Talk:Pi/Archive 3

Pi near a black hole?
I read somewhere that near a black hole a circle's circumfrence around the black hole can be different than pi times its diameter. Can someone who understands physics better than I do add something to the article? Pakaran 21:40, 29 July 2005 (UTC)


 * This is true (well its true anywhere really, just more obvious there) but is it anything to do with Pi? William M. Connolley 22:09:35, 2005-07-29 (UTC).


 * I doubt it, I think it's that the immense gravity distorts the shape of the circle, hence altering the basic formula to that of an ellipse. - Nintendorulez 18:29, 11 October 2005 (UTC)


 * Yes, altered shape, but I don't think it's an ellipse. I think it's an ellipse (Cassini oval?) McKay 07:57, 17 October 2005 (UTC)


 * in the theory of relativity i think it says that mass and energy, in a force a bit like gravity, distort the curvature of space-time. Is it possible that this curvature changes the relationship between diameter and circumfrence? therefore, if this is corect, pi is not a mathematical constant but a measure of the curvature of space! are there any other articals relating to pi changing due to the curvature of space? I would be intrested to see if I am not the only one to come up with this theory.


 * See the section "non Euclidian universe" above. &pi; is a mathematical constant.  It is the circumference of a circle of diameter 1 in Euclidean space.  In non-Euclidean space, the circumference may be something else.  But it is not called &pi;. --Macrakis 18:02, 31 October 2005 (UTC)


 * In Euclidean space, the ratio between the circumference and the diameter of a circle is always &pi;. In a curved space, this ratio varies, depending on how large the circle is. However, even in a curved space the number 3.14&hellip; has a meaning: if you make the circle smaller and smaller, the ratio between the circumference and the diameter gets closer and closer to 3.14&hellip;. Intuitively, this is because the curvature of the space vanishes if you look very close. -- Jitse Niesen (talk) 18:32, 31 October 2005 (UTC)

As was said by William Connelly in the first reply, this occours everywhere. Gravity of any matter turns spacetime into a manifold, so Euclidian geometry does not apply. This is most noticable near a black hole because the gravity there is so immense. As one's distance from a black hole approaches 0, the force of the black hole's gravity is limited by infinity, making it a "second order pole" so to speak, as opposed to the gravity of other objects which are limited by finite values. Because of this infinite gravity, the distortion is most visible there. But converslyif the circle experiences no distortion beforehand (That is, its shape is already a perfect circle when it encounters this situation) and it is centered on the black hole, it will maintain its shape. Because of its perfect shape, the force on any given point is equal, so all points are pulled in at the same speed toward teh same point. Any inward motion would mean that any point would coincide with both points next to it, so it maintains shape. He Who Is 20:29, 16 June 2006 (UTC)

Least accurate approximations
I just wonder, do we really need the subsection Pi in the section about numerical approximation? Seems like a curiosity, and it looks to me that it there is much more worthy material both before and after it. How about removing this, or otherwise making it a section at the very bottom with a better name? Oleg Alexandrov 17:05, 14 August 2005 (UTC)
 * I like it, but then I rewrote it. Making it a separate section. Septentrionalis 17:55, 14 August 2005 (UTC)

More digits?
I personally know pi out to 100+ digits, should we display only 70 on the main page? In addition, when talking about "pi to n digits" does n include the 3? IMHO, the statemant on the main page "...to a 70 pdeimal places" is correct; howerver, I (as above) often say that I know 100 digits of pi, althoughi don't include the 3 in that count (3.14159 counts as 5 digits). Are my semantics wrong or are both phrases acceptable?
 * Digits is ambiguous, and may or may not count the 3. Decimal places does not count the 3; significant digits does. Septentrionalis 13:06, 7 September 2005 (UTC)


 * The 71st decimal digit is a zero, so 70 seems like a good place to stop. -- Curps 02:41, 25 October 2005 (UTC)

I would like 70, too. I memorized the first 50 decimal places of pi here on Wikipedia (this should be on the Wikipediholic test!) Evan Robidoux 21:20, 18 January 2006 (UTC)
 * This section is essentially an archive; you should see below. Melchoir 22:04, 18 January 2006 (UTC)

