2012 (UTC)

"To ensure compliance with applicable copyright law, please do not sing Wikipedia articles out loud."

There. Fixed. --Joseph Lindenberg (talk) 22:54, 17 December 2012 (UTC)

On a more serious note, the vast majority of people know pi as 3.14. Full stop. So it really makes more sense to use 3.14 in the introduction, so that less-knowledgeable readers aren't initially confused. On the other hand, it's important to immediately inform them that pi doesn't exactly equal 3.14, in case they only read the introduction. --Joseph Lindenberg (talk) 23:53, 17 December 2012 (UTC)

I think this is not a good idea. No doubt many people "know" pi as 3.14, many others as 22/7, still others as "about 3", 3.142, etcetc, all of which are appropriate in some circumstances. But the best way to drive home the fact that 3.14 (in particular) is an approximation is to show a better one. I also thing an encyclopedia should not be full of quasi-legal reduplications such as "approximately but not exactly". So I am reverting to the earlier text. Imaginatorium (talk) 18:23, 18 December 2012 (UTC)

You may be right. I do agree that my wording ("approximately but not exactly 3.14") needed improvement. And it's true that saying pi is "approximately 3.14159" does drive home the point that it's not exactly 3.14. But I think we disagree about how much more common 3.14 is than other approximations like 3.1 or 3.142. (And people who know pi as "about 3" already understand that it's an approximation.) Maybe there's less chance for confusion than I fear though. --Joseph Lindenberg (talk) 19:50, 18 December 2012 (UTC)

If the only purpose of WikiPedia is documenting what "the vast majority of people know", then why bother? Seriously, is anyone going to go to the page on Pi and say, "Bah! This is rubbish! I know pi equals 3.14, what's all this rubbish 159 all over the place?"

When I was at kiddie-school we were at least taught it as "3.1416" and that caused me all sorts of trouble later on when I found out that the 4th digit after the dot was in fact a 5. Similarly, when another teacher told us that pi equals 22/7 I had even greater confusion (he had forgotten to tell us, or didn't know, that 22/7 was in fact an approximation).

It's only a gut-feel, but "3.14159" comes across to me as more informationally enlightening than either 3.14 or 3.1416 - but to go further than that is over-egging it. It may not matter much but I think the extra information conveyed by "3.14159" is more useful it looks on the surface. --Matt Westwood 07:38, 19 December 2012 (UTC)

Not "Bah! This is rubbish!" But rather "I'm not sure I've found the right article. I was looking for information about this number I always hear about as 3.14. But the intro doesn't say anything about 3.14. I know 3.14159 is not the same number as 3.14. So is there a different article about that 3.14 number I vaguely remember from grade school?" OK, maybe I'm underestimating Wikipedia readers. But with a mass-appeal article like this, we shouldn't assume too much of the reader. That said, I'm not convinced I'm right here. Just explaining my thinking. --Joseph Lindenberg (talk) 18:13, 19 December 2012 (UTC)

Yes, I see your point (however confused such readers might be). Somewhere, perhaps in the section on "Approximation", there could be a note about the most common approximations used -- probably, 3.14, 22/7, and just 3, in different context -- and about the possible confusion of these with an exact value. Another thing to add is three dots after the approximation 3.14159... but this can get tricky if it's at the end of a sentence(!) Imaginatorium (talk) 18:00, 20 December 2012 (UTC)

never repeats

Joseph Lindenberg's last edit reminds us of a longstanding problem to which we've never found a very good solution, and perhaps there isn't one. But it's a thorny enough problem that maybe we should talk it out.

Let me get this out of the way first: Wikilinks are not enough. We can't assume people will follow them. So it needs to be as clear and correct as possible in the text itself.

Incomplete list of options, pros, cons:

• never ends and never repeats. This was the version before Joseph's change. Simple and pithy, but susceptible to misunderstanding (the string 381492, for example, presumably occurs an infinite number of times -- isn't that "repeating"?).
• is endlessly long with no repeating pattern of digits. Joseph's solution. Same objection, really — isn't 381492 a repeating pattern of digits?
• is infinitely long and never repeats forever. The shortest solution that I personally actually like. The phrase "never repeats forever" is probably the simplest one that captures the essential two-alternating-quantifier nature of what we're trying to say (for every potential pattern and for every M, there is an N>M such that the decimal expansion of pi at N does not agree with the pattern). It's a little unusual in English, but maybe unusual enough to increase the chance that the wikilink will be followed by anyone confused. Downside: Doesn't 381492 repeat forever?
• is infinitely long and never enters a permanent repeating cycle. Maybe explicit enough, finally, to deal with the 381492 problem, but maybe too awkward to read.

Any better options? Any further opinions on the ones I've listed? --Trovatore (talk) 22:30, 23 December 2012 (UTC)

Of those I prefer the first, but it is imprecise, as is the second, while "never repeats forever" could be read more than one way. How about this which says the same as the fourth but not as verbose or technical?:

• neither ends nor settles into a repeating pattern

--JohnBlackburne^words_deeds 22:41, 23 December 2012 (UTC)

I think it is always best to spell things out. I would suggest:

• "The decimal expansion of pi never settles into a repeating pattern of digits the way rational numbers do. (For example 22/7=3.142857142857142857...)" --agr (talk) 22:51, 23 December 2012 (UTC)

I'm reasonably happy with John Blackburne's suggestion. I think Arnold Reinhold would have a good point if the text were in a section primarily concerned with the decimal representation of pi, but given that this is the lead, and meant to summarize the entire article, I think it gets us a little off-track to belabor the point. --Trovatore (talk) 23:01, 23 December 2012 (UTC)

The problem is not repeating patterns, it is that pi does not sustain a repeating pattern. The Feynman point is an example of why I say this. John W. Nicholson (talk) 23:00, 23 December 2012 (UTC)

What if I changed my version to:

• is endlessly long with no repeating pattern to the digits. --Joseph Lindenberg (talk) 00:06, 24 December 2012 (UTC)

  I think we need the two quantifiers there, never/forever or never/permanently or something along those lines. I implemented John Blackburne's suggestion, amending it to include never/permanently. In my opinion this is better than your latest suggestion, even if you add permanently to it, because a "pattern" could be something other than a permanent repeating cycle. --Trovatore (talk) 00:11, 24 December 2012 (UTC)

To change or not to change?

Currently:

π is an irrational number, which means that it cannot be expressed exactly as a ratio of two integers (such as 22/7 or other fractions that are commonly used to approximate π); consequently, its decimal representation never ends and never settles into a permanent repeating pattern. The digits appear to be, in a certain sense, random, although no proof of this has yet been discovered. More than just irrational, π is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge.

Change to:

π is more than just an irrational number, which means that it cannot be expressed exactly as a ratio of two integers (such as 22/7 or other fractions that are commonly used to approximate π); π is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge. Consequently, its decimal representation never ends and never settles into a permanent repeating pattern. The digits appear to be, in a certain sense, random, although no proof of this has yet been discovered.

Which is better? John W. Nicholson (talk) 00:20, 25 December 2012 (UTC)

The first one. The 'is more than just' is poor style by WP standards, as articles should not foreshadow later text. And it's unnecessary complex. It's an irrational number. It's also a transcendental number. That one implies the other is beyond the scope of this article; readers unsure of the terms can follow the links to see what each means. --JohnBlackburne^words_deeds 01:04, 25 December 2012 (UTC)

Please feel free to make suggested changes. All I am doing is seeing a way to bring the two ideas closer together with the "irrational" statements. No real change in the wording. I will agree that the hyperlinks makes the "which means that..." and "a number that is..." comments unnecessary. However, the "The transcendence of" comment might need more explanation if these are taken away. John W. Nicholson (talk) 01:45, 25 December 2012 (UTC)

P.S. Are we not just stating what is later talked about more thorough? John W. Nicholson (talk) 01:50, 25 December 2012 (UTC)

OEIS references

Just a reader's note about the OEIS references. As I was reading the article these generated a "what the hell is this" reaction. I initially wondered if it was vandalism, but checking it out it seems to be legit. However, the current presentation doesn't give the impression that this is a link to external "See also" type material. If, like me, a reader doesn't know what OEIS is then the way the link is provided is unhelpful. I would like to see it changed to be less jarring and more informative. For example if the rollover showed the title of the target site ("On-Line Encyclopedia of Integer Sequences") then it would immediately become clearer what you could expect to go to (currently you only get this if you happen to roll over the oeis icon). It should possibly use external reference form, although it is true that it goes to a known wiki so maybe that might be unnecessary. It would have been helpful to me if it had looked more like: (see also xxxx). Jontyla (talk) 16:42, 31 December 2012 (UTC)

Pi value has changed

Please add the following :- But now a simple man Mr.Lakshman Gogawale a man has changed this quest.Read the following article:- Matriculate mathematician says he’s nailed down the Pi quest

Monday, July 23, 2012 AT 11:05 AM (IST)

PUNE: If you think it takes a degree from a fancy college to make your mark, well, then think again. And meet Laxman Gogawale. Gogawale, a city-based amateur mathematician who is a mere matriculate, has claimed to have cracked the mystery associated with the number Pi - the mathematical constant specifying the ratio of a circle's circumference to its diameter. What makes Gogawale's claim particularly extraordinary is that his research is being published by the International Organisation of Scientific Research (IOSR) in its May-June edition of its journal of Mathematics. “For the last three years, I was working on demystifying the mystery of Pi. I showed that the exact value of Pi is 17 minus square root of 3 or 17 minus square root of 192. The Pi value discovered by me is 3.1435935394, which is more than the existing value by 0.002000888587,” he told Sakal Times on Thursday. Gogawale said his findings were based on numerous geometrical constructions, arithmetic calculations and algebraic formula and proofs. The 49-year old 'math wizard', who stays in the Dhankawdi area along with his wife and daughter, has around a dozen books to his credit that help students to overcome phobias which so often are related to the subject of Mathematics. Gogawale's students include not only schoolchildren, but also candidates preparing for competitive examinations like MPSC and UPSC as well as bank employees among others. “I could not pursue formal education post SSC, but my deep liking for mathematics never waned at any point in my life,” says Gogawale, who has developed many simple but effective tricks to shorten lengthy mathematical calculations, memorise the annual calendar and perform abacus calculations with ease. “I have covered schools from around 25 districts in Maharashtra and shared whatever little knowledge I have with them. I often tell students, no subject can be as intriguing and interesting as mathematics is, provided they shed their phobias,” he said. Dr A L Deshmukh, a retired mathematics teacher from Laxmanrao Apte school, who has been acquainted with Gogawale for a long period of time, spoke highly about the local mathematician figuring in international journal like IOSR. “It is indeed a prestigious thing to get your research published in IOSR, which is an institution of international repute. Gogawale is the epitome of extraordinary will power, with which he braved all odds to pursue his interest in the field of mathematics,” he told Sakal Times. Or see here

                                                                             With regards-
                                                                          Advait Nandeshwar
                                                                             advait_30

Advait 30 (talk) 14:10, 18 December 2012 (UTC)

Firstly, this looks like a conflict of interest; we are not here to facilitate the self-publishing of your results.

