Talk:Pi/Archive 4

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Digits anyone?

I found quite some time ago there was a series of pages called "pi to X digits", these pages don't seem to exist anymore, and i'd like to know why. Also, there was a page called "digits of pi" not so long ago but this is gone to. This talk page could do with archiving in the near future (it is 84k long!) If there is anyone around here who was involved in the removal of the pages then i'd appreciate to know why they were turned into redirects. 172.205.150.191 11:11, 1 May 2006 (UTC)

Perhaps because Wikipedia is not an indiscriminate collection of information? There are billions and billions of digits that one could add, but they hold no particular encyclopedic interest. The 30 or so digits in the article are sufficient for any conceivable engineering use; people who want to know more digits can use one of the fine links to external pi-digit repositories provided in the article. Henning Makholm 13:49, 1 May 2006 (UTC)

Okay, but where should I go to find a binary or hexadecimal list of pi, up to 50 digits or so? It appears that the main article lists 50 digits in base 10, but I would like to see 50 digits in binary, or hexadecimal. Somebody ought to edit the main page so a list of progressions is given for both binary and hexadecimal, right next to the progression in base 10.

We used to have those articles. Then we decided that wikisource is going to be our depository for raw data dumps, so we moved all such articles there. Then the regulars over there at wikisource decided that they don't want them, they deleted all but one of them, which is still around: s:Pi to 1,000,000 places. That's where you should go for your π digit needs, I guess. -lethe ^{talk +} 06:09, 2 May 2006 (UTC)

That's unfortunately a depository of decimal digits. I was hoping for hex.

What if I told you it's 3.243F6ADAE723BF81181CA9ABB5004DE259A64D575AB995FA9A? Sure, I got the last few places from here, but one random number generator is as good as the next. Melchoir 08:52, 3 May 2006 (UTC)

Or if you want a more reliable hex value: (1) Go grab a hundred decimal digits from one of the many online sources. (2) Acquire an arbitrary-precision calculator, e.g. calc (packaged for Debian as apcalc). (3) Enter the decimal pi, multiply by 2^200, truncate to an integer, and have your calculator display the resulting value in hex. Henning Makholm 09:13, 3 May 2006 (UTC)

Thanks! Now that you pointed it out, it makes plenty of sense.

Archimedes

Why isn't Archimedes mentioned anywhere in the article aside from the introduction? —The preceding unsigned comment was added by 140.247.28.35 (talk • contribs) 22:41, 3 May 2006 (UTC)

Good point. I have added a note about an approximation by Archimedes in the "History" section. -- Meni Rosenfeld (talk) 12:07, 4 May 2006 (UTC)

Infinite series more important than approximations

The property of pi that it can be specified to any number of digits using a series that can be specified in less than 15 digits is far more important than a lot of approximations or discussion about how many digits have been calculated. For one thing, it connects back to how pi was derived (geometrically) in the first place; and to how pi shows up in nature and science in a lot of different--sometimes surprising ways--in mathematics. Here is a suggested explanation (which fits remarkably well in just about any section (approximations, definition, properties, or even trivia--I just don't want to see it left out, especially when so much else is left in that is far less important). It also serves as a good lead-in to historical approximations since there are really two kinds, each with their own histories (finite and infinite precision):

Even though pi is irrational and transcendental, approximations to any arbitrary degree of precision can be created from simple-to-write infinite series. Such series can be used as a definition of the "exact" value of pi, because the value of the infinite series approaches (cyclically) the exact value of pi. The way it is used (usually by computers) is to calculate the value to enough iterations so that the first n digits become stable. One of the earliest and most common of such series is the following: pi = 4/1 - 4/3 + 4/5 - 4/7 + ....

Many further improvements to the above mentioned "historical" approximations were done with the help of computers. A historical account on numerical and formulaic approximations of pi is given in history of numerical approximations of pi. —Preceding unsigned comment added by 70.162.103.106 (talk • contribs) 2006-05-24 01:43:03

There are many problems with this addition (which I intend to remove from the article again as soon as I can safely do under 3RR, unless somebody beats me to it):

1. It is not a particular property of pi that it can be approximated by "simple" series expansions. That is true for many interesting trancendental numbers.
2. The very fact that many digits have been calculated also in itself implies that there are definite ways to calculuate arbitrary amounts of digits.
3. The article already does mention the Leibniz series (1/1-1/3+1/5-1/7+...) in the appropriate section.
4. Leibniz' series is by far not the most common method of approximating pi -- it converges too extremely slowly to be of any interest to practical calculation. Much better series for doing this are known. In particular, the claim that this series is usually used in computer approximations of pi is just false. See Leibniz formula for pi: it takes billions of terms just to get 10 correct decimals.
5. For the same reason, the series is horribly badly suited to serve as a definition of pi -- about the only thing one can do with the definition is to prove it equivalent to one of the other existing useful definitions, and work from the latter no matter whether one wants to find applications or digits of pi.
6. There is no such thing as an "infinite-precision approximation".
7. The fact that pi shows up all over analysis is not particularly connected to the Leibniz series. A better candidate for the fundamental connection is the fact that the arc-length parameterization of the unit circle in Euclidean geometry happens to satisfy a particularly simple differential equation. (This can ultimately be used to explain why the Leibniz series works, rather than vice versa).

Henning Makholm 11:02, 24 May 2006 (UTC)

Trivia!

The Bloodhound Gang has a song called "3.14," known colloquially as "The Vagina Song." Given that the essence of the joke is "pi/pie" should this be included, or is it too juvenile?

Pi Day

OK, my friends and I are major nerds and we celebrate pi day every year by wearing pi day shirts we painted, eating pies, memorazing digits of pi, making pi day decorations, and yelling at the tops of our lungs at 3/14 at 1:59:26 and any other random pi related things we can think of. I'd like to mention ways that people celebrate pi day, but I'm pretty sure my friends and I are the only people who do that. Would it be appropriate to write about it under the pi day section? I know of several math teachers that let their kids have pie in class so I think that would at least appropriate to mention. If anyone else out there celebrates pi day, then let me know what you do.

Pi to 1000000 decimal places

I decided to give the link instead of breaking the horizontal scroll, so here it is. It was a site made for the sole purpose of showing off pi to 1000000 places, and the author has an alternate site, so I don't think this is bandwidth theft... Random the Scrambled 12:15, 29 May 2006 (UTC)

Thank you. I'm happy to see that I have now seen pi to 1000000 places thanks to this site. My life is complete and it doesn't take up to much bandwidth. It works for me

Rewrite

I've made some progress on a rewrite of this article. Contributions welcome; beware of unfinished sentences, etc. Fredrik Johansson 22:24, 29 May 2006 (UTC)

I cleaned up the definition section and separated out the numerical value discussion. I took out the claim that advanced textbooks define pi in terms of trig functions. They generally do no such thing. I would be inclined to break up the numerical value into groups of five digits as is done in the e article (not adding any digits), any objections?--agr 14:21, 30 May 2006 (UTC)

You haven't edited my proposed rewrite; did you post this comment in the wrong section? Fredrik Johansson 16:39, 30 May 2006 (UTC)

I guess I did. --agr 16:51, 30 May 2006 (UTC)

Digit creep: Why 3.14159 is the right approximation for the introduction

I have reverted a couple of attempts to refine the value in the introduction to 3.141592, and feel I ought to explain my reasons: To avoid confusion, the short value in the introduction should be one that can be interpreted as a truncated approximation as well as a round-to-nearest one. The possible choices are then 3, 3.1, 3.14, 3.14159, 3.14159265, 3.14159265358979 and so forth. Of these, 3 and 3.1 are obviously too imprecise, 3.14 is believed by some to be exact (which mistake we should not encourage), and giving 8 or 14 decimals seem to be excessively many for a short introduction. The only remaining possibility is 3.14159, which I believe should therefore be retained. Henning Makholm 20:03, 1 June 2006 (UTC)

I support this. Random the Scrambled 00:12, 13 June 2006 (UTC)

3.141592653589 is the most common form of PI... you are wrong, I am right, and length is better —The preceding unsigned comment was added by 131.247.243.34 (talk) 02:41, 11 December 2006 (UTC).

3.141592653589 may be the most common form of PI, however, when entered by hand, few enter more than six digits realistically. —The preceding unsigned comment was added by 70.73.118.166 (talk) 06:09, 5 February 2007 (UTC).

The other (if not the main) reason why 3.14159 is most commonly used is because 7 (the number of syllables you use to say it) is a magic number. ~ Keiji (iNVERTED) (Talk | Contribs) 07:16, 5 February 2007 (UTC)

move to π?

Maybe this article should be π instead, and pi should redirect to it.

Nice thought, but no. Not all browsers handle special characters well, particularly those used by the visually impared. Also Wikipedia automatically capitalizes the first letter of all articles so you get Π instead (which does redirect here).--agr 22:52, 11 June 2006 (UTC)

I think it is a good idea. π & ∏ are part of the extended ASCII set and are supported by almost everything. Dread Lord CyberSkull ✎☠ 00:22, 19 August 2006 (UTC)

But Π is never this number. Very bad idea. Gene Nygaard 23:03, 6 October 2006 (UTC)

The template {{lowercase}} allows ∏ to be displayed as π. It has been used in π (film). Just64helpin 17:39, 18 January 2007 (UTC)

Pination link

I just reverted to remove a link to Pination - a visual display of Pi with different digits representing different numbers. My feeling is that since (i) it is essentially an interesting display, not an academic article and (ii) the front page currently has incorrect information ("no pattern in the digits has been found") on it, people who are researching the article will probably not need the link. It has been placed and removed several times, so I am moving it here for further comment. Thoughts? --TeaDrinker 02:59, 14 June 2006 (UTC)

I have also removed the link just now, and I would have removed it yesterday except that Henning was faster. -- Jitse Niesen (talk) 08:10, 14 June 2006 (UTC)

Just removed it again :-( Madmath789 08:53, 14 June 2006 (UTC)

Hi, it's me to add the pination link to the article. I just started to edit in wikipedia article few months ago, so i am a new comer. Before i added the link, i read the guideline thoroughly to check if it is valid to add the link there, it seems there is no problem in my understanding. I think all of you are experienced wikipedians. I would be appreciate if you can give me some guidelines where can i share link like this one, which may not be totally related to the article, but elaborate by it. I cannot expect all of you are interested in this idea, but i would like to share with someone in the world. Prwong 16:13, 16 June 2006 (GMT)

Is it worth it to calculate digits?