Halloween exception
Pi is a numerical constant always equal to 3.14... except for Halloween when it's made of pumpkin: Pumpkin Pi. You can carve it out and then have a positive and a negative Pumpkin Pi. If you teach math it makes an unexpected treat for your students. Jclerman 19:20, 31 October 2005 (UTC)
 * You, sir, are a terrible, terrible person. I gotta remember that when I finish my math degree and start teaching high schoolers! :-D DevastatorIIC 21:48, 1 November 2005 (UTC)

What about the gang of four? I think it's digraceful to make such a mockery of a fantastic example of mathmatical reasoning. Keith

Rivers and pi
If a river is old enough that is with a rather meandering and stable path it is known that the ratio between the length of the river and the line connecting its mouth and source yields pi. Would somebody kindly put it into the article? --Dennis Valeev 23:21, 3 November 2005 (UTC)


 * I don't know about that. It seems you could only expect it to work if the river forms a series of semicircles, all of whose centers lie on a single straight line. I've seen some pictures of meandering rivers, and I seem to recall that they're much more creative. In fact, even if the landscape has a simple geometry, the ratio you speak of is probably controlled by the amount of water flow, the altitude of its source, etc., and it could take lots of values. Melchoir 19:32, 29 November 2005 (UTC)

The mathworld entry on pi (http://mathworld.wolfram.com/Pi.html) lists this, with a reference, but no explanation. It seems clear that this is not an actual definition of pi by any means, but an observation that some property of the motion of rivers over a long period of time tends to force the ratio to approach pi. One of the references given is the popular math book Fermat's Enigma, if anyone has this book maybe they could shed some light, provide statistics or reasoning behind the ratio. --Monguin61 22:06, 14 December 2005 (UTC)


 * Okay, it's here. It seems the time-averaged ratio tends to pi, but the instantaneous ratio undergoes large fluctuations. Due to erosion, the ratio tends to grow, but the river erases any loops it develops, dropping the ratio suddenly; see Oxbow lake. In this model, there is no such thing as a stable path. I think it's interesting enough to put in the article Meander, with a link from here. Melchoir 22:26, 14 December 2005 (UTC)
 * Thanks for the reference. Unfortunately I can't access the Science/JSTOR archive from home. I need to go to the university library to access it. This is not the work I'm trying to remember. It's a book, I think published by the USGS, discussing math and rivers (?) by an Arizona geologist, older than the Science article. Perhaps it's mentioned there. I'll have to see it sometime. Definitely, such reference(s) should be in the Meander article. Then after we understand them you can decide if to refer to them in the pi article. Jclerman 23:21, 14 December 2005 (UTC)
 * I think that the author of the book I mentioned is the Luna Leopold who authored the Scientific American article. See this webpage where it says: "For a detailed analysis of the mathematics of meanders and a variety of graphic illustrations, please refer to the article, "River Meanders," by Luna Leopold and W.B. Langheim, Scientific American, June, 1966." Jclerman 23:31, 14 December 2005 (UTC)
 * Well, the SciAm Leopold article doesn't seem to be online, and I'm not making a trip to the library just for this. Melchoir 23:51, 14 December 2005 (UTC)

Symbol for pi "TT" $$/pi$$
Please use the same symbol for pi, throught. The one used in the formulae and in the figure are OK. The other one, used in the text, looks as a TT. For ergonomic reasons the same symbol everywhere. Jclerman 22:21, 4 November 2005 (UTC)
 * The one that looks like a "TT" is the HTML entity for pi, rather than the image-rendered TeX version of pi. The use of the HTML entity instead of the TeX image is in line with the specifications given by the WP:Manual of Style (mathematics). -- Deklund 05:56, 16 November 2005 (UTC)
 * Then change the specs or make an exception to attain a more ergonomically readable text. Perhaps the specs were not written by a reading mathematician. Even the CMS accepts exceptions when warranted Jclerman 07:39, 16 November 2005 (UTC)
 * Yeah, I agree that it sucks that π is not so legible. But I don't support changing to inline tex.  If only we were using Times New Roman. -lethe talk 15:37, 22 December 2005 (UTC)
 * Nothing stopping you from changing your own Wikipedia style so that the pages are Times New Roman. Just add this to User:Lethe/monobook.css:

font-family: "Times New Roman"; }
 * 1) content {
 * &mdash;Chowbok 19:19, 22 March 2006 (UTC)