Secondly, I hate to break it to you, but you're wrong. You say that "I showed that the exact value of Pi is 17 minus square root of 3 or 17 minus square root of 192" - but these two values are not even equal to each other. But more than that - as described in our article, von Lindemann proved that Pi is transcendental, and both your values are algebraic. AlexTiefling (talk) 14:17, 18 December 2012 (UTC)

Not done: Due to concerns already stated by User:AlexTiefling. This seems self-published and not accurate. Vacation^nine 14:37, 18 December 2012 (UTC)

(Off topic, but...) Approximations of the form described above are π ≈ n − √m, or m ≈ (n − π)², with n and m as positive integers; the author above selected n=17 and m=192. (His choice of n=17 and m=3 does not even come close.) Better approximations can be found, e.g., n=24 and m=435, resulting in an error of 0.00175⁺, which is still a rather large difference from true π. — Loadmaster (talk) 18:38, 19 December 2012 (UTC)

(Further off topic, but...) $\pi \approx 17-{\sqrt {192}}=17-8{\sqrt {3}}.$ — Arthur Rubin (talk) 18:29, 3 January 2013 (UTC)

completely random

OK, on to the next sentence of the lead: Current version says:

They appear to be completely random, although no proof of this supposed randomness has yet been discovered.

Now, the radix representation of a normal number is pretty random, but as an opponent of lies to children I have to object to calling them completely random. The decimal representation of pi is certainly not, for example 1-random in the sense of algorithmic randomness. So how do we get the point across without raising the — justified — objection in a reader's mind: "How can they be random if I can generate them deterministically, with a simple computer program?" --Trovatore (talk) 23:46, 23 December 2012 (UTC)

Yes, and the same time explain why "Spigot algorithms" are not making a type of polynomial? John W. Nicholson (talk) 00:09, 24 December 2012 (UTC)

Let's stay focused on the problem at hand, which is hard enough. Remember we're talking about the lead, and every word is at a premium. --Trovatore (talk) 00:12, 24 December 2012 (UTC)

Alright, here's my best effort so far:

They appear to be, in a certain sense, random, although no proof of this fact has yet been discovered.'

The (admittedly weaselly) phrase in a certain sense warns the reader not to over-interpret the claim of randomness, whereas the complicated stuff goes in an explanatory footnote. What do you think? --Trovatore (talk) 00:54, 24 December 2012 (UTC)

Off-topic — anyone know why the <references /> tag isn't working on this page? --Trovatore (talk) 01:01, 24 December 2012 (UTC)

I like it. Just change "They" to "The digits" to fit with the preceding sentence. --Joseph Lindenberg (talk) 01:19, 24 December 2012 (UTC)

Maybe: The digits appear to be, in a certain sense, randomly ordered, although no proof of this fact has yet been discovered. --Joseph Lindenberg (talk) 02:04, 24 December 2012 (UTC)

That looks good to me, although we should lose the bold in the note, articles are not the place for arguments. Martin Hogbin (talk) 10:33, 24 December 2012 (UTC)

What bold? You mean the italics? Those are not intended to be argumentative — they're just meant to keep the reader from skipping over the word "not", which I think might be easy to do, especially in the smaller font. --Trovatore (talk) 11:02, 24 December 2012 (UTC)

Yes, sorry. I am still not sure that we need any emphasis. Even the 'definitely' is superfluous in my opinion. Just stating the facts is more encyclopedic; we can only hope that the readers read what we write. Martin Hogbin (talk) 12:40, 24 December 2012 (UTC)

I don't know; you might be right. At the moment it looks better to me this way, but I just wrote it; I wouldn't be surprised if I'd feel differently in six months. In any case it's a minor point and I won't fight about it if you want to change it. --Trovatore (talk) 12:45, 24 December 2012 (UTC)

Maybe Pseudorandom number generator? John W. Nicholson (talk) 02:50, 24 December 2012 (UTC)

The word "fact" being used for an unproven mathematical observation? I thought those are called a conjecture? John W. Nicholson (talk) 12:28, 24 December 2012 (UTC)

Or we could just drop the word 'fact'. It still makes sense. Martin Hogbin (talk) 13:29, 24 December 2012 (UTC)

How about dropping "of this fact"? This would make it "The digits appear to be, in a certain sense, random,[note 1] although no proof has yet been discovered." — Preceding unsigned comment added by Reddwarf2956 (talk • contribs) 13:39, 24 December 2012 (UTC)

I can agree to that if people insist. As I say below, I think there's little doubt that it's true, though no proof has been found (and for all I know, none may exist), so I think "fact" is fine, but I can see how (for example) formalists could object to it. --Trovatore (talk) 19:30, 24 December 2012 (UTC)

I would prefer something like "no statistical test has yet been found that distinguishes the digits of pi from a random sequence of digits." We should also give the paragraph under "Properties" that discusses the randomness of pi its own heading and perhaps expand it to include various definitions of randomness. The mention in the lede should link to that section.--agr (talk) 13:59, 24 December 2012 (UTC)

Well, your first sentence isn't, strictly speaking, true (consider the statistical test that compares the digits to the digits of pi — the digits of a random number will agree 10% of the time, whereas those of pi will agree 100% of the time). None of the usual definitions of "randomness", so called, apply to pi, but normality almost definitely does, even though this has not been proved (this is why I think "fact" is actually fine). But at the level of the lead I'd prefer to use the commonly understood "random" rather than introducing a less-understood technical term like "normal", as long as we explain ourselves adequately. --Trovatore (talk) 19:30, 24 December 2012 (UTC)

I don't think comparing a sequence with itself can be considered a statistical test of randomness. Pi isn't random by standard definitions, the only practical use for calculations of pi beyond a few dozen digits that I am aware of is to serve as constants in cryptographic algorithms because the have random-like properties but are unlikely to have been selected for hidden weaknesses. And as far as I am aware, the normality criterion applies to any irrational number produced by ordinary computation e.g. roots of polynomials, exponentiation, definite integration, all with rational coefficients, exponents and integration limits. We shouldn't oversimplify these issues in the lede.--agr (talk) 13:25, 25 December 2012 (UTC)

Update: I have incorporated the "fact" suggestion and the one about italics. --Trovatore (talk) 22:49, 24 December 2012 (UTC)

Thanks John W. Nicholson (talk) 23:10, 24 December 2012 (UTC)

I've restored the lead wording to something that is more encyclopedic and readable. "in a certain sense" is too weasely to be in the lead; and footnotes are just plain ugly there. Reader that want to know about the various definition of random (and whether or not pi meets them) can read the body of the article or click on the "normal number' link. The lead is simply a summary of the body ... the lead is not required to explain every nuance and caveat. --Noleander (talk) 20:03, 4 January 2013 (UTC)

The lead is not permitted to be wrong. No lies to children in Wikipedia, ever!

Explanatory notes are a good thing and we should use them more (well distinguished from citations), because they allow the main flow to proceed while making readers aware of aspects that may appear to go against some interpretation of it. --Trovatore (talk) 21:28, 4 January 2013 (UTC)

The word "random" has many definitions, depending on the context. Many reliable sources make statements like "the digits of pi are random" or " .. appear to be random". If the lead mimics those sources, it meets the Verifiability requirement. The lead currently uses the term "statistically random" which should provide plenty of specificity. The body of the article can and should explain the subtleties of what random means in relation to pi. This topic was discussed thoroughly during the Featured Article review last year, and the simpler wording passed the FA review after a great deal of scrutiny. --Noleander (talk) 21:36, 4 January 2013 (UTC)

There is really no mathematically accepted definition of unqualified "random" (or even "statistically random") that pi meets. It (probably) does meet the definition of normality, but we don't want to bring up that technical a notion, in line, in the lead. However I think an explanatory note is a nice compromise, giving a clear warning (unlike a wikilink), but not requiring the uninterested reader to pay attention to that warning. I did not bother to follow the FA discussion (those tend to be incredibly boring debates about hyphens versus endashes and density of inline cites and so on); my concern is that this important article be accessible, but not say anything mathematically untrue. --Trovatore (talk) 09:43, 5 January 2013 (UTC)

I find the explanatory foornote to be a bit overmuch. I don't see a problem with leaving "statistically random" as a blue link to normal number. Sławomir Biały (talk) 14:58, 5 January 2013 (UTC)

The Case for Tau (latest)

"The reason why Tau is a fundamental number is because it is the Identity Operator for Rotation. Pi is lacking in such fundamental utility. Tau is as fundamental to Rotation as Zero is to Addition and One is to Multiplication."

That quote is from a Usenet post to sci.math from last night. The full thread has much more info and is available here: https://groups.google.com/forum/#!topic/sci.math/VEjcIEmP4pc

I was not involved in the decision here on this article where Tau got banished to a redirect: Tau_(2π). It is clear to me that the consensus was critically mistaken. That Usenet thread shows how Tau is a distinct concept from Pi. It is not merely a choice of style or preference.

The current state of this article is as broken as whoever decided to merge the article 1 (number) with Unity_(mathematics). These are distinctly different concepts. There's an infinite set of numbers that can be scaled to Unity, yet only one of those is the Number 1. Unity is a property that the Number 1 inherently has, but that does not make them the same thing. And we can also examine the Prime Quality that the Number 1 has. Everyone is clear that the Number 1 is not a Prime Number. But I expect that there are few who can articulate the exact reason behind this separate categorization. I gave the explicit reason in my second post on that sci.math thread (linked above). In a nutshell, Unity is a property that is inherent to the Number 1, and that property is far more fundamental than the property of being Prime. The Number 1 is not confused with the set of numbers that have Prime Quality. It is so much more fundamental because of its inherent Unity Property that it is not even included in the set of Prime Numbers.

The situation we have today is that the majority of the math community is failing in recognition of the fundamental quality that Tau has, yet Pi does not have. You cannot rotate by Pi and get the same returned. Tau does have this Rotation Identity Quality.

Our job as Wikipedia editors is to select the references that hold up to our highest ability of reason, and reject those that do not make the cut. Or at least relegate them to a footnote when there is a significant level of ignorance among the public at large that chooses for whatever reason to cling to the deficient memes. Pi is destined to become a footnote of history, and we can turn that corner here. The references since 2001 have become increasingly prolific. All we have to do is arrive at the consensus to simply use them.

My recommendation here is to split out the articles, Tau_(2π) and Pi. There is plenty to rebuild the Tau article as a separate and distinct concept, which it is. I also recommend that the articles 1 (number) and Unity_(mathematics) be split back out. This is not like the distinction between Anti-Differentiation versus Integration, or Anti-Addition versus Subtraction, or Anti-Multiplication versus Division. Those are examples of pairs of separate concepts that happen to function in an identical way. In those cases, it makes perfect sense to have only one article. But the distinction between Tau versus Pi, or 1 versus Unity is a fundamental issue of distinctly different concepts that have distinctly different properties and act with distinctly different functions. To merge such articles, and then not even identify nor communicate that distinction is to willfully remain in a state of ignorance. And that grates against the reason why we have Wikipedia, and the reason why we all use it.

The astronomy community can achieve consensus about the most rational position with regard to the notion of Pluto as a planet. The Tau - Pi issue is a challenge to the math community to find inspiration from their example in order to jettison historical baggage that we have inherited with 3.14159...--Tdadamemd (talk) 23:12, 2 January 2013 (UTC)

WP:FRINGE says that what the mathematical community overwhelmingly does governs what Wikipedia covers. That said, we have an article Turn (geometry) that is about 360 degree rotations and that might be a more appropriate target for a Tau (2pi) redirect.--agr (talk) 17:15, 3 January 2013 (UTC)

Only if we redirect Pi to the U-turn article. --Joseph Lindenberg (talk) 20:54, 3 January 2013 (UTC)

To follow up on agr's comment, we do not judge "reason", we judge what is accepted in the appropriate professional community. In addition, in quantum mechanics, 4π seems to be more basic than 2π. This is a minor point, but should be mentioned wherever Tau (2π) ends up, either in Turn (geometry) or here. — Arthur Rubin (talk) 18:23, 3 January 2013 (UTC)

And all the n-sphere surface areas and volumes (including the 4π in 4πr² and the 4/3π in 4/3πr³) come from just repeatedly multiplying by 2π/n
Joseph Lindenberg (talk) 00:39, 4 January 2013 (UTC)
The formula coefficient at each curved red arrow's tip equals the formula coefficient at that arrow's tail times the factor in the arrowhead. --Joseph Lindenberg (talk) 03:09, 4 January 2013 (UTC)

The value of the mathematical constant that people are starting to call "tau" has more related to it than just Turn (geometry). Therefore, it should have its on page. This is why I have started to write a page, see Talk:Tau (2π), which needs to be farther edited on this issue. Someday it might be called tau, but for now it is just the ratio constant of a circle's circumference to radius.