As mentioned in the archived debate on the purpose of calculating digits of pi:

According to the article on pi, "The most pressing open question about π is whether it is normal, i.e. whether any digit block occurs in the expansion of π just as often as one would statistically expect if the digits had been produced completely randomly." This can only be answered by a mathematical study of the digit sequence. Obviously one wouldn't study it by looking it up in an encyclopaedia, but even so, people at home might want to do a bit of a check for themselves, to see if it sounds plausible. :) -- Oliver Pereira 00:20 Nov 24, 2002 (UTC)

But the digits most commonly used are in base-10. A single base. Any patterns found will be most likely specific to base-10. The digits have little mathematical significance; the actual value they represent is what's important. He Who Is 21:57, 16 June 2006 (UTC)

More seriously, while normality holds as closely as may be expected (in base 10) for the millions (or possibly billions) of digits to which it has been tested, this leaves an infinite number of unexamined digits. That's the hard part. Septentrionalis 20:06, 18 June 2006 (UTC)

Now what I think might be interesting is to look at the sequence created by alternating bases or similar concepts, though i doubt that will yield any intersting results either. But I still hold that the most important things to analyze are the algorithms and sequences that generate those digits, since any abnormalities in the digit sequence should logically be reflected in the formulas. --He Who Is^{[ Talk ]} 21:28, 18 June 2006 (UTC)

Interesting thought, might I add my own thought and suggest that you're inspiration for this addition is the pattern of Pi evolving from you thinking exactly what I've thought before…... --PakBehl 18:19, 15 February 2007 (UTC)

Pi has been proved to be normal in base 2. wolfmankurd

The nature of Pi in base two only appears normal because we cannot measure the dimension we exist in without PerceptIon, miscapitalization intended. --PakBehl

That is more than the article itself says (It only says the base-2-normality has been proved equivalent to a certain conjecture). If you have information about a stronger result, please add it to the article, with references. Henning Makholm 18:47, 15 October 2006 (UTC)

Fractional approximation

The approximation 355/113 (3.1415929…) is the best one that may be expressed with a three-digit numerator and denominator.

In fact it's better that that, the next smallest denominator that gives a better approximation isn't till 52163/16604! 195.7.54.2 10:33, 20 June 2006 (UTC)

Trivia deleted

http://en.wikipedia.org/w/index.php?title=Pi&diff=prev&oldid=59749599

Why was that deleted? I found this quote:

"A value of π to 40 digits would be more than enough to compute the circumference of the Milky Way galaxy to an error less than the size of a proton."

From this paper. I dare propose that this isn't even trivia; people (such as myself) see that scientists have calculated it out to billions of digits and assume that much accuracy is necessary or important. Where shall we put that quote back in? --DevastatorIIC 03:19, 22 June 2006 (UTC)

Certainly the misconception that we calculate millions of digits of π so that we can do more precise calculations with it needs to be addressed. The point is that no practical problem ever needs more than a handful, and more digits are either for number-theoretic reasons or for testing computers. That was the point of the removed text, and I thought it was a good one. -lethe ^{talk +} 03:41, 22 June 2006 (UTC)

I have certainly seen similar statements in other (print) encyclopedias, and think that it gives a good sense of how remote from practical considerations these very precise values of π really are. Happy to see it go back in. Madmath789 04:23, 22 June 2006 (UTC)

While I agree that the misconception that many digits are needed for precision should be mentioned, I also believe that it should be reworded. The reason for this is that there are no exact "boundaries" of the Milky Way, nor any other galaxy. There is simply an estimated line by which the density of stars has lesssened to a point that it seems reasonable to consider it outside of the galaxy. Also, the word "cirumfrence" in use with galaxies may create a misconception that the Milky Way is, in fact, a circle. As wiktionary defines circumference: "(geometry) The distance measured around a circle." -- He Who Is^{[ Talk ]} 16:30, 22 June 2006 (UTC)

I have attempted to add a rewording that addresses this to the Numerical value section. Not completely satisfied with the result; in order to make the wording flow better I had to move the "sufficient for engineering and science" sentence from its prominent place at the beginning of a paragraph. Edit away if you have a better solution to that. Henning Makholm 14:44, 23 June 2006 (UTC)

Animations

How many animations that show a circle perimeter straightening do we need (or want)? While animations in general are annoying I can see some presentational value in one here, but why two animations of basically the same idea? We should decide on one and let the other go. FWIW I think that overall Image:Diameter and Pi 1.gif is cleaner and less visually noisy than Image:Pi-unrolled.gif, but it could be confusing that Image:Diameter and Pi 1.gif uses dashed circular arcs to denote "this is the straight line whose length is being measured". Henning Makholm 07:40, 25 June 2006 (UTC)

I think one animation is useful, but not two. I also dislike the curved arc denoting distance, so I vote Pi-unrolled. Perhaps we could enlist someone to make a better one? Maybe a circle unrolling on a coordinate plane? --DevastatorIIC 20:09, 25 June 2006 (UTC)

DESTROY the animations! They chew up bandwidth and wreck the page load time. The page is big enough with all the TeX symbols, the other fancy graphics are overkill. -- Papeschr 13:56, 26 June 2006 (UTC)

To be fair, the animations total only 56.5 KB. The page itself is 40 KB long. I just think they're distracting and of moderate usefulness. --DevastatorIIC 01:08, 27 June 2006 (UTC)

I have now removed Image:Diameter and Pi 1.gif from the article. Henning Makholm 21:16, 27 October 2006 (UTC)

Only when in radians

Before I did any changes I thought I'd at least try and ask here. While reading the page in the definitions section it says that where x is pi, sin(x)=0. It's trivial, but thought it should mention that this is the case when working in radians. I would assume that you needed to be in radians, but others may not. When in degrees, x would of course have to be 180 for sin(x) to be zero, Sin(pi) gives a small number <1, but isn't quite zero. Not sure if i've put this in the right sort of place either having never commented in a discussion section. --Stonysleep 14:51, 2 July 2006 (UTC)

Yes, you have placed the comment in the correct place; And no, there is no need to explicitly state that we are working in radians. The argument of the "sin" function is, by definition, given in radians. If we wish to work with degrees, we must use the symbol °, which is nothing more than a mathematical constant roughly equal to 0.017453, and accurately to π / 180. So "sin (180) = 0" is wrong; however, "sin (180°) = 0" is correct, because

sin (180°) = sin (180 * (π / 180)) = sin (π) = 0

-- Meni Rosenfeld (talk) 17:26, 2 July 2006 (UTC)

While I agree that technically you are not incorrect in not stating that we are working in radians, I believe it may be helpful to users who work mainly in degrees to simply state that radians are being used in the calculation. Though this may be a smaller percentage of your users, I must insist they they be informed, at least in passing.

-- Glooper 22 July 2006

It seems to me that caveats about which input mode our calculators are "in" belong at Trigonometric function. This article should discuss pi. It would be appropriate, for example, to discuss how knowing about pi helps one define the degree such that pi=180 deg. Melchoir 16:45, 22 July 2006 (UTC)

Number Theory

In the section on number theory, should it be mentioned that the average number of ways to write a number as the sum of two perfect squares comes from the fact that a circle of radius r is defined as the set of all points (x,y) such that x²+y² = r², or is this somewhat beyond the scope of the section? -- He Who Is^{[ Talk ]} 17:24, 10 July 2006 (UTC)

Intuitive explanation of calculating pi

I fear that many of our math-related articles scare away non-mathematicians by using advanced math jargon too early in the article, so that the reader never gets to the later parts he can still understand. I've reorded the sections a bit to put most of the accessible information at the top.

I also added a section giving an example of how to approximate pi using only elementary algebra. Then I noticed that the german article seems to have several sections which discuss related ideas. Perhaps some german-speaker can help integrate them. Lunkwill 05:17, 13 July 2006 (UTC)

Wrong title

I see this article has developed the {{wrongtitle}} template. This seems excessive; it's intended for cases like eBay, where there is a clear English name, and Wikipedia cannot spell it correctly. Here there is an English name, pi, and a symbol, and we choose between them. (I think we make the right choice, but that's another story.)

What do other editors think? Septentrionalis 21:00, 16 July 2006 (UTC)

The choice of English name vs. symbol is irrelevant to the problem, technical restrictions force capitalization of both pi and π. The real question is whether capitalized Pi is incorrect in an English title, and having just noticed the capitalization of Indiana Pi Bill, I don't think it is. -- EJ 22:26, 16 July 2006 (UTC)

Here is why I am in favor of the template. The symbol representing 3.141... is π, not the word pi. This is different than the distinction between Greece and Ελλάδα which are in different languages; every English speaker who has taken geometry knows π is the correct symbol. Moreover, the title is capitalized even though the symbol is not Π. Thus the title is doubly wrong.

The reason that the title is not π is a combination of limitations of the wikimedia software and limitations of keyboards of English users. These are technical reasons.

Thus the template is correct in saying that the title is wrong for technical reasons. The template adds a minimal amount of content; most users will ignore it, since they don't care about technical reasons. The few who wonder why we Anglicize everything can follow the link to find out why. CMummert 23:48, 16 July 2006 (UTC)

The name of the symbol, when spelled in English, is pi. You can look up the word in any dictionary. It’s not just Greek letters that have English spellings, either. The English letters have spellings, too (e.g., Aitch, Jay (disambiguation), Zee or Zed). None of the articles on the Greek letters use {{wrongtitle}}: Alpha (letter), Lambda, Pi (letter). Articles about various other hard-to-type symbols don’t use the template, either: Plus-minus sign, Obelus.

Using {{wrongtitle}} because of the capitalization of “Pi” is unnecessary, too. Wikipedia capitalizes all article titles, even the ones with ordinary English words like Pi and Truck that aren’t really proper nouns. If there were no English spelling of the symbol, then I would agree that {{wrongtitle}} would be appropriate to distinguish the uppercase symbol from the lowercase symbol, but since this article’s title uses neither symbol, it’s certainly not using the wrong symbol. --Rob Kennedy 17:19, 3 September 2006 (UTC)

"Pi" is the wrong title. the correct title is "π". People keep mentioning that the symbol has an English spelling, but this article isn't about the symbol. This article is about "π", which is a mathematical constant, that English people are familiar with in that form. (see more below) McKay 01:16, 5 September 2006 (UTC)

The page π actually exists, and is a redirect to Pi. So what is going on here? Technical restrictions my ass. MediaWiki can easily handle Unicode in titles. ~iNVERTED | Rob (Talk | Contribs) 21:39, 4 September 2006 (UTC)

The page you’re referring to is actually at Π, that is, capital pi. If the title is going to be a Greek character, then it should indeed be lowercase since this is an article on the mathematical symbol, not a letter of the alphabet. The “technical restriction” involved is that Wikipedia capitalizes the first characters of article titles, even non-English characters. But since this article’s title isn’t the symbol but the English word, the technical restrictions do not apply. --Rob Kennedy 22:57, 4 September 2006 (UTC)

If you would have read the discussion you would have seen that the page you mention is the Greek capital letter, which in fact means MULTIPLICATION. Its redirect is incorrect. It has been edited now. Jclerman 22:53, 4 September 2006 (UTC)

Oh. Well, if the page is supposed to be called Pi, then there shouldn't be a technical restrictions template on here... ~iNVERTED | Rob (Talk | Contribs) 23:19, 4 September 2006 (UTC)

Some people have mentioned that we should move to "π" That would eliminate 1/2 the problem, but we would still have to have a {{wrongtitle|π}}, but it does fix one problem I guess I would support such a move. The reason I don't do this is because it looks ugly in most people's browsers "http://en.wikipedia.org/wiki/%CE%A0". But I'm fine with either one. McKay 01:16, 5 September 2006 (UTC)

Oh, and I reverted the change to Π, because it's the same article as π, which should link here, even more than Π should link to any of the product related pages. McKay 01:16, 5 September 2006 (UTC)

It is true that the current version of Mediawiki can handle Unicode article titles, but it doesn't alphabetize them correctly (that is, π is not alphabetized under p). This is especially a problem in category pages.

