Talk:Pi

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)

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)

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)

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)

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)

QEIS references

Just a reader's note about the QEIS 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)