Sorry Arthur Rubin, but I have not heard anyone say that they though 4π (2τ if you like) is more fundamental than 2π (τ). However, I have seen 4π being used with surface area of a unit sphere and twice the period of τ and that said, there has being use a lot of use but this is nothing basic.

John W. Nicholson (talk) 20:35, 3 January 2013 (UTC)

Only a tiny fringe group of people are doing this. I consider this usage to be non-notable, and its promotion to be distorting and irrelevant. AlexTiefling (talk) 21:03, 3 January 2013 (UTC)

@AlexTiefling Where is this "tiny fringe group of people are doing this" which I am assuming you mean calling "4π seems to be more basic than 2π"? I have not heard of this until now. John W. Nicholson (talk) 00:59, 4 January 2013 (UTC)

@Joseph Lindenberg, The "N SpheresVolumeAndSurfaceArea" illustration does not explain what it is clearly. So, what is it? And, why is it important? John W. Nicholson (talk) 01:43, 4 January 2013 (UTC)

There's a more thorough description on my website sites.google.com/site/taubeforeitwascool in the section titled A Different Pair of Formulas for Every Dimension. Basically, people sometimes argue that neither 2π (the coefficient of the circle circumference formula) nor π (the coefficient of the circle area formula) is fundamental outside of 2 dimensions. Circles are the set of all points a distance r from a center point IN TWO DIMENSIONS. What's so special about 2 dimensions? Why not consider 3 dimensions? or 4? or 5? In 3 dimensions for example, you have 4π (the coefficient of the sphere surface area formula) and 4/3π (the coefficient of the sphere volume formula). Why not call one of those fundamental? It's a good argument, until you notice that all of these different coefficients are related in a very simple way that involves 2π. --Joseph Lindenberg (talk) 02:29, 4 January 2013 (UTC)

Simple rotation is movement in a 2-D plane.

@agr (ArnoldReinhold) above...

I fail to see how Tau counts as a fringe theory. If you click the link you provided to the Wikipolicy, you find this definition:

"We use the term fringe theory in a very broad sense to describe ideas that depart significantly from the prevailing or mainstream view in its particular field. For example, fringe theories in science depart significantly from mainstream science and have little or no scientific support."

There is not a single scientist who can prove that Tau is wrong or mistaken. I'm not even aware of a single person attempting to prove Tau is erroneous. The primary "controversy" is simply which ratio is better to use. And any push here among editors to establish separate articles for Tau and Pi can be done with having absolutely nothing to do with telling anyone which one they should use. So there is no Fringe. Not even a controversy. We are simply debating whether it deserves a separate article, or whether it is best to keep the merge.

And notice that this very same Wikipolicy, further down, directs us that it is proper to have an article about Moon Landing Hoax Theories, even though not a single reputable scientist supports that. (I can say that with certainty, because the moment a credible scientist voices support for Apollo Hoax, they instantly lose their credibility.)

So the point is not whether Tau is used by enough members of the math community. It could be used by a total of Zero mathematicians on the entire planet, yet it is still notable enough for a separate article because the concept has been thoroughly and broadly established.--Tdadamemd (talk) 04:38, 4 January 2013 (UTC)

"We are simply debating whether it deserves a separate article, or whether it is best to keep the merge." With that in mind, and noticing that there are credible pages which are for separate mathematical constants (for example Gelfond's constant), which has fewer page-hits than Tau_(2π) and 2π combined, I say that this page needs a formal split. By having a Request for comments be made and the new split page be called "Ratio of circumference to radius" (C/r). With all hyperlinks to pi which deserves to go to C/r be changed to reflect this split and make links for the readers of any first use of 2pi 2π within a page to pi and second use to have a hyperlink to C/r. John W. Nicholson (talk) 08:42, 4 January 2013 (UTC)

The theory that tau is better than π perfectly fits the WP definition of fringe theory given above: the mainstream view in science is to use π as one of the main mathematical constant and millions of people (students, searchers and engineers) use π without knowing anything about tau; on the other hand, tau is supported only by few people that are not recognized by any established scientific community. Moreover the theory that tau is better than π does not have any scientific support, being based only on aesthetic arguments (some formulas look better).

This discussion has already occurred here. The result of this deletion discussion was keep with the following comment "Thus, the administrative action here is to close the discussion as keep. However, I see a strong consensus that the article should be renamed or merged somewhere, and given the degree of participation here I am prepared to call this a local consensus to the effect that, while notable, the topic is best addressed within another article." The current of state of redirecting "tau (2π)" to a section of π article is the result of this "local consensus".

D.Lazard (talk) 11:23, 4 January 2013 (UTC)

No, that is not what is being discussed. What was discussed was if tau was fringe by a definition that a few of you defined outside of the Fringe:WP that Tdadamemd pointed out. In other words there was no reason for removing the Tau (2π) page because other than you (as a group) don't like it. This is wrong, and should not be done. It only makes the people who do support the issue talk, change, and cause unending problems for a page, pi, that really does not deserve this. Go look at what has been wrote so far on my User:Reddwarf2956/Ratio of circumference to radius page. This is the direction that I am going for: a page for a mathematical constant which is used in math, science, engineering and other fields. So, it might not be as popular as pi, but it is really used. Go look at it. John W. Nicholson (talk) 18:13, 4 January 2013 (UTC)

I don't always use tau Arthur, but when I do, I prefer that it represent dos π.
--Joseph Lindenberg (talk) 02:15, 5 January 2013 (UTC)

More nonsense from the Tauists (WP:EGG intended). The use of τ for 2π is uncommon, even among people who use τ, and WP:FRINGE. The proposal to use a named constant for 2π is just uncommon. — Arthur Rubin (talk) 22:29, 4 January 2013 (UTC)

The Pi WP:EGG is the intended guess. Because my page is not an WP:EGG, nor does it mention &tau except to make a "In popular culture" statement or even much of 2π, I do not see how you can talk about WP:FRINGE. It is focused on C/r = 6.283185307179... and where it is used, its history, and other things. Saying that C/r is fringe is really like saying pi is fringe because it is not as important as one. Tell me do know why there is a page on the square root of 535.49165552476473650...? It gets fewer hits than Tau (2π), yet don't see you calling it fringe and going around demanding it deleted. Please, just stop it, your point is just pointless. John W. Nicholson (talk) 01:59, 5 January 2013 (UTC)

Hello, my 2-cents. I'm not a mathematician, but I was following articles while surfing, and ended up on the "Pi-Day" one. When reading about Tau I was curious, and followed the link http://en.wikipedia.org/wiki/Tau_%282%CF%80%29#In_popular_culture. I ended up in the "Popular culture" part of "Pi", where Tau is mentioned in a very brief paragraph. I didn't immediately realize the article was ABOUT PI, NOT about Tau, so I scrolled up a bit to find context, then had to scroll more, until I realize I'm reading about Pi. In short - I understand the diatribe regarding "Pi or Tau" (and I find it interesting), but I propose a (short) page be dedicated to Tau so one interested in Tau effectively read information regarding Tau when searching for it. If one gets curious about Pi, links at the bottom will be provided as "additional reference" or similar. For example, I was more interested in WHY Tau is proposed as an alternative, but did not (easily) find any explanation. THAT could be a good way to start a dedicated "Tau" page... ;) .--David Be (talk) 23:37, 4 January 2013 (UTC)

Wikipedia used to have something like that, David. Here ya go: en.wikipedia.org/w/index.php?title=Tau_(2%CF%80)&oldid=481819644 --Joseph Lindenberg (talk) 23:53, 4 January 2013 (UTC)

I would like to say I am sorry that you cound not find what you were looking for, David. I hope that we, as editors, will soon have another page which will be useful for you, David, also. I feel your 2-cents is just one of the many other Wikipedia customers who try to view the page Tau (2π) but get redirected like a WP:EGG. The problem is that there is to much pious advocacy for pi WP:NOTADVOCATE and not enough neutral point of view WP:NPOV. Until this is changes the existence of a page on the number 6.283185307179... is questionable. So, I hope you will join us and help us make a new page about this constant and which would include information about tau. I have start a page User:Reddwarf2956/Ratio of circumference to radius, but it needs help with the edits from others before I think it is OK to 'publish' if you will. And then I will need a lot of people agreeing that it is a valid and good page which needs to exist (that is where you come in).

In the mean time, try looking at [[1]] and the related links there.

John W. Nicholson (talk) 01:26, 5 January 2013 (UTC)

I think it is important that the mathematics does not get lost in the nominology here. Statements above such as "...the Tau article as a separate and distinct concept, which it is." are simply wrong, mathematically: Tau is precisely another name for the value 2pi, just as pi is precisely another name for the value tau/2. In fact, mathematically, I think it is important to point out (in the pi article) that in a sense the choice of pi as the "named" constant is quite arbitrary and historical, and that mathematics would be unchanged (except for notation) if a name had been assigned to 2pi or pi/4*. Quite naturally, then, there _should_ be a mention on the pi page of the tau naming suggestion.

• I think we should call pi/4 kappa, which would at least be more hellenically informed than the 'tau' idea.

Imaginatorium (talk) 05:31, 5 January 2013 (UTC)

I agree with Imaginatorium when they say, '...I think it is important to point out (in the pi article) that in a sense the choice of pi as the "named" constant is quite arbitrary and historical, and that mathematics would be unchanged (except for notation) if a name had been assigned to 2pi or pi/4'

It is also equally important to note that whatever the arguments may be, we are stuck with Pi as the named constant that is likely to be used by mathematicians for the next few centuries at least. The reason it is unlikely to change is, exactly as Imaginatorium points out, that it really does not matter that much either way. What is certain though is that Pi is the constant universally used by mathematicians today and that Tau is almost never used.