The consensus about article naming (WP:NAME and its subpages) seems to be that the title should be spelled out as pi with a redirect from π. I predict that any attempt to move the article to π would be reverted very quickly, as happend with mu recursive function a few weeks ago. I point to the comment by McKay (01:16, 5 September 2006 (UTC)) above for a good summary of why the wrongtitle template should remain. CMummert 01:49, 5 September 2006 (UTC)

"pi" should begin with a lower-case initial when it refers to the mathematical constant. Michael Hardy 20:30, 7 September 2006 (UTC)

It is reasonable to say "pi" in lieu of "π", but in mathematical use, it's a lower-case π. Upper-case Π is a product operator, something entirely different. The correct rendering of those in the latin script is "pi" and "Pi", respectively. Meaning that the constant is (initial miniscule) "pi", Just like sigma is generally standard deviation while Sigma is invariably summation.

Problem with Ludolph finding first 32 decimals in 1615

"The German mathematician Ludolph van Ceulen in 1615 computed the first 32 decimal places of π. He was so proud of this accomplishment that he had them inscribed on his tombstone."

In his page, it says he died in 1610. How is it possible he computed the first 32 decimals of pi 5 years after he died?

The things people will do for calculating π :)

Seriously, I've looked up the matter, and I have found conflicting references regarding the time of his computation - my more or less trusted source only says that 35 digits (not 32, btw) was as far as he got by his death in 1610. I've changed the sentence accordingly. -- Meni Rosenfeld (talk) 07:00, 23 July 2006 (UTC)

Good Article nomination has failed

The Good article nomination for Pi/Archive 4 has failed, for the following reason:

I am failing the nomination of the article for a number of reasons.

1. The page could be a lot more accessible to readers with a limited mathematical background, especially since there are many more technical articles on specific aspects of pi. The page seems to have been hijacked by mathematicians: things like pi mnemonics (which mathematicians rightly consider unimportant) should appear much earlier and there should be more content on the history of mankind's fascination with pi.
2. A number of sections are disorganized and look like an accumulation of information tidbits. For instance the early approximations section needs a rewrite and is too long given that there is a separate article for that history. The formulae section is also pretty bad in that respect: there is no unity in the material presented nor is there any serious effort to motivate the presence of these formulas.
3. There is still a Trivia section which is evidence that the page is still being built. Of course there is not much edit-warring but the page is still very actively edited.

Pascal.Tesson 08:15, 23 July 2006 (UTC)

PS: I just noticed the to-do list on top of this talk page. The criticism there is very well put. I would add this: the history section seems to focus only on the practical matter of calculating pi which is not only a very narrow view of the subject but a particularly hard one to appreciate for the layman. Pascal.Tesson 08:23, 23 July 2006 (UTC)

I agree with failing, though I don't agree with all of the criticism: things like pi mnemonics just aren't very important at all. I'll take the opportunity to advertise User:Fredrik/Pi again, though it's still not finished and I haven't been able to to work on it recently. Fredrik Johansson 09:38, 23 July 2006 (UTC)

Actually I also find mnemonics not so important but I feel they should be mentioned (if only in passing) earlier than they are currently. In any case, I am very impressed by User:Fredrik/Pi which I think has the right spirit. Why not go live with it?Pascal.Tesson 11:26, 23 July 2006 (UTC)

Thanks, but I think the empty sections need some content first... Fredrik Johansson 22:57, 19 August 2006 (UTC)

Best approximation ever

I have discovered the best ratio of π accuracy to characters for an approximation.

As an example:

22/7 requires 4 characters and equals 3.142857142857142857..., which is correct to 3 significant figures or 0.75 per character.

355/113 requires 7 characters and equals 3.141592920353982300..., which is correct to 7 significant figures or one per character.

So the best is ³√31, which requires 4 characters and equals 3.141380652391393004..., which is correct to 4 significant figures or one per character as well. But it beats 355/113 because it has the virtue of brevity and memorability.

I challenge anyone to find a better one. User:Gee Eight 5 August 2006 20.03 UTC

3 requires 1 character and is correct to 1 significant digit. And it clearly beats your cube root in terms of brevity and memorability. -- EJ 20:11, 5 August 2006 (UTC)

Anyway, π also requires 1 character, and it is correct to infinitely many significant digits. -- EJ 20:24, 5 August 2006 (UTC)

I know what you're trying to convey, but I believe we are to assume he meant a finite composition of elementary operations on integers. 74.132.209.231 20:54, 16 August 2006 (UTC)

What's wrong with thinking of 355/113 as 113\355, which is quite memorable? — Arthur Rubin | (talk) 17:45, 21 August 2006 (UTC)

For a ratio better than 1, take the decimal expansion and round it just before the Feynman point. Fredrik Johansson 18:03, 21 August 2006 (UTC)

"No pattern in the digits" -- absolutely incorrect

From the Numerical Value section: "Despite much analytical work, and supercomputer calculations that have determined over 1 trillion digits of π, no pattern in the digits has ever been found." Well of course there's a pattern in the digits! For one, we have the (yes, trivial) pattern that.. they are the decimal expansion of Pi, an extremely interesting number. On a less trivial note, we have the Bailey-Borwein-Plouffe formula. Saying there is "no pattern" is both wrong and misleading to students. There is, at worst, a complicated pattern. I suggest the line should instead read that there is no simple pattern and perhaps reference BBP here. Please comment. 74.132.209.231 18:53, 14 August 2006 (UTC)

I agree that writing "no simple pattern" would be less ambiguous. However, whether the current formulation is incorrect or not depends on what we mean by "pattern". In my opinion, neither of your counterexamples can really be called a "pattern", though this can be argued. Writing "no simple pattern" implies that there is a pattern, which is, according to my interpretation of what a pattern is, both incorrect and misleading. I'll have no objections if others agree with this formulation, but I would like to hear if you have other ideas for writing this. -- Meni Rosenfeld (talk) 19:04, 14 August 2006 (UTC)

Thanks for your response. I agree with you to an extent, for what that's worth, but we're going to have to come to an agreement on what a pattern is. I can think of nothing but to refer to pattern: "A pattern is a form, template, or model (or, more abstractly, a set of rules) which can be used to make or to generate things or parts of a thing, especially if the things that are generated have enough in common for the underlying pattern to be inferred or discerned, in which case the things are said to exhibit the pattern." I believe BBP satisfies this and so is an unqualified pattern. At the same time, I believe most will agree it's not a "simple" pattern. That's how I come to "no simple pattern" being the best presentation. I'd be glad to hear more and from others. 74.132.209.231 20:47, 16 August 2006 (UTC)

I see your point, and while I still feel uncomfortable calling BBP a pattern, I believe most people will agree that it is, just a complicated one. Indeed, "no simple pattern" seems to capture the best of both views, and I've changed the article accordingly. -- Meni Rosenfeld (talk) 04:45, 17 August 2006 (UTC)

Sorry to have jumped in on the Pi page on this without first having consulted the Talk page. As 74.132.209.231 points out, there is of course trivially a formula for the nth digit of π and indeed any well-defined number x (entier(x*10^n) mod 10); and it is certainly interesting that BBP gives you a formula that can be evaluated in less time than calculating all n digits. The question is whether that adds up to a "pattern", simple or not. I think not.

The word "pattern" is not a formal word; it is an appeal to the reader's intuition. I don't see how any normal reader would find that BBP-type formulas correspond to the intuition of "pattern" when you look at the resources required to calculate the nth digit. I suppose you could formalize this somehow in terms of complexity of calculation, but I don't think that's necessary. On the other hand, I do think it's worthwhile to surface BBP-type calculations right after the "no pattern" sentence, e.g. "However, it is possible to calculate the nth digit of π without calculating all previous digits." Again, this is not a rigorous statement, but we're looking for intuition, not rigor, here. --Macrakis 15:09, 17 August 2006 (UTC)

If we received the sequence 3.14159... in a radio transmission, we would certainly call that a pattern. The pattern is: it's the digits of π. Moreover, π is a nonrandom number in the sense of algorithmic randomness, and nonrandomness intuitively means that a pattern exists. I agree that it is intuitively true that there is no simple pattern in π. CMummert 15:17, 17 August 2006 (UTC)

By that definition of "pattern", every well-defined number has a pattern in its digits, so it is vacuous and therefore uninteresting to claim that pi "has a pattern in its digits". When people ask "is there a pattern to the digits of pi?", surely they mean something stronger than "is pi a well-defined number" or "can you calculate the digits of pi". --Macrakis 15:29, 17 August 2006 (UTC)

Yes, I would say that every real number whose decimal digits can be enumerated by an algorithm has a pattern in its digits. That leaves the rest of the real numbers which do not have patterns. This is a pretty standard way of understanding the word pattern in the study of algorithmic randomness. I agree it is uninteresting to say π has a pattern, and false to say it has no pattern. I do mean something stronger when I say a sequence has no pattern: I mean that it is algorithmically random. I don't see how using some vague, intuitive meaning for no pattern that conflicts with a standard usage is helpful in the article, especially when so many people agree that no simple pattern is accurate. CMummert 15:45, 17 August 2006 (UTC)

I would define a pattern as "simple" if calculating the n-th digit is an [essentially] O(1) operation. By the way, it is perhaps worth mentioning that there does not exist a Machin-type BBP formula for π in any nonbinary base. Fredrik Johansson 15:32, 17 August 2006 (UTC)

I don't think it helps readers to insist on a formal definition of "having a pattern" as equivalent to "computable" even if it may be used that way (informally, I would guess) in the study of algorithmic randomness. Computing the digits by computing the value certainly doesn't count in my book as a pattern, complicated or not. The BBP formula makes things more interesting, agreed, but still doesn't correspond to my intuition of 'pattern'. Talking about O(1) etc. (actually, it would have to be O(log(n)) because of the cost of arithmetic on n-size numbers) is over-formalization for this intuition.... --Macrakis 16:16, 17 August 2006 (UTC)

The existence of a procedure for enumerating the digits of π does count in many people's mind as a pattern; that's why this discussion started. Only Macrakis seems to be opposed to the word simple, while the other three editors represented above feel it is at best unobjectionable. I am going to reinsert the word simple. CMummert 19:02, 25 August 2006 (UTC)

How about considering whether a statitician could show any difference between an arbitary chunk of one million digits of pi and the same number of genuine random digits? Other than if he was able to discover that the sequence came from a pi approximation. I understood that 'non-randomness' has not be shown for pi (although clearly the numbers are not random). Anyway, does any arbitary sequence of random digits alwaysn appear in pi, or is there any sequence that will never appear. —Preceding unsigned comment added by Gomez2002 (talk • contribs) 2006-11-02 13:51:51

Essentially, that is what is meant by pi being "normal", which is mentioned in the article as the most important open problem (i.e.: nobody has proved the answer conclusively to be yes or no) about pi. Henning Makholm 19:51, 2 November 2006 (UTC)

The following discussion is an archived debate of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the debate was no move. -- tariqabjotu 01:41, 25 August 2006 (UTC)

Move Pi to π, the official discussion!