I Disagree ,the current symbol makes it hard to read ,and in first glance I thought this article was about something else(like the greek letter system) ,All uses of Pi in writing and reading uses the samwe symbol. Load time is neglegable because the same singal symbol will be loaded throughout the article. Big HTML format can fix further readibliy issues ,such as in $$\pi$$ ( $$\pi$$ ).I just need to go over all it's occurances ,help me not to miss anything.-- Procrastinating@ talk2me 10:22, 29 January 2006 (UTC)

Use letter, not image Tex formulae don't display well in-line. In fact, inline images in general don't render well, especially cross-browser -- it is hard to get baselines to align and character sizes to be consistent with text. What is more, you can't change their size by changing your browser text size (universal usability issue). Tex formulae are especially problematic for a single character, because it will be in Tex's choice of font, rather than a font that is consistent with the rest of the text. Another (more minor) problem is that you can cut and paste text reliably if it has inline images. If the letter &pi; looks ugly or illegible in your browser, you should get better fonts -- after all, it will affect the letter in Greek text, not just math. --Macrakis 15:59, 29 January 2006 (UTC)


 * Indeed, no need to write all in LaTeX. The problem is not HTML vs LaTeX, but the choice of the font: Move your mouse pointer over this &pi; - in my browser, the "pi" in the text looks ugly (I hate it !!), but the pi in the "popup" is very nice. (Also, page titles with &pi; look ugly, but in the Window's title they look nice (at least for me).) I also would appreciate to know if I can just change some browser settings and/or WP prefs to have a nicer "pi"... &mdash; MFH:Talk 14:48, 22 March 2006 (UTC)
 * See my reply to lethe, above. &mdash;Chowbok 19:19, 22 March 2006 (UTC)

The nicer tex pi is the only'' correct symbol. The TT pi is a capital pi, and should not be used. The standard symbol for the mathematical constant is lowercase pi, which is the pi used in the TeX sections.

But π is the letter pi in Arial font, which is standard on all Wikipedia's pages. User:Gee Eight 5 August 2006 19.41 UTC

2pi?
If I start an article on 2pi and describe its fundamentality and utility relative to pi, what will it take to get you, kind reader, to vote keep when it hits AfD? I'd like to know in advance. Melchoir 07:34, 28 November 2005 (UTC)


 * I'll vote delete. -lethe talk 15:36, 22 December 2005 (UTC)


 * Vote delete. (you can as easily make another 4pi article ,even more usfull) The Procrastinator 02:08, 30 December 2005 (UTC)


 * Actually, yes, 4pi is also more useful than pi; but in mathematics and physics, 2pi is more useful than either. Anyway, I'm not looking for a fight, so you don't have to worry about an article. Melchoir 20:22, 7 January 2006 (UTC)


 * I agree with your point of view; but write a paragraph here, of the form: "From some points of view, the choice of &pi; rather than 2&pi; as the fundamental constant is a historical accident. The frequency of sine and cosine is..." i'll defend it. Septentrionalis 23:02, 10 January 2006 (UTC)


 * oh wow ! that's a great very insightfull new passege ,please do add it. The Procrastinator 00:24, 11 January 2006 (UTC)


 * you might win me to defend it, too. 2&pi; occurs in Fourier transforms, the Gaussian distribution, Planck's constant (we all know that h-bar is the real one), and many more. &mdash; MFH:Talk 20:42, 16 March 2006 (UTC)


 * Septentrionalis's comment belongs in the &pi; article. There is no reason for a separate 2&pi; article, any more than there is a reason for an i&pi; or sqrt(-5) article&mdash;though they have interesting properties.... --Macrakis 21:16, 16 March 2006 (UTC)