All this shows the logic of restoring the Tau article where a rather pointless but extant argument of which is the 'best' constant to name can be expounded. Apart from a few short sentences, this article, and its discussion page, can then be reserved for the only Pi-based constant that is actually used by mathematicians today. Martin Hogbin (talk) 10:47, 5 January 2013 (UTC)

If I'm reading you correctly, I tend to agree: There is probably enough material on tau as a social phenomenon for an article. But that's what the article should be about. It should not be about mathematical aspects that are not different in any important way from mathematical aspects of pi. (That doesn't mean it can't have any math in it — the arguments used by the tauists, and some by their opponents, have mathematical aspects, and those aspects are fine for the article.) --Trovatore (talk) 10:54, 5 January 2013 (UTC)

It looks like we agree, there never was much of a consensus to delete the Tau article anyway. There is a social phenomenon worthy of an article and there is no reason that it cannot mention the reasons that its supporters prefer it to Pi but we must take care that it does not become a promotional or discussion article for Tau. Martin Hogbin (talk) 20:10, 5 January 2013 (UTC)

Explanatory notes should be separate from citations

Their purposes are quite different, sometimes almost opposite. A citation is intended to show where the material came from and how to check it out. An explanatory note (which is something we should do more of) is intended to give extra information that might be excessively wordy to readers not interested in that level of detail. The reader should not have to go all the way down to the notes section to find out which it is. --Trovatore (talk) 03:14, 8 January 2013 (UTC)

The MOS does not mandate one convention over the other. See WP:CITEVAR. Articles may separate citations from notes; or integrate them. Either is fine. Many FA-class articles integrate citations with notes. Most top-class books also do so. When this article reached FA status, the convention established for this article, without dissent, was to integrate cites with notes. If an editor, such as yourself, wants to propose changing the convention to separated, you may do so (I suggest an RfC) but please provide a compelling reason. Absent a compelling reason, stylistic changes are not encouraged in WP, because it leads to endless disputes over relatively unimportant matters. See WP:RETAIN. When it comes to stylistic choices: the best policy is to stick with whatever was first presented in the article, and instead focus on substantive changes. --Noleander (talk) 03:28, 8 January 2013 (UTC)

A substantive change that would benefit from the separated notes is the explanatory note for the claim that the digits of pi are "random", which is not strictly speaking true in any accepted meaning of that word. You claimed the note was "unencyclopedic", which I think was just wrong. I do take note of Sławomir's opinion on this, however, so I'm less inclined to fight over it than I would be without that — but the problem with his take is that wikilinks should be completely ignored when calculating whether what the text says is misleading or not, as we can't assume that people will follow them (or even see them, as the article may be in print form). --Trovatore (talk) 03:34, 8 January 2013 (UTC)

I agree with you that explanatory footnotes can be a great benefit to readers. I'm a big fan of them. I agree with you that adding an explanatory footnote about random/normal/algorithmically predictable/etc is a great idea. I'll even help you write it. The only point I'm trying to make here is that the stylistic convention for this article is to put both citations and explanatory footnotes in a single subsection (for reasons explained in WP:RETAIN and WP:CITEVAR). WP has a shortage of editors, so it is better if we work together on improving content rather than arguing the merits of one style vs another. --Noleander (talk) 03:39, 8 January 2013 (UTC)

Proposed explanatory footnote

Trovatore: Here is the footnote you originally had:

The decimal expansion of π is not algorithmically random, because it can be produced by a computer program. However, the digits appear to be distributed much as those of a random number are, as measured by simple statistical tests. See normal number.

I think that is pretty good. Here is another variant that may be useful:

The term "random" has several meanings within mathematics. The digits of π are not algorithmically random, because they can be predicted by algorithms which generate digits of pi. However, the digits of pi appear to be normal, which is a kind of statistical randomness.

Feel free to put a footnote like either of these in the body where the normality property is discussed. I'd avoid putting this footnote in the lead because the stylistic convention for this article is to avoid footnotes in the lead. --Noleander (talk) 03:45, 8 January 2013 (UTC)

It seems to me that explanatory notes in the lead are a separate issue from citations in the lead. I agree with banning citations from the lead (plenty of time later — the lead summarizes the body so if you doubt the claim or want to know where it comes from, find it in the body and then find the citation there). Explanatory notes, especially ones that explain that what's said in the flowing text is not quite true, are a different issue — if you don't read the the rest of the article, you may never find out that it's not quite true. That strikes me as a significantly stronger justification for a footnote than impatience to give the citation is. --Trovatore (talk) 04:17, 8 January 2013 (UTC)

"Algorithmically random" is a WP:OR neologism, that is not used in algorithmic. On the other hand, the article on random numbers is incomplete, as centered on a single randomness test. The property of the digits of π is much stronger than that: none of the known randomness tests allows to distinguish π from a true random sequence (see Knuth's book for the discussion of this matter). Thus, if a footnote should be added, I propose something like

The digits of π are not a true random sequence, as they can be produced deterministically by an algorithm. They form a pseudorandom sequence that the known randomness tests can not distinguish from a random sequence.

On the other hand, the need of a footnote comes from the use of "statistically random", which is incorrect here. I propose to rewrite the sentence of the lead as

The digits appear to be randomly distributed, although no proof of this has yet been discovered.

D.Lazard (talk) 08:23, 8 January 2013 (UTC)

π does not form a pseudorandom sequence because it can be easily distinguished from a truly random sequence by a simple computer program (that compares the sequence to π). I like the rest of your suggestion, though. Nageh (talk) 09:57, 8 January 2013 (UTC)

By definition, a pseudorandom sequence is not random and is generally generated by a deterministic algorithm/program called pseudorandom number generator. Thus a pseudorandom sequence is not random because two runs of the program (with the same starting point) generate the same sequence. This is exactly the case of the digits of π which form a pseudorandom sequence. The only reason for not using π in pseudorandom number generators is the lack of an algorithm giving quickly the ith digit without computing all the preceding ones. D.Lazard (talk) 10:27, 8 January 2013 (UTC)

I think Nageh is using the cryptographic notion of PRNG. --Trovatore (talk) 10:29, 8 January 2013 (UTC)

Even the weaker notion of pseudorandomness AFAIK involves the use of an unknown (secret) seed value to the pseudorandom generator. Since there is no seed in a π computing algorithm the output cannot be claimed to be pseudorandom. Anyway, a reference to such claim will surely settle this dispute. Nageh (talk) 10:48, 8 January 2013 (UTC)

I like Lazard's suggestions for both the body/footnote & the lead; with the exception that I concur that the word "pseudorandom" could be improved since (even tho technical correct?) it may confuse some readers who equate pseudorandom with a modulus-based computer algorithm. --Noleander (talk) 15:29, 8 January 2013 (UTC)

I went ahead and implemented Lazard's suggestion for the lead "The digits appear to be randomly distributed, ...". Anyone should fee free to revert if they are not happy with it. --Noleander (talk) 15:55, 8 January 2013 (UTC)

Monte Carlo methods

I am looking at the section "Monte Carlo methods" and wondering if any of the 'dots' of the sector overlap? In other words, can (x_n,y_n) = (x_m,y_m) for any n ≠ m? John W. Nicholson (talk) 21:05, 9 January 2013 (UTC)

If we are talking about continuous coordinate values the probability of this happening is zero. But it wouldn't hurt if there were an overlap, you just count the dot that many times. Nageh (talk) 09:47, 10 January 2013 (UTC)

The article does not say if continuous coordinate values are used or not. Should it? Should it explain that it does not matter also? Also, I see copying rotating by π/2,π, and 3π/2 (from center) as to have a way to use the same 'dots' 4 times. Does this change anything? John W. Nicholson (talk) 12:41, 10 January 2013 (UTC)

The method describes a practical experiment: in reality we generally assume measurement values to be continuous. But it really does not matter whether they are continuous or discrete, just count any overlapping dots as many times. So, no, I don't think any additional explanation is necessary. Neither is for rotating the setup. Nageh (talk) 13:05, 10 January 2013 (UTC)

Should the article explain the connection with pie?

Especially since the pi/pie homophone doesn't exist in many countries. I hadn't noticed this omission until Hyuganatsu's oddly-explained edit. The "pie aren't squared, pie are round" joke might be worth mentioning and explaining too, since it's so (painfully) common. --Joseph Lindenberg (talk) 03:46, 15 January 2013 (UTC)

Another oddity is the lack of radius. Does any one know why there is nothing stating π = C/(2r)? --John W. Nicholson (talk) 08:49, 15 January 2013 (UTC)

Sign your posts please, John. I signed the one above for you so people don't think it was part of my post. --Joseph Lindenberg (talk) 04:31, 16 January 2013 (UTC)

Sorry, and thanks. I do wish there was an autosign and save button. John W. Nicholson (talk) 11:27, 16 January 2013 (UTC)

This is the English Wikipedia. Explaining that pi and pie have the same pronunciation in English seems over the top pedantic. Editions in other languages can choose to include the Delft pie image or not, and explain it or not, as they see fit.--agr (talk) 22:36, 17 January 2013 (UTC)

The popular culture association of π with pie is what I meant should be mentioned in the article. Maybe you're right though about not needing to explain that their identical pronunciation is why this association exists. --Joseph Lindenberg (talk) 00:07, 18 January 2013 (UTC)

I do think that the pronounciation, if mentioned, should be moved out of the image caption at least. Sławomir Biały (talk) 13:06, 22 January 2013 (UTC)

I think the current caption, with a link to homophone, strikes a reasonable balance.--agr (talk) 15:43, 22 January 2013 (UTC)

Edit request on 23 January 2013

There is a minor discrepancy between two paragraphs (the final paragraph under the heading "Polygon approximation era" and the first paragraph under the heading "Infinite series". The numbers referring to the year when Jamshid al-Kashi beat the previous record number of calculated digits of pi do not match. One number is more specific than the other. I suggest replacing the phrase "around 1930" with "in 1924", to match the date given in the previous paragraph. 131.156.137.14 (talk) 02:53, 23 January 2013 (UTC)

Those years are not in the article. I guess you mean 1430 and 1424. PrimeHunter (talk) 03:15, 23 January 2013 (UTC)

Appears to be fixed now. --Jnorton7558 (talk) 01:08, 24 January 2013 (UTC)

Talk:Tau_(2π)#Redir_to_article_where_topic_is_actually_discussed

Please see Talk:Tau_(2π)#Redir_to_article_where_topic_is_actually_discussed John W. Nicholson (talk) 02:57, 23 January 2013 (UTC)

Recent discussion of this issue has all taken place here on this Talk page. Let's not scatter the discussion to multiple places. --Joseph Lindenberg (talk) 03:29, 24 January 2013 (UTC)

William Oughtred

Referring to π, the article states,

"The Greek letter had been used earlier for geometric concepts. For example, in 1631 it was used by William Oughtred to represent the half-circumference of a circle."

The source is Pi Unleashed, p.166, which says,

"In his Clavis Mathematicae Oughtred used the symbol π to denote a length equal to half the circumference of a circle and the symbol δ for the half a diameter when he established the proportion 7:22 = δ:π = 113:355"

But the source mischaracterizes what Oughtred actually wrote in Clavis Mathematicae. I think a better characterization is found in Pi: A Source Book, which says that Oughtred,

"designated the ratio of circumference of a circle to its diameter by π/δ. π and δ were not separately defined, but undoubtedly π stood for periphery and δ for diameter."

--Joseph Lindenberg (talk) 12:17, 27 January 2013 (UTC)

It looks like at least two spots in the book talks about 113 and 355. One is page 66 (looks like in section 16) the other is pages 100 and 101. Because I do not know Latin, I can not read it. It looks like there is talk about both π/δ and δ/π in section 16. John W. Nicholson (talk) 20:57, 27 January 2013 (UTC)

Yes, I was indeed referring to page 66 of Clavis Mathematicae. (I think that's section 18 though, not 16.) I do see what you say about Oughtred using 355/113 on pages 100-101, but he doesn't use π or δ there. Page 66 seems to be what Pi Unleashed is referring to. While I don't read Latin either and would appreciate someone who does chiming in here, it seems pretty clear to me that Oughtred has written something along the lines of,

    If in a circle with 7/22 = δ/π = 113/355 then
    δ/π = 2R/P (P=periphery)  and  π/δ = 1/2P/R (R=semidiameter)
    δ/π = R2/CircularArea     and  π/δ = 1/4P2/CircularArea
    δ/π = 2R3/CylinderVolume  and  π2/δ2 = 1/4P3/CylinderVolume
    δ/π = 4/3R3/SphereVolume    and  π2/δ2 = 1/6P3/SphereVolume
    δ/π = 2/3R3/ConeVolume      and  π2/δ2 = 1/12P3/ConeVolume

where Oughtred's π/δ is our modern-day π = 3.14... --Joseph Lindenberg (talk) 22:06, 27 January 2013 (UTC)

Clearly something is wrong with the Volumes. If Oughtred's π/δ is our modern-day π, then Oughtred's π²/δ² is our modern-day π² and there is no talk about the height of the cone or cylinder. John W. Nicholson (talk) 02:26, 28 January 2013 (UTC)

It appears to be assumed the height is 2R. All the formulas check if that's the case. And it's a classic geometry problem. The thing is, Oughtred isn't using π to denote half the circumference and δ for half the diameter, as Pi Unleashed claims. He's just saying, in the second quoted line above, that their ratios are equal. --Joseph Lindenberg (talk) 02:53, 28 January 2013 (UTC)

Here is another source that describes Oughtred as using δ/π to represent diameter/periphery. Just to clarify some dates, while Clavis Mathematicae was first published in 1631, the two sources I've provided seem to indicate this use of π first showed up in the 1647 edition. --Joseph Lindenberg (talk) 06:06, 28 January 2013 (UTC)

This gives a short but extremely complete explanation. --Joseph Lindenberg (talk) 06:54, 28 January 2013 (UTC)

The above page is somewhat mysterious: who is David Darling, and where did he get his "Encyclopedia of Science" from? No source is shown, and the article is a masterpiece of illogic. It claims: "[Oughtred] first used the name "pi" for the number 3.141... He wrote it π.δ,..." (What exactly is the referent of "it"? pi? So he wrote "pi" as something else, which hardly counts as "writing pi".