• Support: I think Pi should be moved to π. Rendering of the character shouldn't be a problem on older systems as one may think. Dread Lord CyberSkull ✎☠ 00:30, 19 August 2006 (UTC)
• Oppose per #wrongtitle and #move to π? above. Remember, what the system will do is move it to Π, thanks to how WP handles article capitalization. Septentrionalis 01:12, 19 August 2006 (UTC)
• Oppose per the capitalization issue. Also, it is easier to type at current location. Oleg Alexandrov (talk) 02:01, 19 August 2006 (UTC)
• Oppose reluctantly. I looked deeply into pages like WP:NAME and could find no explicit support for naming articles without ASCII titles. I agree that the correct title should be π, but I think that we are currently stuck with the wrongtitle template as a temporary solution. This issue goes far beyond π; see mu operator and lambda calculus and gamma function and phi function and delta function and likely many more. (Although the software currently accepts non-ASCII titles, it alphabetizes them incorrectly, among other problems. See Category:Recursion theory for an example of the results of a misguided attempt to rename mu operator to μ operator. ) CMummert 02:16, 19 August 2006 (UTC)
• Oppose. Why are we wasting our time debating this again?! --KSmrq^T 03:10, 19 August 2006 (UTC)
• Oppose. People would generally look up Pi not π in an encyclopedia. Hence the article should be at Pi. Cedars 08:35, 19 August 2006 (UTC)
• Oppose as per all comments in opposition above. Michael Kinyon 14:02, 19 August 2006 (UTC)
• Oppose. I don't see it as an issue of rendering. In English, one writes the name for this number as "pi". I see this often even in mathematical documents typeset using TeX, which has no issues with printing Greek characters. --C S (Talk) 16:52, 20 August 2006 (UTC)

It seems that the templates have been restored, and unlikely that a consensus in favor of renaming the article will be found. In July I proposed adding a paragraph to the WP math conventions to address situations like this. See Wikipedia talk:WikiProject Mathematics/Conventions#Greek letters. CMummert 11:32, 19 August 2006 (UTC)

• Oppose - unnecessary risking confusion. -- Beardo 09:42, 21 August 2006 (UTC)
• Support eventually, oppose for now. Of course the article should really be at π. The arguments about what people will type in are not persuasive; obviously pi would remain, as a redirect, so that's a non-issue. We need to get on the developers' case to fix this technical issue, and then the article should be moved. --Trovatore 23:12, 23 August 2006 (UTC)
  • Further comment on technical issue Here's the way I think it should be resolved: As now, you shouldn't be able to use upper- or lower-case initial (Latin) letters distinctively. We don't want foo and Foo going to different pages. But that's OK; each page can simply have a flag that indicates whether the initial letter should be rendered minuscule or majiscule. For non-Latin letters, even this is too much of a restriction -- there's no good reason ω-logic and Ω-logic shouldn't be different articles (although I don't know any standard meaing for the former, it could have one). --Trovatore 23:12, 23 August 2006 (UTC)
• Oppose. Keep it simple ASCII. I don't see why it is a problem, unless you are completly neurotic, and obsessive compulsive, in which case you have bigger problems in your life than this. Besides, the default capital-first letter will shatter the neurotic, obsessive compulsive attitude with Π, which is IMHO more ugly than Pi. +Mwtoews 16:50, 24 August 2006 (UTC)

Correction to the preceding entry: Π, in a math font, should have its own entry because it means the product of the terms of a sequence. BTW, the obsession discussed above is treated by picologists in clinics that treat obsessive compilsive disorders. Jclerman 17:05, 24 August 2006 (UTC)

Good point, that is: product (mathematics) is represented the Greek symbol Π. (I'm a bit shocked that the Summation article is light years fancier than product (mathematics) ... what? no TeX markup??). I was really re-commenting about the technical restriction in regard to the case of the fist letter. +Mwtoews 23:41, 24 August 2006 (UTC)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Misleading digits and bits

The article shows as of August 19, 2006:

In 1997, David H. Bailey, Peter Borwein and Simon Plouffe published a paper (Bailey, 1997) on a new formula for π as an infinite series:

(fomula here...)

This formula permits one to fairly readily compute the kth binary or hexadecimal digit of π, without having to compute the preceding k − 1 digits. Bailey's website contains the derivation as well as implementations in various programming languages. The PiHex project computed 64-bits around the quadrillionth bit of π (which turns out to be 0).

Comment: Better said "digit" not "bit, especially since it is not specified if the digit is binary or hexadecimal. And ah, who cares what the digit is, zero or one, or zero through 15 (hex)? Would someone care to edit this please? —The preceding unsigned comment was added by 65.96.106.226 (talk • contribs) .

I don't understand. What is misleading and better said how? Fredrik Johansson 20:44, 19 August 2006 (UTC)

"Bit" arrives for the first time here (I believe) in this essay on PI, and arrives without definition or explanation. Since the prior explanation describes "kth binary or hexadecimal digit" why diverge from the "digit" terminology and introduce a new term? But worse, for the the digit factoid cited, it is not stated whether the base is two or sixteen. --Yellowdesk 18:40, 21 August 2006 (UTC)

Well, it doesn't really matter. If it's binary, do it four times, and you've got a hex digit. If it's hex, you've got four bits, and if you like you can throw away three of them. But I haven't read the passage in the article; could be it could stand clarification. --Trovatore 02:04, 24 August 2006 (UTC)

The problem was that it is allegedly unclear whether the text refers to the quadrillionth binary digit or hexadecimal digit (difinitely not the same thing). But it is clear - this page clearly mentions the quadrillionth binary digit. And if we have already mentioned that the bit was computed, we might as well state what it is. This sentence should probably remain as it is. -- Meni Rosenfeld (talk) 09:25, 24 August 2006 (UTC)

That quote would settle it for me: 'clearly mentions the quadrillionth binary digit' I'll look at the source. If it says digit, then digit is what it should say.Yellowdesk 07:09, 6 September 2006 (UTC)

Surely you know that "bit" stands for "binary digit"? -- Meni Rosenfeld (talk) 08:35, 6 September 2006 (UTC)

Paper on normality and link to chaos

The open questions mention a webpage in the text pages above. I think the paper it refers to is: http://crd.lbl.gov/~dhbailey/dhbpapers/bcrandom.pdf and that it should be linked to directly or via citeseer.

Heliac's revert

This revert sure could have used an edit summary, but is still legitimate. This section's purpose is to demonstrate that π can be calculated with a naive method, and only one example is required for that. Numerous "real" methods of calculating π are discussed later in the article. -- Meni Rosenfeld (talk) 18:53, 25 August 2006 (UTC)

I have no objections to that. I unreverted primarily in an attempt to show the anonymous contributor that getting well-meant additions removed completely without explanation and argument is not what one should expect from Wikipedia in general. If things can be kept civil, I wouldn't mind getting rid of the secion completely. It is too complex compared to the precision one gets. If we want to describe a conceptually simple but computationally stupid way to approximate pi, why not just add the side lengths of a fine polygonal approximation to a circle (not necessarily a regular one, just e.g. one where the numerically smaller of each corner's coordinates is rational)? Henning Makholm 12:58, 28 August 2006 (UTC)

I understand. I, too, am not sure about the necessity of this section, but I believe it does serve some purpose. About using perimeters of polygons, I think this method would be more complex than what we want for such an introductory section. -- Meni Rosenfeld (talk) 18:41, 28 August 2006 (UTC)

Images?

Paul August has added (diff) images of mathematicians to the "Formulae" section. I do not think these images really belong in this article. Any thoughts? -- Meni Rosenfeld (talk) 09:55, 28 August 2006 (UTC)

I agree. They are not relevant as illustations of the topic of the article, and the article is long enough without them. (Yes, I know some people use browser windows small enough that the images occupy space that would otherwise be vacant, but that is not a universal thruth). Henning Makholm 12:46, 28 August 2006 (UTC)

More than a day without objections. I'm removing the images. -- Meni Rosenfeld (talk) 18:27, 29 August 2006 (UTC)

Memorising pi approximations?

How the heck can anyone remember pi to over 80'000 decimals without looking it up? How can anyone remember pi to more than 20 or 30 decimals, for that matter? JIP | Talk 18:48, 30 August 2006 (UTC)

There are people with good memory, or more importantly, a memory which is good for this kind of thing - the amount of information in 80,000 digits of pi is negligible compared to what the human brain can contain, but most people's memory isn't suited for this accurate memorization digit by digit. I guess an average person has memorized more than a dozen phone numbers - memorizing a hundred digits of pi is just as easy. I personally know 80 digits or so from memorizing them a while back - which is, of course, very little, but still more than your stated 20-30. -- Meni Rosenfeld (talk) 10:56, 31 August 2006 (UTC)

I find it easiest to split the digits into "words" of 3-7 digits and choosing the splitting points to emphasize patterns. For example, I've memorized the beginning of π as 3.1415926 - 535 - 8 - 979 - 323 - 8 - 46264 - 3383...; note how all groups after the first are symmetrical except for the appearance of a few 8's. I'm fairly certain the average (young) person could learn at least several hundred digits of π this way, given some time and sufficient determination. Fredrik Johansson 11:25, 31 August 2006 (UTC)

I've memorised 33 decimal places, the first 28 just roll off the tongue as one word, the last 5 are split into a seperate word. Even more interestingly is that I can't seem to forget it. —The preceding unsigned comment was added by 213.48.15.234 (talk) 13:08, 20 February 2007 (UTC).

π vs 2π and the unit circle

I posted a paragraph discussing why pi goes only halfway around the unit circle, and was very careful to keep it factual and unopinionated. No matter -- boom, almost immediately deleted by somebody who says he "can't find anything in the immediate suggestion that I would use." Great. I could reinstate the paragraph, but then he would probably delete it again, and the quickness with which he did it the first time indicates that he's devoting a great deal of time to making himself the personal watchdog of this article.