 * Let's forget about sqrt(-5), this means either nothing, or anything... Let's turn to the point:
 * What he wants to say, is that the article IS in fact about HALF the fundamental constant 2&pi;, let's call it "circle number" (something better has to be found, since this term (at least Kreiszahl in German) means again half of 2&pi;): This is not 2 times the constant &pi;, but it IS the fundamental constant! I.e., the current page is about "half the circle number"! It's stupid to have an article about the half of a fundamental constant! Who would ever think of a page about "e/2"? We should delete the &pi; page, and replace it by something like "For historical reasons, the greek letter &pi; was introduced as symbol for half the value of the fundamental constant 2&pi;. &mdash; MFH:Talk 15:09, 22 March 2006 (UTC)


 * I agree completely that the fundumental constant should have been 2&pi;, and that therefore it is tempting to write the article 2&pi; and delete Pi or reduce it to a footnote. However, we can't ignore the fact that the constant that is used throughout the world is &pi;. Wikipedia is not the place to introduce neologisms, so the only thing we can do is add the aforementioned paragraph. And even that - only if we find a reference directly discussing this issue. Our personal opinions don't count. -- Meni Rosenfeld (talk) 17:28, 22 March 2006 (UTC)

Woah, woah woah! What are you talking about?!?! &pi; is so much more natural than 2&pi;. For lack of originality, I'm going to call this new number, &rho; Sure you get "circumfrence = &rho;r", and various physics and statistics formulas a little cleaner (though many are based on surface area of spherical functions, so they would still be 2&rho; or 4&rho;), but you're missing the point. in two dimensions, "circle's area = &pi;r2" there's "the most remarkable formula in mathematics" "ei&pi; + 1 = 0". This formula wouldn't have recieved the press it's recieved if it looked like "e&rho;i/2 + 1 = 0", and look, it even spells "pi" (almost). I'm sorry, but I just can't buy the fact that 2&pi; is more natural than &pi;. McKay 03:39, 10 August 2006 (UTC)


 * Ok, so there are two places where &pi; is more natural, compared with pretty much everything else. The fact that the area is &pi;r2 cancels out with the perimeter being &rho;r. The other formula isn't considered by everyone to be so remarkable - like you implied, its charm is more of a recreational curiousity, with all those constants appearing so neatly. With &rho;, it would be less aesthetic but make more sense mathematically. So yes, there are arguments in favor of &pi;, but they are overwhelmingly outweighed by those in favor of 2&pi;. -- Meni Rosenfeld (talk) 08:10, 10 August 2006 (UTC)


 * And the really fundamental fact is that eρi = 1; the formula for -1 is a consequence. Septentrionalis 18:50, 7 September 2006 (UTC)


 * Are y'all so sure about the area formula? What is it saying, really? If you remember the general formula for the area of a polar curve:
 * $$A=\int_0^{\rho}\frac{r^2}{2}d\theta.$$
 * For a circle, r is constant, so
 * $$A=\frac{r^2}{2}\int_0^{\rho}d\theta=\frac{\rho r^2}{2}.$$
 * This form shows you where it comes from, and and if students memorized it, they'd find the general integral easier to remember. If you "simplify" it by defining a constant as &rho;/2, you lose the explicit appearance of the measure of all angles and the factor of a half, both of which are intrinsic to the problem.
 * As for Euler, using pi sure gives it a sense of mystery, but e&rho;i/2 shows its true colors: the other square root of unity. Again, the 1/2 is meaningful and does not need to be cancelled or defined away. Got any others? Melchoir 19:47, 14 August 2006 (UTC)

I'm with you. But since Wikipedia is not the right place; let's set up an advocacy website elsewhere! Does &rho; stand for "revolution"? Fredrik Johansson 20:28, 14 August 2006 (UTC)

Constants for the masses!
In order to simplify mathematics, the value of PI should be declared to exactly equal (sqrt1+sqrt2). The value of e should be exactly (1+sqrt3). Millions of schoolchildren would benefit from these simplyfications. 195.70.32.136 14:57, 22 December 2005 (UTC)