Anyway, here's my take on the original page (my Latin is very rusty). I do not think he uses (.) for division (seems very unlikely if only because it later became a symbol for multiplication; remember the raised dot convention is American). I think the :: is the proportionality symbol, which I remember from a schoolboy pocketbook long lost. Usually you write a:b::c:d for "A is to B as C is to D". Of course this means that A/B = C/D, but it is not quite the same thing. I write pi and delta for the Greek letters, for simplicity.

   If in a circle it be that 7:22 :: delta:pi : 113:355 then

I don't know exactly what this means, since both sets of numbers are different approximations, but it obviously refers to the ratio of diameter (in Greek, abbreviated to its initial letter) to periphery (ditto).

   delta : pi :: 2R : P(eriphery)  and  pi : delta :: 1/2 P : R (R=semidiameter)

This line really appears to be a map from Greek terms (which would presumably have been standard, since the Greeks did geometry) to Latin terms, but in Greek he's using "periphery", in Latin "radius", glossed 'semi-diameter'. In no way does pi stand for the ratio p/d, since it clearly stands for 'periphery'.

For example, looking at the right-hand bit of the last but one:

   pi2 : delta2 :: 1/6 P3 : S(phere [volume])

This is a very odd sort of Greek-Latin equivalence, since the pi on the left is essentially the same as the P on the right, but it comes out right when you cancel them. Anyway, it seems to me that this is (if anything) evidence that Oughtred had no notion at all of writing a symbol for the ratio pi/delta or P/2R. Imaginatorium (talk) 17:17, 29 January 2013 (UTC)

Reason for π?

In the Name section is this:

"In 1748, Euler used π in his widely read work Introductio in analysin infinitorum (he wrote: "for the sake of brevity we will write this number as π; thus π is equal to half the circumference of a circle of radius 1") and the practice was universally adopted thereafter in the Western world."

My question is on the mathematical clarity of why. Why is π "equal to half the circumference of a circle of radius 1" and not "equal the circumference of a circle of radius 1"? In other words, what mathematical reasons, not historical reasons, does pi have for being half of the ratio of circumference to radius and not the ratio of circumference to radius?

Why is there no mention of this? Why is there no mathematical representation of π to the radius except for this quote?

After one reads the Name section these questions above come to mind. Should there be a section which answers them?

John W. Nicholson (talk) 14:17, 5 January 2013 (UTC)

• Why Euler did choose to give a name to half the cicumference and not to the whole circumference? Only Euler could answer if he were yet alive! It may be the subject of a Ph.D. thesis on history of mathematics to try to answer this question. Unless if this historical research has already been done and published, this is not the work of WP editors to solve this question; it would be WP:OR. D.Lazard (talk) 14:40, 5 January 2013 (UTC)

Euler was only responsible for popularizing the convention of using the greek letter π to represent 3.14. The convention of focusing on 3.14 instead of 6.28 was solidly established long before Euler.  (Diameter is physically easier to measure than radius, so ancient people who never did math more complicated than C = 3.14∙d or C = 6.28∙r focused on 3.14.)  I suspect that Euler did realize the 6.28 number would be more appropriate for mathematicians to use but wasn't bothered by it enough to try and change that convention. --Joseph Lindenberg (talk) 21:18, 5 January 2013 (UTC)

I see no basis for a claim that 6.28... would be more appropriate for mathematicians to use. There are numerous important formulas where π appears without a factor of two, the area of a circle for example, or the volume of the n-sphere. Indeed Euler's celebrated formula e^iπ = -1 is a sharper result than e^i2π = 1, the former trivially implies the latter, but the latter does not imply the former. One could just as well argue that π/2 is a better choice for a fundamental constant since perpendicularity is so central to geometry. There is some arbitrariness in the choice. Mathematics would survive if any multiple of π were chosen to be honored with a symbol, or indeed if no standard symbol existed. But a choice was made long ago and it's not going to change, even if there were a good reason. --agr (talk) 13:35, 6 January 2013 (UTC)

• Well, that was a nice opinion. No facts, complete opinion. The volume of the n-sphere is addressed in the section 5.1 "Surface area and volume of a hypersphere" in the Tau Manifesto, and it is illustrated by Joseph Lindenberg on this page. When you say "Indeed Euler's celebrated formula e^iπ = -1 is a sharper result than e^i2π = 1, the former trivially implies the latter, but the latter does not imply the former.", as far as I can tell you are just stating an opinion. While I can see the point that you trying get across with τ/4, the argument falls apart when state as I did. Namely, the perpendicularity of a quarter turn. One of the solid statements in geometry is the intersection of two lines. The sum of all of the angles is not τ/4, τ/2, or anything else except τ. Every angle makes two statement at once. One is the interior angle the other is the exterior angle, these add up to be τ. So, when you are talking about the perpendicularity of τ/4 you are ignoring the exterior angle. The solid foundation of a lot of mathematics is the unit circle where x^2 + y^2 = r^2 = 1. (Note: no 'd', for diameter, here.) Yes, dimensions higher than 1 have perpendicularity, but that is more than just geometry.

In my opinion, the reasons for the needed change is multilevel. On one level you have people learning what angles are and how they are measured them, they tend to be confused with the needless added factor of 2 which just adds miscommunication. It is just like calling 1 a prime number (which took some time but did change). While reading "Mathematics would survive if any multiple of π were chosen to be honored with a symbol, or indeed if no standard symbol existed." I can not help but think 'why "multiple of π" when π is defined as a fraction of C/r?' And with this thought, I think about all of the discoveries which are made by treating thing different. For example, defining i as square root of -1. By removing this factor of 2 and using tau, new and unsought ideas and mathematics may come forward. Third, beauty. Some say e^iπ = -1 is beautiful, but it hold a nasty -1 which only says that you have gone halfway around. While e^iτ = 1 is clean and complete. There is more, but it is, as of now, just opinion.

We need to recognize that your opinion and my opinion does not matter to the Wikipedia audience and what they are looking for. Are they looking for your or my opinion? No. So, what are they looking for? See David Be's comment above and you get an insight as to what one is looking for. We should think about and build upon this. John W. Nicholson (talk) 00:26, 7 January 2013 (UTC)

• The 1/2 in the area of a circle formula has been explained to death — by integration, by sector area = 1/2θr², by multicolor rolling-up triangle, by limit of polygon area = 1/2·apothem·perimeter. N-spheres haven't gotten as much attention, but the simple pattern illustrated above (all formulas are just the result of repeatedly multiplying by 2π/n) seems more fundamental than the traditional formula involving a gamma function. Yeah, e^iπ = −1 holds more information than e^iτ = 1, but if we used η = π/2 then e^iη = i holds even more information. There's no limit to how far down that road you could go. Eta proponents could scoff that pi doesn't even get you to an imaginary number. It's certainly true that convenience arguments can be made for subdivisions of any basic unit. If we used tau/24 we could label common angles (30°,45°,60°, etc.) without fractions. Some have even suggested we should use tau/360. But as one of my favorite silly analogies goes, even though many people choose to buy dill pickle halves, cucumbers don't naturally grow that way. --Joseph Lindenberg (talk) 00:47, 7 January 2013 (UTC)

That Euler's formula e^iπ = -1 is a sharper result than e^i2π = 1, is not a matter of opinion. The first implies the second. The second does not imply the first. Just knowing e^i2π = 1 tells you nothing about e^iπ, e^iπ/2, or e^iπ/4, for example. They could all be one as well. Far from being "ugly," the -1 in Euler's formula provides important information. It not only answers the question of what value e^iπ takes, it rules out e^iπ/n being one for all positive n. Indeed it lets you easily compute values like e^iπ/2, and e^iπ/4 directly.--agr (talk) 20:01, 7 January 2013 (UTC)

No it doesn't. That's why I said there's no limit to how far down that road of subdividing 2π you could go. You can always just square the second equation to get the first, but not vice versa:

e^i2π = 1 is implied by, but does not imply, e^iπ = −1

e^iπ = −1 is implied by, but does not imply, e^iπ/2 = i

e^iπ/2 = i is implied by, but does not imply, e^iπ/4 = 1/√2 + i/√2

and so on and so on. (OK Trovatore, I think we're done now. Sorry.) --Joseph Lindenberg (talk) 00:08, 8 January 2013 (UTC)

• • Guys, please: This started out as a legitimate question about Euler's motivation, a possibly relevant point to mention in this article, or in a split-out tau article (about the phenomenon) if one is ever resurrected. It now seems to have devolved into an argument about whether the tauists are right, which is absolutely off-topic at talk:pi. --Trovatore (talk) 20:21, 7 January 2013 (UTC)

Agreed. Tau is very much a fringe position, and I see no advantage to its inclusion or further promotion in this article, and I'm very tired of its recurrence on this talk page. Pi is what the world uses. That's all. AlexTiefling (talk) 21:02, 7 January 2013 (UTC)

My comment is equally to both sides. It is reasonable to discuss what reasons historical figures had for making one choice or another, because that is a potentially useful addition to this article, or to the tau one if it's split out again. But this is not the forum to discuss whether mathematics should switch to tau — either why it should or why it shouldn't. --Trovatore (talk) 21:19, 7 January 2013 (UTC)

OK. I completely agree with D. Lazard that Euler's motivation is unknown. So while the most obvious explanation to me is that he was just adhering to the long-established convention of giving 3.14... special status, he never explicitly said that. And unless somebody locates scholarly writings on the question, Wikipedia forbids us from connecting the dots ourselves. But yeah, defining pi as half the perimeter of a circle of radius 1 does seem really odd. Which is why I think Euler must have known that 3.14... was an inelegant choice. But history had already made that choice, and like quite a few mathematicians today, he wasn't bothered enough by the imperfection to try and change it. --Joseph Lindenberg (talk) 22:56, 7 January 2013 (UTC)

While I agree with the above comments by Joseph Lindenberg, I see a problem. Namely, if there is *no* real mathematical reason *not* to have a page for tau, then by default the reason stated by David Be and others is the reason to have page for tau. By which I mean -- people are looking for it. There is no doubt that the period of the sine and cosine is the mathematical constant that looks like it will be named tau. The diagram above by Joseph Lindenberg uses 2π. You can argue the name of the constant, but the constant still exist and is found in many places. So, unless a consensus agrees to take-in everything that can be wrote about tau as a constant and place it in pi, I do not see how this current situation is WP:NPOV with 6.283185307179.... Plus, it does not make sense to keep the two constants together because of the same reason the pages half, one, two ... exist. They are different values with different identities and usefulness. Just look at A058291 of the OEIS and ask yourself why would it be inside the page with pi when this is a sequence for tau = 2pi = 6.283185307179.... Clearly, the arguments to hold them together are getting silly. It is time to end this shotgun wedding. John W. Nicholson (talk) 05:12, 8 January 2013 (UTC)

The full surrounding text from where Euler introduces the symbol π shows he was just following the convention of his predecessors, who had gone to great length to calculate the 3.14 number:

       Therefore we may put the radius of the circle or the whole sine to be = 1 and it is
clear enough that the periphery of this circle cannot be expressed exactly in rational
numbers; but by approximations the semi–circumference of this circle has been found to be
             = 3, 14159 26535 89793 23846 26433 83279 50288 41971 69399 37510
                  58209 74944 59230 78164 06286 20899 86280 34825 34211 70679
                  82148 08651 32823 06647 09384 46+
    for which number for the sake of brevity I may write as
                                                π,
    thus so that there shall be π = semi–circumference of the circle, whose radius = 1, or
    π will be the length of the arc of 180 degrees.