Wikipedia's useful, no doubt, but it will always play second fiddle to a good search engine like Google as long as it's ruled by whoever has the most time/determination to enforce their way. The next time I see some relevant information missing from a Wikipedia article, I think I'll just make a good webpage about it instead. —The preceding unsigned comment was added by DarelRex (talk • contribs) 14:29, 31 August 2006 (UTC)

I think the section you wrote was pretty good, and many of the editors who watch this article have expressed sympathy with your point. At the same time, I support its deletion, as would most of them, not just Arthur Rubin. To understand my perspective, note that we've discussed this matter before: #2pi? above. No matter how neutral one tries to stay, the bottom line is that we're not aware of any reliable sources that address pi vs. 2pi. Without at least one source, it is impossible to follow Wikipedia's core content policies: for short, WP:V, WP:NOR, and WP:NPOV.

So actually, the deletion was an outgrowth of community discussion and long-standing policy, in our best traditions, not the action of one lone watchdog. The information you seek to add is missing not just from Wikipedia but from the published record in general. Rather than make another webpage about pi, you should seriously consider writing an article for a suitable mathematics journal! Melchoir 14:51, 31 August 2006 (UTC)

My apologies for not contacting "you" (User:DarelRex) directly. At the time I deleted it, the first paragraph was unsourced, the bullet points would be inappropriate even if sourced (IMHO), and the final paragraph would be speculation, even if it were sourced. We're only allowed 255 characters in edit summaries, so I am sometimes more brief than appropriate. If you can find WP:RS for the first paragraph, I'd be happy to see it in the article. (For what it's worth, we'd lose the "elegant" 113\355 as an aproximation for "π" if it were doubled.) — Arthur Rubin | (talk) 17:02, 31 August 2006 (UTC)

The "problem" is not the definition of the constant itself; it's the definition of unit circle. To the ancients, diameter was basic. It's easy to see why. A jar with unit diameter takes up that much room on the shelf. More recently, radius has come to be thought of basic. This serves the needs of the analytic geometer but otherwise doesn't make much sense. But even the analysts realized that the definition of the constant was far too well established to replace with circumference/radius. So one full turn of the modern unit circle is 2π and that is that. John Reid 18:36, 31 August 2006 (UTC)

It's not specifically analytic. Even Euclid in the Elements chose as his basic postulate that a circle can be drawn given its center and radius. It appears that even those we consider "the ancients" must have been guided by even older tradition when they considered a diameter the measure of a circle. Henning Makholm 09:54, 1 September 2006 (UTC)

But Euclid's principal employment of the circle (after the constructions of Book I) was as the locus of the right angles of right-angled triangle with the diameter as hypotenuse. Septentrionalis 19:18, 7 September 2006 (UTC)

You forgot science. Trust me, radii make a lot of sense. And who knows, given recent events, old definitions are not sacred. I fully expect that someday there will stir a debate over 2pi. I hope I live to see it. Melchoir 18:50, 31 August 2006 (UTC)

"π Is Wrong!" is an article (well, sort of) in The Mathematical Intelligencer 23 (2001), vol. 3, that discusses the topic of "π vs 2π". — Telking 14:58, 26 January 2007 (UTC)

I think perhaps here we see why many mathematical realists don't like to be called "Platonists". Just because they think there's a right answer to whether the continuum hypothesis is true, doesn't mean they want to be associated with the notion that one of the pair radius/diameter is "essential" and the other "derived". (Not, I should say, that I have any idea whether Plato would have thought that).

The change from π to 2π will never happen (or at least not for a very long time), not because making π basic is "inherently" better, but simply because the changeover costs would be high and the benefits speculative at best. --Trovatore 15:47, 1 September 2006 (UTC)

WP:HORSE. John Reid 12:27, 2 September 2006 (UTC)

I think this issue is interesting. Please do not restart discussion. For future reference, though, the paragraph deleted can be found here.

RandomP 20:08, 26 September 2006 (UTC)

Pi-unrolled

Image:Pi-unrolled.gif

Workshop

There has been some criticism of this work -- unfortunately, somewhat diffuse. I'm astonished to see it was even nominated as a Featured Picture Candidate but it follows that if it can be improved to this standard, I should make the effort. I've solicited additional comments but more are needed. I'm sure all understand it's quite a job to rework every frame of an animation and that, having done the job 4 times already, I'd like very much to be sure the 5th version is the last.

I call your attention to the Specs section. It's much more useful to me if editors simply edit these specs to suit themselves, rather than making long, detailed text comments. Don't worry about overwriting other editor's specs; I will take all history into account. Let's do this in true wiki-fashion. John Reid 14:01, 2 September 2006 (UTC)

Workshop closed. John Reid 21:32, 15 October 2006 (UTC)

FP version

The (6th) version uploaded distinctly as Image:Pi-unrolled-720.gif has been promoted to FP. Note that a thumb caching bug means that all efforts to manually purge old versions seem to fail. Please, in the article, leave the "720" code for a couple weeks. John Reid 21:32, 15 October 2006 (UTC)

Wrong title?

I do not agree that this article should be titled π, even if that were technically possible; then again I hold that Gamma function is the proper name of the function whose symbol is Γ(x); for the same reasons that Factorial is the name of the function symbolized n!. I therefore dispute the {{wrongtitle}} tag. Septentrionalis 19:25, 7 September 2006 (UTC)

Seconded. The whole "correct"/"incorrect" language is particularly unencyclopedic, not to mention distracting. Melchoir 20:41, 7 September 2006 (UTC)

Well, in any case, whether the article should be π or pi, the title is incorrect, and wikipedia policy says we should have that in either case. There is another discussion above, where the wrongtitle tag is there basically by consensus. McKay 23:16, 7 September 2006 (UTC)

Incorrect? Are we comfortable using the first words of the article to call Borwein and Borwein incorrect?[1][2] How about the article's other references?[3][4][5][6] Are we so militant about choosing one of many typography variants that we're going to put an italicized notice at the top of the article calling all other variants wrong? Melchoir 23:37, 7 September 2006 (UTC)

Well, let's look at these one at a time, shall we?

• [7]

  Sure, I'll call them wrong, because they are inconsistent in their usage of the term throughout the book. It's as if they don't know what to do. One could argue that it could be done either way.

• [8]

  more inconsistency. They don't even remain consistent in the index.

• [9]

  this one appears interesting. They never use "pi" except in the title, one place in a figure, and when referencing other people's titles.

• [10]

  another interesting one. Again only in the title (and the url).

• [11]

  This one basically proves my point. Did you look at the back page? (Google book allows you to go to the back page.) The back says "A HISTORY OF π (PI)" as if this were a techinical limitation. Also, do a search (google does this too) for "pi" google's search doesn't return instances of π, and there are exactly 3 hits. One, on the front flap, and two other cases from a computer printout. This printout is older (1961). I'm not sure what character set they were using back then, but ASCII didn't come out until 1967, and it didn't have a glyph for π. I wish I could tell who wrote the flap content, but the back flap's content is restricted for some reason, but they typically aren't used

• [12]

  I can't believe that you referenced this one. This one is also silly for you to include. Sure axriv.org uses "pi", but the title of the article in the attached pdf is "A Faster Product for π and a New..."

What I'm trying to say is the reason that "pi" appears everywhere, is that using π is a technical limitation. Lets go to amazon.com, and search for "pi".

1. "π", a movie. Amazon has a technical restriction on π, they can't use it in their titles.
2. "Life of Pi" a tiger named "Pi" from a chinese word having nothing to do with the greek.
3. related to the movie
4. related to the movie
5. related to the movie
6. "History of π" another example of the technical limitation.
7. "π: A biography..."
8. worthless
9. worthless...

So, I don't think that the usage of "pi" is mostly supported by technical limitations. McKay 22:51, 9 September 2006 (UTC)

Okay, you do feel comfortable calling Borwein and Borwein wrong, and everyone who uses "pi" as a title inconsistent. I do not subscribe to your POV, and I don't see why our article should push it. Melchoir 22:59, 9 September 2006 (UTC)

McKay inserted amd I removed the following citations in the article. They are noted here for reference; the next step here would be a {{disputed-intro}} tag - or whatever it is.

• The Concise Oxford Dictionary of Mathematics, Christopher Clapham, Second Edition, 1996. They alphabetize and label their entry "pi" (lowercase), and only use π in the entry
• HP 48G Series User's Guide, Hewlett Packard, 1994. They only use π in their guide
• Mathematics for the Million, Lancelot Hoghen, F.R.S., 47th printing, Fourth edition, 1968. They only use π, and alphabetize the index entry on π between "Phoenecians" and "Pilgrim"

This is one which agrees with the present title, presumably for the same reasons WP uses, and two which disagree. Added to Melchior's evidence, this is fairly good evidence for the proposition that (as usual) the name and the symbol differ. If so, we should, as we do, use both; one to name the article and the other in most of the content. Septentrionalis 16:54, 8 September 2006 (UTC)

Or the new refs can be cited in the "The letter π" section, which is our encyclopedic attempt at characterizing the problem. Melchoir 17:06, 8 September 2006 (UTC)

Personally, what I think it shows, is that "pi" can be used as an article name, particularly for use in alphabetization. But when referring to it as a mathematical constant (which is the purpose of this article), π should always be used. If you want to talk about the symbol for which the constant was chosen, the symbol has a romanization. McKay 03:37, 9 September 2006 (UTC)

(Maybe this is a dead horse, but if you want my opinion...) In handwriting and typeset documents, yes. But in electronic communication, "pi" is very common, and while that isn't a reason to use it, it's a reason not to call it "incorrect". Melchoir 03:49, 9 September 2006 (UTC)

I reverted the change that removed the wrongtitle template again. There was no consensus to remove the template. I added the <ref>s because someone added a {{fact}}. If the title really were Pi, why isn't that used all over the article? I'm not in favor of a move, for several reasons, But until someone can show me a more authoritative reference than The Concise Oxford Dictionary of Mathematics I think I make a pretty good case. McKay 03:57, 9 September 2006 (UTC)

The template is petty, POV, unencyclopedic, and distracting. It does not benefit the reader. Why should it appear in the article? Melchoir 04:03, 9 September 2006 (UTC)

Exactly. It is, in addition to being incorrect since "Pi" is a correct title (though not the only possible correct title), extremely ugly and doesn't benefit the reader in any way. A perfect example of editor-centric clutter. Fredrik Johansson 12:49, 10 September 2006 (UTC)

Endorse Greek letter as theoretically correct title of article; silly to actually retitle it though. All articles should be titled with the basic Roman character set; I don't endorse accented letters, let alone Greek, special symbols, or double-byte/unicode in titles. A-Z, a-z, 0-9, apostrophe, and the standard hyphen only, plus parens for dab. This is because of the way articles are indexed and searched.

But yes, π is the correct name and symbol for the concept -- in any language. If this were a printed work, I would title it:

Pi (π)

John Reid 12:52, 10 September 2006 (UTC)

π is correct, but "Pi" is also correct. So there is no way the current title can be "incorrect". But you even seem to admit this fact yourself, so why do you endorse the template? Discussing alternative article names on the talk page is fine, but why on earth do readers need to be distracted by this, as the first thing they see in the article? The notation is explained clearly enough in the section "The letter π" for anyone who might actually be confused, so what purpose does this hideous template really serve? Fredrik Johansson 13:10, 10 September 2006 (UTC)

Yeah, I think we should save {{wrongtitle}} and {{lowercase}} for cases where the title as actually displayed is genuinely wrong or misleading. E (mathematical constant) is the canonical example of an article where the template genuinely is needed, but here it's probably not. This is a distinct question to whether we would move the article to π (lowercase) if we could—I would be in favor of that, and I think we should pressure the developers to remove the uppercasing for non-Latin letters. --Trovatore 21:54, 10 September 2006 (UTC)

Agree, it is clear that "pi" is correct (and correctly capitalized at the beginning of sentences or headers, or when initial capitalization is turned on in this wiki for article names. There is nothing "incorrect" about the title. Gene Nygaard 15:45, 22 September 2006 (UTC)

It's not just capitalization; the category sorting algorithm doesn't alphabetize Greek letters correctly. If those two problems were fixed, I would be in favor of moving this article to π with a redirect from pi and Pi. Same for Gamma function, Mu operator, lambda calculus, etc. This opinion is not universal; see the post of Septentrionalis, 19:25, 7 September 2006. CMummert 17:02, 22 September 2006 (UTC)

The sorting you can take care of by adding a sort key (looks similar to piping used with links, but works differently); that's something that needs to be done every time somebody creates an article with an é or a Č or an í or whatever; it isn't just Greek letters that don't sort according to English sorting rules, and the Unicode number sorting we get is not proper sorting in any language's sorting rules. Of course, far too many people fail to do that, so we have lots of mixed up entries in categories which might well remain hidden from someone looking in those categories. Furthermore, I'd never want any software solution which sorted ρ as if it were the three Latin letters "rho". Put me in the camp that would oppose moving this page to a lowercase π even if initial capitalization were not turned on in this Wikipedia, and even if it were then sorted in categories using the |Pi sort key. Gene Nygaard 22:00, 22 September 2006 (UTC)

Aesthetics

I think this might be the worst looking lead section in Wikipedia. Fredrik Johansson 19:29, 7 September 2006 (UTC)

I'm afraid I have to agree that the bit that I see when I look at the top of the page is pretty hideous aesthetically, and it could do with a bit of attention from someone who knows a bit about page layout. On another matter, I rather like the section on the Serbian version which has a nice section on the historical progress of calculations of the decimal expansion of Pi - anyone think something similar might be nice for our version? Madmath789 19:48, 7 September 2006 (UTC)

Once the unfinished sections in User:Fredrik/Pi get fixed (other editors are welcome to help out), I think we will have a much nicer version ready. Fredrik Johansson 20:00, 7 September 2006 (UTC)

If this version can be tweaked so that the animation must lie next to the TOC (in some browsers the TOC overlays the animation), it might do; dab header on top, followed by text and image of π; followed by TOC and animation. Septentrionalis 17:00, 8 September 2006 (UTC)

You know, I don't like the animations at all. At least not at the top of the page. Also, I put {TOCright} on there, but got reverted in the flurry of vandalisms/reversions. I think it makes the page look much nicer. (My version). --DevastatorIIC 09:49, 21 September 2006 (UTC)

When I created the animation, I added it to the article way down in Trivia. John Reid 17:55, 24 September 2006 (UTC)

parsing error

Can some expert fix this paragraph:

$\pi \,\!$ can also be expressed acording to Machin's Formula:

Failed to parse (syntax error): {\displaystyle 1/4 \pi = 4 tan^&minus;1 (1/5) - tan^&minus;1 (1/239).\,\!}

• NOTE: tangents should be inverse tangents.

Jclerman 16:36, 2 October 2006 (UTC)

In German it seems to be this the intended code:

$4\arctan \left({\frac {1}{5}}\right)-\arctan \left({\frac {1}{239}}\right)={\frac {\pi }{4}}$

Jclerman 16:50, 2 October 2006 (UTC)

Calculating π

I think the section "Calculating π" is too long and out of place. it seems to be addressed to people with limited math skills, but then includes a double summation formula (which could be simply eliminated). It goes on to suggest a procedure that pretty much requires writing a computer program to get any accuracy. It doesn't mention a much simpler method, cutting out a large circle out and weighing it. The section might make more sense as an intro to the numerical approximation section, but as is I think it will turn a lay reader off before some other section that are more accessible.--agr 11:44, 6 October 2006 (UTC)

I agree in general, and I wouldn't mind having the section removed. However, I don't think that weighing a circular object counts as "calculating" pi. The intention of the section seems to be to demonstrate to lay readers that it makes sense for there to be well-defined procedures for approximating pi rationally, even though pi itself is not rational -- i.e., to counter the false inference that because pi does not have a concrete fractional value, it is somehow a matter of opnion which approximation comes closest. (No, I don't think the section reaches that goal, but weighing cardboard wouldn't either). Henning Makholm 21:30, 6 October 2006 (UTC)

I'll see what can be done about the double summation, but I think the section should stay. (Disclaimer; I wrote it.) Even with a significant math background, I had never really understood what it meant to calculate pi -- it was always some sort of deep mathematical magic. So I think it's worthwhile to give people an intuitive sense of how "physical" constants can be calculated with infinite precision (even if the procedure is inefficient with pen and paper). Also note that the german version of this article (a featured article on that wikipedia) includes a similar section, including pseudocode. Lunkwill 19:34, 7 October 2006 (UTC)

Thanks for removing the double summation. However, I think this article is too long and disorganized. It might makes sense to partition most of the equations into the List of formulas involving Pi and start a new article on Computing Pi. This grid approach might make a good intro for the latter. I also think that is is not a good idea to expect readers to connect the dots. We should be explicit that the purpose of this paragraph is to a way of computing Pi that most people can understand. It might also make sense to include That pseudo code.

Finally I would also question the section on the naturality of Pi. It has two disjoint points to make, one that the value of Pi does not change because the universe may be non-Euclidian (should have its own section), and the second that Pi pops up in physics formulas. The latter paragraph then points out that Pi could be eliminated by a different choice of units, but doesn't mention that Pi would then appear in other formulas where it does not in SI units, e.g. the capacitance of a pair of plates. I'm not sure we need to get into this at all here. --agr 03:06, 10 October 2006 (UTC)

Sounds good to me. Be bold! Lunkwill 19:11, 10 October 2006 (UTC)

How many digits?

The article says there are 50 digits in

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510

but shouldn't the count include the 3 in the ones place? In a similar confusion, I'd like to ask for clarification one of the userboxes that reads, "This user knows by heart the first 54 digits in the decimal representation of pi." Shouldn't that count also include the first "3"? I'd really like to be cleared up. Thanks! Xiner 01:16, 9 October 2006 (UTC)

False. The article says something different: The numerical value of π truncated to 50 decimal places is:

Jclerman 01:22, 9 October 2006 (UTC)

Um, actually I was referring to the paragraph that immediately follows. You may argue that the word "digits" is modified by the longer phrase in the previous paragraph; I wonder if that's enough. In any case, I still wonder also about the userbox question. Xiner 13:05, 9 October 2006 (UTC)

Not sure what the exact reasoning is, but "places" in Pi commonly refers to everything following the decimal point. So 3.1415926535 is pi to 10 decimal places, not 11. This is the standard usage both here and outside Wikipedia. -- Moondigger 15:46, 16 October 2006 (UTC)

I think that's as good an answer as I'll get. Thanks. Xiner 16:55, 16 October 2006 (UTC)

error? (number theory section)

• The product of (1 − 1/p²) over the primes, p, is 6/π².

I'm not sure, but isn't that supposed to say π²/6 ? Kevin Hughes 15:52, 15 October 2006 (UTC)

That would be impossible, since all the terms in the product are less than 1. You're confusing it with the product of p² / (p²-1), which is its reciprocal. -- Meni Rosenfeld (talk) 16:13, 15 October 2006 (UTC)

Okay, thanks for the explanation! :-) Kevin Hughes 19:07, 15 October 2006 (UTC)

any formula which uses simple math operations to calculate π must go on forever

What do you mean? A formula does not go on like the bunny in the ad. Jclerman 14:58, 19 October 2006 (UTC)

Not addressed to me, but I have an answer. Consider the following formula for calculating Pi:

$\pi$ = 4 – 4⁄3 + 4⁄5 – 4⁄7 + 4⁄9 – 4⁄11 ...

This formula uses simple math operations -- addition and subtraction of fractions. The elipses (...) at the end of the formula indicate that you must continue in the same fashion by adding 4⁄13, subtracting 4⁄15, and so on. The formula "goes on forever," refining the accuracy of its Pi estimation as it goes. -- Moondigger 15:14, 19 October 2006 (UTC)

This is equivilent to saying that pi is an irrational number. Any foumula containing only a integers and a fininte number addition, subtraction, multiplication and division operators, can be reduced to a rational number. --Salix alba (talk) 20:42, 19 October 2006 (UTC)

But just saying that it is irrational does not prove that it cannot be represented as an expression with finite terms. ~iNVERTED | Rob (Talk | Contribs) 21:26, 19 October 2006 (UTC)

Depends what you mean by expression: what operators are allowed? If as above you restrict to +,-,*,/ then as the rationals Q is closed under these operation, any expression involving two rationals one one of these operators is also in Q. By induction on number of operators you can show that any finite number of operations is also in Q. You can also go further, by allowing n-th roots. Expressions involving a finite number of these will give a subset of the Algebraic number's q.v. Its know that pi is not an algebraic number. So pi can't be expressed using a finite number of these operations. --Salix alba (talk) 21:53, 19 October 2006 (UTC)

Incorrect approximation?

How is the following supposed to be an approximation of Pi accurate to 9 decimal places?

$(63/25)(17+15{\sqrt {5}})/(7+15{\sqrt {5}})$

I've tried evaluating it as stated and came nowhere near 3.141592653. Did I make a stupid error, or is this totally bogus? If bogus, it should be deleted from the article. -- Moondigger 00:35, 20 October 2006 (UTC)

Nevermind. I made a stupid error. -- Moondigger 00:47, 20 October 2006 (UTC)

Always and only π, never Π.

As noted before on this page, the Archimedian constant is never denoted with a capital Π, always with a small π. This was one reason a move of the article name to π was rejected; it was claimed that this would have been capitalised rendering the impossible representation Π.