Notice that Euler starts out considering the full circumference (periphery) of a circle with radius 1 and declares this number is irrational. Euler is talking about 6.28... here, not 3.14... But then he pivots to acknowledge that the semi-circumference of this circle "has been found to be" a very impressive string of 128 digits. This particular approximation was calculated by Thomas Fantet de Lagny and was the best available at the time. No doubt it was the result of enormous effort, and like earlier attempts by other mathematicians, focused on the 3.14 number rather than the 6.28 number. Euler was just following the tradition of his predecessors here. --Joseph Lindenberg (talk) 23:14, 10 January 2013 (UTC)

"Therefore"? (Something had to be stated before this.) How about afterwards? Just guessing, the first used of 2π happens on the next page?

I am still surprised by fact that he did not calculate 6.2831853071795... from this number and say 'for the sake of brevity I may write as π, thus so that there shall be π = circumference of the circle, whose radius = 1, or π will be the length of the arc of 360 degrees.'

--John W. Nicholson (talk) 02:00, 11 January 2013 (UTC)

There was actually nothing but a short chapter intro ahead of this. Here's the full chapter 8 pdf. --Joseph Lindenberg (talk) 02:33, 11 January 2013 (UTC)

Thanks. It looks like I nailed it with my guess.--John W. Nicholson (talk) 04:32, 11 January 2013 (UTC)

In 1706, on the very same page as the first use (ever in history) of the Greek letter π to represent circumference/diameter, William Jones made it clear he understood that people had locked their attention on the 3.14... number a very long time before him:  (And Euler wasn't even born yet.)

Therefore the (radius is to 1/2 periphery, or) diameter is to the periphery, as 1.000... to 3.141592653 5897932384 6264338327 9502884197 1693993751 0582097494 4592307816 4062862089 9862803482 5342117067 9+. True to above a 100 places; as computed by the accurate and ready pen of the truly ingenious Mr. John Machin. Purely as an instance of the vast advantage arithmetical calculations receive from the modern analysis, in a subject that has been of so engaging a nature, as to have employed the minds of the most eminent mathematicians, in all ages, to the consideration of it. For as the exact proportion between the diameter and the circumference can never be expressed in numbers; so the improvements of those enquirers the more plainly appeared, by how much the more easy and ready, they rendered the way to find a proportion the nearest possible. But the method of series (as improved by Mr. Newton, and Mr. Halley) performs this with great facility, when compared with the intricate and prolix ways of Archimedes, Vieta, Van Ceulen, Metius, Snellius, Lansbergius, etc. Though some of them were said to have (in this case) set bounds to human improvements, and to have left nothing for posterity to boast of. But we see no reason why the indefatigable labor of our ancestors should restrain us to those limits, which by means of the modern geometry, are made so easy to surpass.

--Joseph Lindenberg (talk) 05:45, 14 January 2013 (UTC)

• This still leans on the subjective observational history and not the objective math like the circle equation. It seems there is nothing that can be solid on this footing. I am guessing again;is 2π used in the next page or two? John W. Nicholson (talk) 16:25, 15 January 2013 (UTC)

The link I gave above has the full 304-page work. --Joseph Lindenberg (talk) 00:30, 16 January 2013 (UTC)

For whatever it's worth, I've found that the very first time Euler used π, in his 1736 Mechanica, chapter 3, proposition 34, corollary 1; he used the traditional definition of circumference/diameter. --Joseph Lindenberg (talk) 08:42, 6 February 2013 (UTC)

Pronunciation

why do you call it PAI? in greek it is pronounced PI (like your letter, pee) — Preceding unsigned comment added by 94.69.0.179 (talk) 18:18, 31 January 2013 (UTC)

Because English spelling is like that, full of irregularly spelled and pronounced words.--JohnBlackburne^words_deeds 19:18, 31 January 2013 (UTC)

And celebrating March 14 by consuming π would make for a very different holiday. --Joseph Lindenberg (talk) 11:16, 1 February 2013 (UTC)

Apologies for indulging myself in a short off-topic remark, but surely the answer is obvious and indeed contained in the question: We don't pronounce it like p because then it would be confused with p. Some English speakers pronounce φ as "fie" and some as "fee", but we all say "pie", for precisely this reason. --Trovatore (talk) 03:05, 7 February 2013 (UTC)

This article should refer to Daniel Tammet

The Wikipedia article Daniel Tammet says that Tammet holds the European record for quoting pi to the most digits, and says that he cited pi to 22, 514 digits - this is surely worth mentioning in this article. ACEOREVIVED (talk) 16:47, 7 February 2013 (UTC)

Maybe that fact would be appropriate for the Piphilology article, which is devoted to memorizing digits of pi. This pi article is a top-level overview, which should probably mention the world record, but not the records from individual continents. --Noleander (talk) 16:55, 7 February 2013 (UTC)

Thank you for the feedback. I have put the information in that article.ACEOREVIVED (talk) 21:14, 7 February 2013 (UTC)

Edit request on 27 January 2013

Small change: In the "rate of convergence" section, it says: ".. can get as close to π as desired. It converges quite slowly, though – after 500,000 terms, it produces only five correct decimal digits of π." This should be changed to read "50,000" terms or "six correct decimal digits". This is due to the number of terms being (10^n-1)/2 with n the number of decimal places. Thank you. 161.73.12.43 (talk) 16:38, 27 January 2013 (UTC)

Isn't 500,000 six decimal digits? It seems like 50,000 is only 5 digits. Banaticus (talk) 19:55, 10 February 2013 (UTC)

500,000 gives the approximation correct to five digits to the right of the decimal point. See the cited source. Sławomir Biały (talk) 22:37, 10 February 2013 (UTC)

Bible Error discussion

There is an interesting dicussion here about the so-called Bible error from First Kings, ch 7. maybe it could be referenced or included in the discussion. http://www.purplemath.com/modules/bibleval.htm — Preceding unsigned comment added by 173.181.26.18 (talk) 21:45, 29 January 2013 (UTC)

The article is not mathematically interesting, and looks awfully like special pleading. The writers of the bible used a perfectly good rough approximation of pi as 3. So nothing to include. Imaginatorium (talk) 08:00, 30 January 2013 (UTC)

This is not new. I myself wrote something along the exact same lines in 1991 (here), based on what I read in Petr Beckmann's A History of Pi about Rabbi Nehemiah's writings in his Mishnat ha-Middot on pi. The trouble is finding credible references that seriously consider (from a scholarly point of view) this as a plausible explanation. — Loadmaster (talk) 21:01, 30 January 2013 (UTC)

A much more extensive treatment of this topic is in Approximations of π#Imputed biblical value. Maybe where it's discussed in this article, we should just use a "See also" wikilink to that. I actually think this subject would fit better at Biblical inerrancy#Scientific and historical criticism or Science and the Bible, since biblical inerrancy is really why most people are interested in it. --Joseph Lindenberg (talk) 16:24, 17 February 2013 (UTC)
I went ahead and added the wikilink. I'll let others (Noleander?) decide whether to scale back what's in this article to just a general statement about people having tried to explain away the bible discrepancy. --Joseph Lindenberg (talk) 00:42, 18 February 2013 (UTC)

Without Tau

Here is a paper which does not talk about tau, but it is criticial of pi:

http://math.unipa.it/~grim/Quad18_Kupkova_08.pdf

"In fact, if they really want to follow the curriculum and at the same time support students understanding, the only manageable way of using radians is the π = 180° equivalence. So, in students understanding, radians have nothing to do with the length of the arc on the unit circle."

John W. Nicholson (talk) 13:55, 10 February 2013 (UTC)

I didn't really see it as being critical of pi. Wouldn't their argument still apply if everyone were using tau? Maybe I didn't examine the paper closely enough, but what they seemed to be criticizing was how radians are introduced to young students as just another arbitrary-size angle unit. That we teach π radians = 180° the same way we teach 2.54 centimeters = 1 inch. Just a pointless alternative unit with a messy conversion factor, as far as the students are concerned. --Joseph Lindenberg (talk) 15:09, 17 February 2013 (UTC)

New article on Tau

I have started a new article on Tau, which can be found here. Tau is the definition of a notable WP:FRINGE theory. According to WP:Fringe in a nutshell,

Fringe theory in a nutshell: To maintain a neutral point of view, an idea that is not broadly supported by scholarship in its field must not be given undue weight in an article about a mainstream idea. More extensive treatment should be reserved for an article about the idea, which must meet the test of notability. Additionally, when the subject of an article is the minority viewpoint itself, the proper contextual relationship between minority and majority viewpoints must be clear.

My article constitutes a "more extensive treatment". I think my sources clearly demonstrate notability, and I can dig up more if we need them. I think I have the proper contextual relationship between tau and pi.

I want to move this article to the article namespace, however given the history and controversiality of this topic, I think gaining consensus here first would be wise.Tazerdadog (talk) 18:10, 27 January 2013 (UTC)

We've already had this discussion, I don't see that your article introduces anything new; it just has far more advocacy. One of the major problems with older versions of the previous article was it painted it as a serious controversy, with significant proponents on either side. In reality there are a handful of people pushing it and no-one opposing it as there's nothing to oppose.--JohnBlackburne^words_deeds 21:11, 27 January 2013 (UTC)

So are you claiming that my article fails Neutral point of view or Notability? I want a substantial, neutral article on this topic, and will gladly remove any bias or invite another interested editor to do the same. I thought I had enough perspective in the article to avoid "advocacy". If you would like to suggest or make any changes, feel free to do so - they would be greatly appreciated. Note: While I personally believe tau is probably a better constant, I don't think it makes a significant difference Tazerdadog (talk) 21:54, 27 January 2013 (UTC)

The discussion is here, where all the arguments were thrashed out in detail. And as some of your article is copied from that before it was merged I think you should be aware of it.--JohnBlackburne^words_deeds 22:37, 27 January 2013 (UTC)

JohnBlackburne, the talk at the link you provided are not a neutral point of view and the decision to merge was unclear at best. Because the talk here indicates this not the correct place for this, again NPOV, I highly suggest that with this page is moved to the User:Tazerdadog/Tau_(Proposed_mathematical_constant) talk page and talk about it. Show the editor some respect, look at it, and comment on how to improve it. I think a lot of people who thinks this should be separate article have been hushed for to long. John W. Nicholson (talk) 00:19, 28 January 2013 (UTC)

The discussion was a standard Wikipedia Request for Comment. The consensus was that the article should be merged to Pi. That's how Wikipedia works, by consensus. No-one was 'hushed', everyone had their opportunity to participate in the discussion. Re-read the discussion if it is unclear to you, I think the closing administrator summarised it well.