Against this background, I'm a bit surprised that there have been a number of capital Π's in the article for more than five months. Am I missing something? JoergenB 01:29, 20 October 2006 (UTC)

Here is one reason: The May change to Π may have been reverted; but for some reason, the small π is π in slanted and is π in boldface, which at least with my browser yields a capital letter image. This seems to be an html problem rather than a wiki one. Anyhow, please sustain from italising or boldfacing π! JoergenB 01:47, 20 October 2006 (UTC)

Etymology

Is it περίμετρον or περίμετρος? As I said, my source was Henry George Liddell, Robert Scott, A Greek-English Lexicon, lemma on peri-metron. It's also mentioned in Earliest Uses of Symbols for Constants, though this is probably not the most reliable source.

I had a look in the Oxford English Dictionary. That gives the following etymology for perimeter:

< classical Latin perimetros circumference < ancient Greek περίμετρος, use as noun (short for περίμετρος γραμμη) of περίμετρος, adjective < περί - PERI- prefix + μετρον measure (see METRE n.^1). Cf. ancient Greek περίμετρον, post-classical Latin perimetrum (15th cent, 1686 in British sources, first attested in a glossary). Cf. French prmte (1538 in Middle French as perimetre), Spanish permtro (1582 or earlier), Italian perimetro (1581). [The French and Spanish didn't copy properly, but they're not relevant here]

For possible confusion between this word and PARAMETER n. see discussion s.v.

I'm not sure what to make of this, but it seems to say that περίμετρον exist, but that the English perimeter does not derive from it.

Finally, I don't understand the edit summary "I challenge you to find «περίμετρος» in _ANY_ Greek/Greek dictionary!" Does this refer to monolingual dictionaries in ancient Greek? I've never seen any of those. -- Jitse Niesen (talk) 02:45, 22 October 2006 (UTC)

Hi, first of all, regarding the edit summary, I made a typing mistake, it should have read:

"I challenge you to find «περίμετρον» in _ANY_ Greek/Greek dictionary!"

What I meant is that you are not going to find it in any greek/greek dictionary because that form does not exist in (ancient, hellenistic koine or modern) greek. Perhaps (if I may risk a guess) it was a false extrapolation from the latin perimetrum which you mentioned (and of which I was previously not aware of). This would be a prefectly possible (and minor) mistake for some editor whose native language was other than greek but would not escape the eye of a native speaker.

Regrettably I don't have my copy of the dictionary of Δημητράκος with me right now so that I can send you a digital picture of the appropriate page for you to look at and see that «περίμετρον» won't be in there. If you would like that, please give me some time.

(Obviously, to answer your previous question, Δημητράκος is i) ancient/koine/medieval/modern (all four) to modern Greek ii) more authoritative as having been compiled by greeks. Why would the definitions themselves have to be in ancient?)

By the way, it is ἡ περίμετρος in both ancient and modern greek. Similarly, the term "diameter" is ἡ διάμετρος in both ancient/modern. And sorry if I sound abrupt overall, I do not mean to be quarrelsome. Regards, Contributor175 02:36, 1 November 2006 (UTC)

Both τό περίμετρον and ἡ περίμετρος (γραμμή) are found in Ancient Greek and are about equally common in the Perseus Project's corpus[13]. -- but περίμετρος has other meanings as well. περίμετρον is found in Herodotus, Aristotle, Lucian, ...; περίμετρος is found in the same text by Aristotle (Mir.) as well as in Theophrastus, Polybius, .... --Macrakis 03:04, 1 November 2006 (UTC)

Nevertheless, given the etymology in the OED that I quoted, I think we should use the female form. -- Jitse Niesen (talk) 03:21, 1 November 2006 (UTC)

I stand corrected. Contributor175 13:22, 1 November 2006 (UTC)

I eventually managed to look this up the dictionary of Δημητράκος which indeed lists both (unlike what my original impression was). The issue was already settled of course but I would not want anyone reading this to get the false assumption this was an error in the dictionary of Δημητράκος. I would like to thank both of you for helping clarify the issue and promise to do better fact-checking in the future. Contributor175 20:17, 5 November 2006 (UTC)

Time Cube Pi

[14]: I propose that Time Cube Pi be mentioned in this article. Even though it may totally incorrect, you should still mention it because there is a strong association, and particularly as a See Also. -- Zondor 04:11, 23 October 2006 (UTC)

• Support -- Zondor 04:11, 23 October 2006 (UTC)
• Oppose. Let's hold the line on stupid trivia. A little bit of it's OK, but too much of it crufts up the article. --Trovatore 04:35, 23 October 2006 (UTC)
• Oppose. The mathematical claims in Time cube are rubbish, and the article is likely to be deleted soon. Madmath789 06:15, 23 October 2006 (UTC)
• If the article is kept then it definately should be included. It doesn't matter if its incorrect or not. This article does not necessarily need to be in the context of mathematics only. Otherwise, it is POV towards mathematics. Wikipedia is a general encyclopaedia not only a mathematical one. -- Zondor 09:38, 23 October 2006 (UTC)
• Support. ~ iNVERTED | Rob (Talk | Contribs) 09:47, 23 October 2006 (UTC)
• Oppose. Time Cube is nn, and its relation to pi is marginal. Will we now add the time cube to the "see also" section of every article on which it has something silly to say? If anything, the proper place would be at the "fictional references" section, but since the necessity of this section is questionable anyway, there's no reason to add more items to it. Your last comment sounds like "it is POV towards truth and facts". I'll take that "POV" anyday. -- Meni Rosenfeld (talk) 10:02, 23 October 2006 (UTC)
• There is no strong association. The statement "pi = whatever" may be important in the Time Cube world of ideas, but Time Cube is of no importance in the world of ideas surrounding pi. To put it in another way, this article should not contain all knowledge regarding pi, only the important bits. I'd argue that not mentioning Time Cube would be NPOV. To quote WP:NPOV: If a viewpoint is held by an extremely small (or vastly limited) minority, it does not belong in Wikipedia (except perhaps in some ancillary article). -- Jitse Niesen (talk) 10:28, 23 October 2006 (UTC)
  • Then it belongs in the Trivia section among other useless items as well (WP:POKEMON). Not fictional because it is a real life claim. If the article is kept, then it is notable. We explicitly mention that it is widely considered a crank claim. It appears to be talking about the mathematical Pi and hence the association. This is all dependent on whether the article is kept and the text is correct. -- Zondor 11:34, 23 October 2006 (UTC)
    • If the Trivia section contains useless items, they should be removed. Even if the Time Cube article is kept, and if it would follow that Time Cube is notable enough to be in Wikipedia, it does not follow that it is notable enough to be in this article. I agree that there is an association; my point is that the association is not strong enough to warrant inclusion in this article. -- Jitse Niesen (talk) 12:15, 23 October 2006 (UTC)
• Oppose. Information should be added to this article if it is relevant and notable. The addition of the Time Cube theory of Pi to this article would lend it relevancy and notability that it doesn't already have. -- Moondigger 12:43, 23 October 2006 (UTC)
  • Tell me how are most of the entries in Trivia and Fictional references are anymore more notable than the Time Cube claim? Agent 3.14 in Spy Hard? 314 seconds in The Matrix Reloaded? A9.com search engine offers discounts of (π/2)% on purchases? A song called "Three Point One Four"? Futurama? Simpsons? Kate Bush? Why not a Time Cube crank claim of 3.20? Besides this, you want an encyclopaedia that is not too narrow minded on the mathematical side. I want to know everything about Pi including notable fictional references, trivia, alternate views, how it tastes, how it smells. -- Zondor 13:52, 23 October 2006 (UTC)
    • (Edit conflict with Salix alba; inserting my comment here.) Because, quite frankly, all of those things are notable outside of their own subjects -- known to millions of people unassociated with Wikipedia or Gene Ray. Come on, you aren't honestly trying to equate the Time Cube theory's extremely limited notability with movies, songs, television shows and musicians millions of people are familiar with outside of the context of this article? Again, listing the Time Cube Pi theory here would lend it notability it does not already have, equating it (in some ways) with The Simpsons, Kate Bush, etc. It doesn't belong here because it simply isn't relevant or notable enough. And yes, The Simpsons, The Matrix Reloaded, etc are all notable enough. -- Moondigger 14:15, 23 October 2006 (UTC)
• Oppose no need to spread TimeCube material beyond its wikipage. Reply to Zondor, a much larger number of people have heard of Spy Hard/The Matrix/A9/Futurama/Simpsons/Kate Bush than Time Cube, and they all got the first three digits right. --Salix alba (talk) 14:06, 23 October 2006 (UTC)
• Response to Zondor I don't say that those other references are any better. I wouldn't mind junking the whole lot, particularly if they're taken as precedent to let in crap like this. But a few trivial references are tolerable, provided we hold the line and don't permit a cruft explosion. --Trovatore 16:13, 23 October 2006 (UTC)
• Oppose -- there is far too much triviacruft on the page. The trivia section apparently tries to be an exhaustive list of all times in history an allusion to pi has been published or broadcast in any medium apart from math research and education. That is both utterly useless and condemned to failure. Nix it all, I say. Henning Makholm 16:39, 23 October 2006 (UTC)
• Comment I wouldn't support elimination of all trivia or fictional references, though (looking through them now) I would support trimming both sections. -- Moondigger 17:24, 23 October 2006 (UTC)

• Oppose -- A suggestion to mention it at History of numerical approximations of π#Less accurate approximations I could take seriously; altough even there it would need a better reference than to a section of a wiki page with no further directions. The See also section of this article definitely is not appropriate. If other entries there also mainly consist of incorrect claims on exact values, they also should be deleted, or moved to the History of numerical approximations of π. JoergenB 18:58, 23 October 2006 (UTC)
  • [15]: Support to move to a sub page. -- Zondor 04:34, 24 October 2006 (UTC)

Numbers template

I suggest we add {{numbers}} to this article 204.81.77.4 15:12, 23 October 2006 (UTC) preceding comment edited by Trovatore 16:17, 27 October 2006 (UTC), to avoid transcluding the template into this page

Pi will either repeat or terminate

It is not irrational. this is proven in its very definition: "The ratio of a circle's circumference to its diameter." The key word is ratio. It will repeat or terminate somewhere down the line. We just haven't found it yet.Xparasite9 16:02, 27 October 2006 (UTC)

No. A rational number is the ratio of two integers. A circle's diamater and circumference can't be both integers (unless you consider the degenerate case of a point, which we don't). Pi has been proven to be irrational. -- Meni Rosenfeld (talk) 16:57, 27 October 2006 (UTC)

Daniel Tammet

The information in Trivia about him knowing the most digits of pi is now incorrect and seriously outdated. A few weeks in October or November 2006 a man memorised, I think, about 100,000 - correct or not he beat Daniel's record. Needs to be changed. —The preceding unsigned comment was added by Algebra man (talk • contribs) 22:53, 12 November 2006 (UTC)

The ultimate value of PI

There you can read that PI can have a limit at 1.3511 trillion digits.

• Watley Review
• Infosatellite

This limit was discovered by Professor Yasumasa Kanada while trying calculate PI up to 1.5 trillion places.

Have you read this? Mindmatrix 14:45, 14 November 2006 (UTC)

But what's with Infosatellite article? This Infosatellite article says the same.