This need not be permanent; it may be Tau becomes independently notable one day. But I don't see it now, in particular in this draft article which seems to include much the same content as the previously merged one, not least as some of it is directly copied.--JohnBlackburne^words_deeds 01:00, 28 January 2013 (UTC)

It has become notable. See comments by David Be above, just for what he was looking for, this alone, throws out your argument. If you wish talk about this more please continue at User:Tazerdadog/Tau_(Proposed_mathematical_constant) with valid arguments for or against the writing which is there. John W. Nicholson (talk) 01:46, 28 January 2013 (UTC)

Notability requires significant coverage in reliable sources that are independent of the subject. And as far as I can see the only sources that satisfy that are the same sources that were in the merged article (in fact these are some of the content copied and pasted from that article). So there is nothing new establishing notability.--JohnBlackburne^words_deeds 03:04, 28 January 2013 (UTC)

I couldn't have said it better myself. Notability requires significant coverage in reliable sources independent of the subject. I think my article meets that criterion. If you disagree, by all means let's get a third opinion. I will see if I can't substantially rephrase the content to be different, I wrote everything but the in popular culture and history stuff from scratch. I will rework those parts when I get time. Tazerdadog (talk) 06:42, 28 January 2013 (UTC)

I could also find more sources if that is the issue. They are plentiful, and do exist. However, I think that the article would not benefit from their inclusion, as it is a little cluttered with sources as it is, and every statement that in my editorial opinion should be referenced is referenced (if you disagree on this, let me know on my draft's talk page so I can source them). Tazerdadog (talk) 06:48, 28 January 2013 (UTC)

It might help the tauist case if you could get your facts a bit more accurate. There is no new proposed new constant, only a proposed new name for an existing constant. That is how mathematics works: as a matter of fact, if you write a mathematically interesting and useful book about 2pi using 'tau' to refer to it, people will buy it and read it -- idiosyncratic notation is egregiously OK in maths. I plan to add something to the pi article mentioning the 'tau' suggestion at some stage, and pointing out that the choice of pi as the named constant is mathematically arbitrary (but historically concluded). Apart from the obvious fact that you could choose to name the ratio p/d (pi=tau/2), p/r (2pi=tau), p/4r (pi/2=tau/4) or (my favourite) the ratio of a circular arc centred on one vertex of an equilateral triangle through the other two vertices (=pi/3=tau/6='beta'), the fact that pi is transcendental means that the algebraically interesting structure (Q[pi] = Q[tau] etc) is the same anyway. In other words the (mathematically) interesting properties of pi and tau and beta and the rest are the same anyway. But I need some time, and help... Imaginatorium (talk) 06:50, 28 January 2013 (UTC)

The claim made by Hartl, Palais, and other tauists is not that 2π/𝜏 is a new constant with any new properties, or that it changes mathematics in any way. The claim is that formulae are expressed in a cleaner, beautiful, or more aesthetically pleasing manner when using tau. I will make a note to edit the page to make perfectly clear that the math is the same regardless of your choice of circle-constant. Tazerdadog (talk) 07:42, 28 January 2013 (UTC)

As the only truly dissenting voice appears to be JohnBlackburne, I am going to go ahead and move my article to mainspace in about 24 hours unless someone else objects. I have reviewed everything you have presented, JohnBlackburne and I feel that current local consensus on the draft is in favor, and that the policies are on my side. In particular, the WP:GNG seems to me to be satisfied by the sources I am currently using, and there are other sources (search tau pi circle to see a good chunk of them) that also exist to show notability (although I don't think they would improve the article, which is why they are not in the article). Because my article meets the general notability guideline, it can be made into an article per WP:FRINGE, in exactly the same way as face on mars, Flat earth society, or even Stanley Meyer's water fuel cell. I have tried hard to make it WP:NPOV, and I think it both explains tau clearly, and emphasizes it's relationship to mainstream mathematics (Namely yet another superfluous constant). GIven all of this, I fail to find a credible policy-based objection (According to my interpretation. Yours may be different). I have also read through the RFC, and feel that it was based on an assumption that the sourcing was weak. The sources now exist. As for the AfD, the main problem seemed to be the title. I feel by title is more appropriate. Finally consensus can change, and I feel fairly confident that it has changed. Regards, Tazerdadog (talk) 21:29, 29 January 2013 (UTC)

I think your proposed article is a decent attempt at an NPOV treatment, but I have a problem with the lede. Tau is not a "proposed mathematical constant," it is a proposed new name for a well known constant, 2π or circumference/radius for a circle, if you wish. In either case, 2π should be mentioned before the approximate decimal value. --agr (talk) 00:22, 30 January 2013 (UTC)

Agreed, and I will make that change. The problem is that I don't know what to call it. Tau (Proposed name for 2π) sounds kind of dumb, and implies that the article is about the name, and not the constant. Tau (2π movement) is another idea, but it still falls well short. I will keep thinking about this. In the mean time if anyone has a better or more desctiptive title, please do let me know. Tazerdadog (talk) 00:46, 30 January 2013 (UTC)

A discussion here in November 2011 on a similar topic resulted in the phrase "alternative notation for 2π". You might want to move the 2π to the beginning of that phrase though, so people typing the word tau into Wikipedia's search box can more easily spot it in the autocomplete. Maybe something like "Tau (2π alternative notation)". --Joseph Lindenberg (talk) 05:05, 30 January 2013 (UTC)

I would appreciate it greatly if you would link me to that discussion. That is an idea, but "alternative" implies IMHO a higher degree of acceptance than Tau actually has. I really want to keep the part in parentheses succinct, but seeing as the name was the biggest bones of contention, I also want to get it right - perhaps Tau (2π proposed notation)?

Tazerdadog (talk) 05:27, 30 January 2013 (UTC)

Here ya go. Personally, I consider Tau (2π) the most logical page title. The purpose of a disambiguator in parentheses is simply to make clear which tau you're talking about, not to confer or imply some official endorsement by, or preference of, the mathematics community. In fact, show me where else Wikipedia demands such a warning be in the page title itself. Do alternative medicine articles require a "not accepted by the medical community" warning in their titles? --Joseph Lindenberg (talk) 09:40, 30 January 2013 (UTC)

I'll give a third opinion if you don't mind a relative layman's perspective. I have no bias or strong opinion on the subject, the only reason I'm really aware of the subject is that my birthday happens to be June 28, or "Tau Day". I looked at the article and the main thing that struck me was the overall nature of the sources; they seemed to be more "Slow news day"-type sources, rather than mathematics-related sources, which are the kind of sources I would expect to find on a mathematics-related article. As it stands now the sources in the article bring to mind WP:NOTNEWSPAPER's comment that "While news coverage can be useful source material for encyclopedic topics, most newsworthy events do not qualify for inclusion". I don't see any sources that are in that version of the article that weren't in the previous version, and the RfC determined that those sources were insufficient to warrant a separate article so if you don't mind me asking, what sources have been introduced or could be introduced into the article that would make it substantially different and to warrant a separate article?

I also think if the article were to be moved into mainspace, the parenthetical disambiguation would need to be changed, unless I'm just critically misunderstanding the whole "mathematical concept" thing. The page Tau appears to give a more apt summary by calling it "a proposed name" as opposed to "proposed mathematical constant". My understanding is that as mathematical constant it is certainly nothing new and the only thing different is the way in which it is expressed. I'm not trying to suggest that the subject doesn't belong on Wikipedia, but I would say that the references currently in the article don't really express a need to have a separate article, especially since an RfC already came to the consensus that they did with a version of the article that uses the same references. My advice would be to improve the references with mathematics-related sources, showing some use of Tau or discussing it in some way. As for the name, I looked at the references currently in the article and most of them seem to use its relation to pi as the most concise description: "The proper number is 2pi, or tau", so I think Tau (2pi) or Tau (2π) might be a better name for it. - SudoGhost 06:08, 30 January 2013 (UTC)

I don't see that there can be any reasoned objection to the existence of this article, since there is a "notable" (if very fringe) campaign to rewrite standard formulae using tau for 2pi. But the title should be right: "proposed constant" is wrong, and even "proposed name for a constant" is wrong, mathematically speaking. If I decide to write a paper using nonstandard terminology, I simply go ahead. "In this paper 'tau' means 2pi." No need for any proposing. So the title should be either "Tau (mathematical constant)" or, more explicitly "Tau (2pi)". Imaginatorium (talk) 06:31, 30 January 2013 (UTC)

There was an established RfC that was closed by an uninvolved administrator showing the objection to such an article, which is about as clear an objection as one can get on Wikipedia. I don't know what you mean by "you don't see that there can be any reasoned objection", since the RfC shows that there quite obviously already was. Either the sources need to be substantially improved or a new RfC should be created to determine if consensus has changed, but unless one or both of those things happen I don't think it likely for there to be an article for Tau. - SudoGhost 07:02, 30 January 2013 (UTC)

I will hold off on the move to mainspace until I have improved the sourcing to better demonstrate notability. I would argue that the RfC was flawed in its basic assumptions, but that is not for me to decide. In either case, the sources are there, I just need to put them in. Thanks for the uninvolved opinion SudoGhost Tazerdadog (talk) 14:13, 30 January 2013 (UTC)

The sources have now been dug up. Most of them are on the talk page, as I think that most of them add no real value to the article. They do, however, provide a strong claim of notability to tau. If nobody objects, I'm probably going to move this to article space sometime tomorrow. If people do object, then its probably time for a new RfC. Thanks in advance, Tazerdadog (talk) 08:08, 3 February 2013 (UTC)

The whole tau proposal is A fringe theory from the point of view of Wikipedia, and requires secondary sources that are independent of the subject of the article. I have not seen any sources that I think would qualify. (The only sources are of the "junk food news" variety mentioned explicitly in WP:FRINGE.) While I do see some evidence that the tau proposal might eventually garner some scientific coverage meriting a Wikipedia article, that doesn't seem to have happened yet. It is certainly true that there are more sources available now than at the time of the previous RfC, they do not seem to have improved. Sławomir Biały (talk) 21:40, 3 February 2013 (UTC)

I would highly suggest that you read David Be's comments above and realize that he was not looking for pi. Which says two things. One, tau is demonstrated notable. Second is that it needs to be separated for reasons of WP:NPOV. You can say it is fringe theory but it is notable enough that people are looking for it and requesting in comments. John W. Nicholson (talk) 01:45, 4 February 2013 (UTC)

Not everything that people would be interested in reading about belong in an encyclopedia. The notability of a fringe theory is established by its prevalence in sources that are independent of the subject. In particular, that means not opeds, not YouTube videos, not self-published manifestos, but real scholarly works in properly peer reviewed venues. Sławomir Biały (talk) 02:13, 4 February 2013 (UTC)

While I agree that not everything that people are interested in should have an article, I disagree with your assessment of the notability of Tau. I believe that your interpretation of the policy in question is extremely narrow. Tazerdadog (talk) 03:52, 4 February 2013 (UTC)

I have to agree with Tazerdadog here. The notability bar in WP:Fringe is not that high. Fringe theories don't get "real scholarly works in properly peer reviewed venues" almost by definition. I'd like Tazerdadog to show the sources for all the items in his list that are not self published, but there are enough good sources in his list to move forward. --agr (talk) 06:10, 4 February 2013 (UTC)

For everyone's convenience, here is the list of the sources I have thus far found.Tazerdadog (talk) 06:32, 4 February 2013 (UTC)

I will trawl through all of the sources tomorrow sometime to extract the non-self published ones. In the meantime, the sources are below if anyone is curious. Tazerdadog (talk) 06:59, 4 February 2013 (UTC)

Arnold, the bar is quite clear. From WP:FRINGE: "A fringe subject (a fringe theory, organization or aspect of a fringe theory) is considered notable enough for a dedicated article if it has been referenced extensively, and in a serious and reliable manner, in at least one major publication that is independent of their promulgators and popularizers." The question is, has this bar been met or hasn't it? Sławomir Biały (talk) 12:25, 4 February 2013 (UTC)

• When the sources in the list below are full of not only the same type of "slow news day" sources that are no different than the ones discussed in the RfC, but also personal blogs like this and this that wouldn't even be acceptable as a source let alone a source that establishes any notability, it certainly looks like citation bombardment; throwing everything in a Google search to the wall and hoping something sticks. The news articles are exactly the type that fall under WP:NOTNEWSPAPER: "While news coverage can be useful source material for encyclopedic topics, most newsworthy events do not qualify for inclusion." If the only sources are blogs and news pieces then it doesn't warrant an article, that's the consensus the RfC reached and nothing has been introduced that would make that consensus any different, just more of the same stuff. Quality, not quantity. - SudoGhost 12:42, 4 February 2013 (UTC)

• OK, it is not 42 (which is in Wikipedia), but close 47. See 47 below which is now used as a reference. I am sure a MAA publication in April (not pi or tau day) is not WP:NOTNEWSPAPER and it is "at least one major publication that is independent of their promulgators and popularizers". Or, is it not? He at least brings the notable level up because it show serious people are thinking and talking about the subject matter even when you clam they are not.

John W. Nicholson (talk) 12:13, 6 February 2013 (UTC)

I can't find the MAA publication you mention on the list. Could you point it out? Again, it would really help if self-published sources were removed or segregated, as they have no relevance to this discussion.--agr (talk) 12:46, 6 February 2013 (UTC)

Opps, I meant 46 here, however see my comment below with the same time and date and realize that it is better to have just one list. In the user space article, [6]. Or, this link http://www.maa.org/Mathhorizons/apr12_aftermath.pdf

John W. Nicholson (talk) 04:05, 7 February 2013 (UTC)

(break for length)

Now can we go on and start this article? Or do we have to waste more time talking about how it would be nice to get these tauist off this pious article? :p <tounge-in-cheek> Please feel free to bring you complaints of tau references to the page. Otherwise, do I have to point to something that I am sure you already know about? Like we are in a WP:BURO or this subject matter is WP:NOTSTUPID or something else? This argument against a tau article is just getting more and more pointless and non-NPOV.

John W. Nicholson (talk) 12:13, 6 February 2013 (UTC)

It is neither WP:BURO nor is it "non-NPOV" or "pointless" just because you disagree with the consensus of the RfC; the sources are more numerous, but are still the same type of references. More of the same crap is still crap, piling it on higher doesn't change that. Unless some better sources are found, there's nothing that warrants a separate article. - SudoGhost 14:37, 6 February 2013 (UTC)

I agree. It's quite strange that things like YouTube videos and cartoons have been advanced as potential sources for the article. I have no doubt that eventually there will be reliable sources that are credibly independent of the subject of the article. But until that time, it would obviously violate WP:NPOV (and a host of other pillars) to have an article based solely on the opinions of those in favor of a fringe idea. Surely that is not too difficult to grasp. Sławomir Biały (talk) 01:52, 7 February 2013 (UTC)

If you think something needs to be edited with this future article, I would suggest that you go to the page and edit it. Coming here to talk about it does not help in fact it is a waste of time on edits. If you continue to make statements here they might start being ignored because of this. Because pi is about pi, and pi is not about keeping other constants from having their "day in the sun", this future article should end the pi WP:NPOV and WP:BURO issues. So, from now on, that is the place to talk, to change, and to edit things with this future article. If there is no comments there, I see no reason not to have the article to go live, references included. If you don't like a reference, I suggest that you label it with WP:whatever-you-think-it-volates and make a comment on why you think it should be removed from the list. Please do not remove it from the list until the people there agrees to do so in a cooperative way. While this article is not live yet, the arguments that I am seeing here are not helping to change how that article will be worded. I see threats like "there's nothing that warrants a separate article", as stated above, as just that a threat. I would highly suggest that you read WP:NOTBATTLEGROUND if you think that way. John W. Nicholson (talk) 04:05, 7 February 2013 (UTC)

I have to disagree with moving it to article-space at the moment. While my personal belief is that the article is about a notable topic, verified by reliable sources and written from a neutral point of view, the consensus here is very unclear. Lacking a clear consensus, the previous one, which is the RFC, is in effect. Please do hold off on a move until consensus clarifies one way or another. I do believe the article belongs in article space personally, but this position is not clearly supported. In addition, I do agree that the proper place for this discussion is the the proposed article's talk page. Tazerdadog (talk) 05:02, 7 February 2013 (UTC)

I can see that I may have confused thing for some people with my statements, so let me be clear. I you have any comments to make with this issue about tau do as Tazerdadog suggest: "the proper place for this discussion is the the proposed article's talk page." Do this so that we can have it all at one place and not split between pi (which is not really being edited for pi with the comments for/against tau) and tau as propose page. I know the tau page is not ready until there is a consensus there, not here. People can argue all they want here about the existence of the proposed tau page here, but I for one will start to ignore it because that conversation needs to be taking place on the proposed tau page alone. I am sure when a consensus does happen there a RFC will be made at that time as to make sure we have input from everyone and notice of this RFC will be placed in pages like Talk:pi, Talk:Tau_(2π), and others. However, we need to first have a 'complete' article before a RFC issued. John W. Nicholson (talk) 07:20, 7 February 2013 (UTC)

I can't see how your repeated reference to WP:BURO is at all relevant. It's fine to invoke this in the spirit of doing something that might violate the spirit of a guideline if there is a clear consensus for doing it. It's quite another to think that it automatically means that you are right simply because what you are proposing violates policies. That's clearly a perverse interpretation. As for WP:NOTBATTLEGROUND, this does not mean that there will never be content disputes. It cautions against "ideological battles", but I have certainly never been ideological in this discussion. My personal opinions on τ versus π have never once entered this discussion, although I can't say the same for other participants. Finally, I'm not sure why you seem to think it's ok to propose a new article here, but then at the first sign of dissenting opinions to demand that everyone should write their replies elsewhere. Sławomir Biały (talk) 13:00, 7 February 2013 (UTC)

John, when you read "There's nothing here that warrants an article" as a threat, you seriously need to rethink how you're reading things, not least of all because accusing someone of making threats is an accusation about personal behavior that lacks evidence. It does not matter if you "see no reason not to have the article to go live", the RfC, which was closed by an uninvolved administrator, concluded that the subject did not warrant a separate article, so you "not seeing" something does not throw consensus out the window. The references in the article are the same type that consensus concluded as insufficient, so either the references need to be improved, or consensus needs to change. Short of one or both of those happening, the subject does not warrant an article. That is not a "threat", that was the RfC consensus. Before you cite WP:BURO again you might want to read it first, particularly the part about consensus-based discussion, seeing as how you're trying to argue against the consensus, not any policy or guideline. - SudoGhost 14:01, 7 February 2013 (UTC)

• (Editor invited into this discussion post retirement) In my opinion, Tau has already got quite a bit of coverage from reliable sources. And as such, an article of the same needs to be etched out on Wikipedia. As for the draft article under question and the various issues related to them, I'll like to offer my 2 paise.

• First, the lead needs to clarify what Tau is, and needs to stray away from ambiguous words like proposed constant. We need to be clear cut in explaining that it is a constant that is proposed for widespread usage at the expense of the more common pi.
• Second, I prefer the name "Tau (2π)" because of its preciseness in explaining the scenario. But we must also try to look into other typing-friendly alternatives.
• Next, the various sections of the article must be changed. Rather than focusing on the arguments for and against, we must include them in the lead, and try to incorporate more examples and relevance into how much it is accepted in the mathematical community, and the general public as a whole.
• Although graphics are usually good, we may use a little less of them in this article, so as to not show the obvious in a deceptive way (A first glance tends to give the indication its something new, but then we realise its the same as pi, with one minor difference.)

These are the main things I had to say. As for the article, I definitely support it, but the article needs reworking and some bold trimming before we bring it into the mainspace. TheOriginalSoni (talk) 15:22, 7 February 2013 (UTC)

You say ".. a constant that is proposed for widespread us[ag]e at the expense of the more common pi." But this could be misleading. "Proposed" makes it sound as though the Internation Committe for the Standardisation of Mathematical Terminology has urged the adoption of some new term, much as atmospheric pressures changed from millibars to hectoPascals. But this is not true at all: the "tau" movement is, however "notable", totally a fringe campaingn. Perhaps most importantly it ignores the fact that in mathematics writers can and do make up their own terminology all the time, just so long as it is defined. So no "proposal" is required -- anyone who thinks their paper will be improved by writing tau for 2pi can do so.

I was corrected above, because I said I couldn't see any reasonable objection to a tau page. (But in a sense, "reason" means something different from "rules", which are what I hadn't understood properly.) I certainly think that it is tactically better to have a tau page, because it avoids endless rather boring discussions like this one. Imaginatorium (talk) 05:47, 8 February 2013 (UTC)

Comment - There was an article on tau, (here is the archive of it), and the article was deleted (or merged) in April 2012 because of an RfC in its Talk page. That was about 10 months ago. The comments in the RfC were rather divided: at least 6 editors !voted for Keep .. it certainly was not unanimous by any means. As mentioned above, consensus can change. My recommendation for editors that want a new article on tau is to continue gathering sources for another month or two, prepare the best article you can, then when April 2013 arrives (one year from the deletion) post the new article into the Tau_(2π) page and start another RfC to see if the community thinks that the sources demonstrate that the Notability requirement has been met. --Noleander (talk) 15:51, 7 February 2013 (UTC)

Procedural question - Assume for the moment that the new article is going to get good enough to satisfy everybody that it should become the new Tau_(2π) article. Will there be any problem with merging the Talk pages of the old and new articles? Would it make the eventual move easier if development discussion took place at Talk:Tau_(2π) instead of User_talk:Tazerdadog/Tau_(Proposed_mathematical_constant)? We don't want to lose either the discussions of the past 1.5 years, or the discussions we will be having during the next two months. And if discussions occur on both Talk pages in the coming months, the merged result will look confusing. Alternatively, we could post a message at Talk:Tau_(2π) that all discussion should now occur at User_talk:Tazerdadog/Tau_(Proposed_mathematical_constant). Suggestions? --Joseph Lindenberg (talk) 02:15, 8 February 2013 (UTC)

Good points. I suppose it doesnt matter where the "merge" discussion happens, as long as it is co-located and prominent notices are made at all relevant pages. Proponents of the new article (Tazerdadog?) should take responsibility for selecting a centralized discussion location, and then posting notices on all the relevant talk pages. --Noleander (talk) 02:21, 8 February 2013 (UTC)

RFC

I have started a RFC on the notability of tau on the talk page of the article in my userspace. The RFC can be found here

List of sources about tau on the proposed article's Talk page (link)

Newly published SAMS programming book (dead tree) that uses tau. books.google.com/books?id=BFda3Z71Y5YC&printsec=frontcover --Joseph Lindenberg (talk) 03:24, 19 February 2013 (UTC)