The reporter failed to understand what was going on; neither the first time nor the last. Septentrionalis 18:58, 14 November 2006 (UTC)

Keep image

Keep the moving Pi image please. It illustrates in an interesting fasion the principlee of Pi. Maunus 15:28, 19 November 2006 (UTC)

I don't recall anybody having proposed to remove it recently. Animations are bothersome in general, but I think the consensus is to grudgingly accept that it would be difficult to convey the same information in a static image. Henning Makholm 16:51, 19 November 2006 (UTC)

I am glad.Maunus 17:19, 19 November 2006 (UTC)

Animated images are fine, as long as the final frame shows useful information. This for the benefit of users (like me) who disable looping of animated images in our web browsers (e.g., NetScape can be configured to show only one cycle of animation, which leaves the final frame as a static image). — Loadmaster 20:20, 20 December 2006 (UTC)

User:Eric Ng's contributions

I've incorporate the section including his contributions below. Unless published, it's WP:OR, and cannot be included in the article. However, they are interesting, if correct. I'm reverting the article to its previous status.

• General Viète Product:

By $\pi =\left(m\sin {\frac {\pi }{m}}\right)\sec {\frac {\pi }{2m}}\sec {\frac {\pi }{4m}}\sec {\frac {\pi }{8m}}\cdot \ldots$

Put $m=2$ gives the Viète Formula

For $m=3$ (by Eric Ng, the contributor, or if there are any independent discoverers please cited above),

$\pi =3\cdot {\frac {2}{\sqrt {2+{\sqrt {3}}}}}\cdot {\frac {2}{\sqrt {2+{\sqrt {2+{\sqrt {3}}}}}}}\cdot {\frac {2}{\sqrt {2+{\sqrt {2+{\sqrt {2+{\sqrt {3}}}}}}}}}\cdot \ldots$

For $m=5$ (by Eric Ng, the contributor, or if there are any independent discoverers please cited above),

$\pi ={\frac {5}{\phi }}\cdot {\frac {2}{\sqrt {2+{\sqrt {\phi {\sqrt {5}}}}}}}\cdot {\frac {2}{\sqrt {2+{\sqrt {2+{\sqrt {\phi {\sqrt {5}}}}}}}}}\cdot {\frac {2}{\sqrt {2+{\sqrt {2+{\sqrt {2+{\sqrt {\phi {\sqrt {5}}}}}}}}}}}\cdot \ldots$

where $\phi ={\frac {1+{\sqrt {5}}}{2}}$ the Golden ratio.

• Sine as an Infinite Product:

By $\sin x=x\prod _{n=1}^{\infty }\left(1-{\frac {x^{2}}{n^{2}\pi ^{2}}}\right)$ (See [16])

Put $x={\frac {\pi }{2}}$ gives the Wallis product

For $x={\frac {\pi }{6}}$ (by Eric Ng, the contributor, or if there are any independent discoverers please be cited),

${\frac {\pi }{3}}=\prod _{n=1}^{\infty }\left({\frac {36n^{2}}{36n^{2}-1}}\right)={\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {12}{11}}\cdot {\frac {12}{13}}\cdot {\frac {18}{17}}\cdot {\frac {18}{19}}\cdot {\frac {24}{23}}\cdot {\frac {24}{25}}\ldots$

— Arthur Rubin | (talk) 15:35, 20 December 2006 (UTC)

Huh?

In the article, it states that pi and e are not algebraically related. What about the 'famous five' equation. e^(i*pi) + 1 = 0. —Preceding unsigned comment added by 69.223.62.238 (talk • contribs) 2006-12-24T21:53:06

This relation is true, but it does not count as an "algebraic relation". For an algebraic relation you would need to exhibit a polynomial P(x,y) in two variables with integer coefficients and powers, such that P(e,π)=0. (By the way, what the article says is not that e and pi are not algebraically related, but merely that it is unknown whether or not they are. However, the smart money appears to be on "are not"). Henning Makholm 00:37, 25 December 2006 (UTC)

deleted line

I excised the following from the article:

Dr. Shanks's son Oliver Shanks, also a mathematician, states
that there is no family connection to William Shanks, and in
fact, his family's roots are in Central Europe.{{citation needed}}

This lacks a citation, and, more importantly, it does not seem to be relevant to the article. --JianLi 03:22, 30 December 2006 (UTC)

Pi

Can I add that Pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998 62803482534211706798214808651328230664709384460955058223172535940812848111745028410 27019385211055596446229489549303819644288109756659334461284756482337867831652712019 09145648566923460348610454326648213393607260249141273724587006606315588174881520920 962829254091715364367892590360011330530548820466521384146951941511609?—The preceding unsigned comment was added by 72.92.84.100 (talk • contribs).

I don't see a compelling need for so many digits. There are links to additional digits, if someone were interested. I would oppose adding more; 50 is enough for any practical purpose. --TeaDrinker 19:13, 5 January 2007 (UTC)

This has been brought up before and it's always been decided that it just adds bloat to the page, especially since there are links to pages with digits. Deathbob 04:35, 14 January 2007 (UTC)

Closing page to non registered users

Non registered users have not posted non revertible contributions to this article frequently enough for it to be productive to keep them able to post; half of the recent edits (or more) are spam and then reverts. I don't know exactly what is required to lock a page to edits by registered users only but it might be a good idea. I mean, it is funny enough when you are reading an article and midway through refresh and find spam, but it is a waste of the Wiki servers' bandwidth, space, etc. Hazelorb 07:36, 11 January 2007 (UTC)

While this idea sounds nice, I don't think the policy supports semi-protection in these circumstances - but you may want to bring this up on WP:AN/I. -- Meni Rosenfeld (talk) 17:24, 11 January 2007 (UTC)

Request went through! Hopefully now we can start working on this article, and see what we've done. Hazelorb 01:06, 14 January 2007 (UTC)

Separate articles

Propose moving the formulae and Trivia sections to completely different articles, as they are highly specialized. As for other edits to this page, I think User:Fredrik/Pi's history section should be incorporated into History of numerical approximations of π which is linked as the main article in 2 sections of this article. I would like to consense a lot of that material into a good blurb and then properly link to that history article. I propose using the other sections of Fredrik's article (especially, "use in math/science" in maybe a slightly briefer form for the blurb section referring to the new formulae page, and the culture blurb exactly as he has intended.)

As for the other sections of this article,

• Maybe relate the sections preceeding History (which will be moved as already planned in the to do list) to lessen the clutter in the TOC, expand said info so it has a right to clutter the TOC, or put properties or any of the other info into the blurb at the top?
• Rewrite both the memorization blurb to be more well rounded and naturality to be less techy
• Open questions as the last section before references/see also

Let me know, I will start making these changes, but I did not want to step on any feet. I did a few minor things already, but these are a little more major. Also, User:Fredrik should feel free to start working in his history section into the appropriate article, and maybe be kind enough to write the blurb for this page?

Hazelorb 04:17, 14 January 2007 (UTC)

I was just about to talk about this but i see i've been beat. Anyway, alot of the formulae section minus things like the physics section would be better housed in Computing Pi. I've been working on it and some peices at the top of the artical have already been moved. Deathbob 04:31, 14 January 2007 (UTC)

Awesome glad someone else is helping with this mess. I did not really even know where to start, haha. Hazelorb 04:47, 14 January 2007 (UTC)

Added {{mergeto |Computing Pi |Talk:Pi }} on specific sections that would be most compatible Deathbob 04:54, 14 January 2007 (UTC)

Note that there is already an article list of formulae involving π. Computing Pi should focus on methods which can actually be used to calculate π efficiently, and IMO should be renamed Methods of computing Pi. -- Meni Rosenfeld (talk) 18:03, 14 January 2007 (UTC)

Well then why are all of those formulas on the main page AND a separate page? It makes no sense. Can we select a few key ones and then link to that formulas page then at least? Hazelorb 21:20, 14 January 2007 (UTC)

Yes. But make sure that the key formulae do remain in the main article (as well as the formulae page). -- Meni Rosenfeld (talk) 21:46, 14 January 2007 (UTC)

Which ones do you think we should keep? Right now we have every formula that could possibly involve pi, which is way too many for the main article (of course you know this). I definitely think it has to be few enough that the subheadings are no longer needed. It would be "Key Formulae" with whichever ones we choose, and the link "main article -- " Also maybe a short explanation (1 sent... 2 sents max) of those ones' immportance/why they are key ones - but the whole explanation could go on the formulae page. Hazelorb 21:52, 14 January 2007 (UTC)

The geometry section is a must to stay here, but for the most part that section is HUGE, especially the Analysis part, people just learning about Pi will not understand it, or care about it. So it think the majority should be split accordingly to the list of formulae involving π page and the Computing Pi page. We have a decent link for computing pi higher up the page, the Formulae section needs one if it doesn't already, after we get the layouts of those 2 pages established then see about renaming them then. Since you have worked on the formulae page you might wish to tag the sections that should be merged completely. As a side note Software_for_calculating_π should probably have cross refs to and from Computing Pi Deathbob 22:32, 14 January 2007 (UTC)

"we have every formula that could possibly involve pi..." That's a bit of a stretch. What the article currently contains doesn't come close to scratching the surface. The formulae which I think can be excluded from the main article are (from the analysis section) Viete's, Faster product, Symmetric, Chebychev and Totient. -- Meni Rosenfeld (talk) 18:05, 15 January 2007 (UTC)

By the way, there is some discussion of this at Wikipedia talk:WikiProject Mathematics#Computing Pi. -- Meni Rosenfeld (talk) 19:24, 15 January 2007 (UTC)

People seem to have stopped talking for the past few days, I wonder if more should be moved over, or what can be done to bring it to thier standards? Deathbob 16:19, 22 January 2007 (UTC)

Pi-unrolled moved to trivia

I see that Hazelorb has moved the pi-unrolled animation to the "Trivia" section, with edit summaries pointing to this talk page. Skimming through a few times, I find no recent discussion of this image -- what have I missed? Had I seen such a proposal, I would have opposed classifying the image as "trivia" -- if it serves any purpose at all in the article, it must be as a first, intuitive, introduction to what the article is about, for readers who are not comfortable with mathematical abstraction. Down in the trivia section I cannot see what purpose it serves. Henning Makholm 01:44, 19 January 2007 (UTC)

I see no discussion, justification, or logic in the move. — Arthur Rubin | (talk) 01:47, 19 January 2007 (UTC)

It was an old discussion. I don't really care where it is in the article, except that at the top of the page it scrolls in 800x600 browsers and the past discussion on this page was in opposition of it being there. (not meaning to cause any controversy here, if you REALLY want it at the top of the article you can move it back, just keep in mind the original creator of the image on this talk page said it was originally in trivia, and that it makes the page scroll). Do we really need both images in the top part is the main point. Hazelorb 22:32, 19 January 2007 (UTC)