You didn't spell simplifications properly. And no, it wouldn't simplify mathematics at all, it'd screw it up. The indefinite integral of e to the x wouldn't be e to the x anymore, it'd be something else. What about ln? Crazy. Deskana 13:11, 23 December 2005 (UTC)

Nowt to mention, sqrt1 = 1. Either way, you can't just "declare" pi and e to be whatever you want. They have specific values, and people don't decide what they are. We only figure out what they are -- He Who Is[ Talk ] 17:05, 27 June 2006 (UTC)

Spelling: Formulæ vs Formulae
Okay, admittedly this doesn't have anything to do with π per se, but a recent revert by Kungfuadam was done without offering any justification. There doesn't seem to be any previous discussion about the use of formulæ, so why is it being used? The accepted plural of formula is formulas or formulae, not formulæ. Doesn't the advocacy of uncommon and archaic spellings, such as formulæ, come under Wikipedia is not a soapbox? -- 203.173.24.77 07:22, 31 December 2005 (UTC)


 * Oxford English Dictionary (subscription may be required) The use of nonstandard spellings would indeed come under WP:SOAPBOX, but the use of standard British spellings specifically does not. —Blotwell 07:43, 26 February 2006 (UTC)

Seconds in a year
Odd that there are π x 10^7 seconds in a year. Well at least to 0.38%

--Geoff Broughton 20:55, 6 January 2006 (UTC)


 * That's a great mnemonic, and it seems to be fairly well-known to astrophysicists. I don't know if it belongs in this article, though. Melchoir 22:02, 6 January 2006 (UTC)


 * When you think about it, a year is a measure of the circumference of our orbit around the Sun, so a relationship to π would not be unexpected, IMHO. PeterBrooks 18:26, 23 January 2006 (UTC)
 * So it would take 10 million seconds to cross the average diameter of the Earth's orbital ellipse at the Earth's speed. User:Gee Eight 5 August 2006 19.46 UTC
 * Very insightful comment. Also, there is a fact that McDonald's has, at certain points in time, sold 3, 31, 314, 3141, 31415, 314159, ... hamburgers. And yes, as they become better manufactured as to approach a perfect circumference the numbers become closer approximations of pi. 198.65.166.209 18:45, 23 January 2006 (UTC)
 * 198.65.166.209's sarcasm is right on the money, and that is why we shouldn't mention this on the article. Melchoir 19:24, 23 January 2006 (UTC)

encyclopedic value 100 digits pi
As an enlightened encyclopedia ,people should reffer here for many reasons. One of these reasons could be finding out a non common approximation of Pi ,So Although not particularly fashionable ,I wish to extend it to 100 digits. It is very hard to find on the Net ,Unlike the 50 digits version. 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068

-get a life

[User:Diza|The Procrastinator]] 02:06, 30 December 2005 (UTC) Since 10 days have passed and no further input has been brought upon this issue ,I take it as the community standpoint. please refrein from further revert wars on this subject. The Procrastinator 19:38, 10 January 2006 (UTC)


 * I apologize, not only on my own behalf but on that of everyone else who has held the length at 50, for not responding to your request sooner. 100 digits is not the community standpoint, and a lack of comment is not a consensus. If you look at the history of the article, as well as this talk page, it seems that there is a general trend to add more and more digits. There is no logical end to this process, and we must restrain ourselves to some limit. Both 50 and 100 are nice round numbers; 50 fits on my browser, and 100 does not.
 * I'm reverting it and adding a reference to the "External links" section, where you might have noticed that the first six links are all resources containing more digits. Apparently it's not that hard to find on the Net, and if anyone really needs the digits, we've pointed to them. That's enough. Melchoir 22:56, 10 January 2006 (UTC)
 * Let's make it a little more obvious. Septentrionalis 00:04, 11 January 2006 (UTC)


 * You'd better change resolution ,because my screen fits all 100 of them easily. yet If this debate Has Already taken place I trust it. I've rearranged some links for better and easier lookup.
 * and god said : Let there be 22/7.
 * The Procrastinator 00:32, 11 January 2006 (UTC)


 * Okay, thanks! As for the screen, I could make by browser larger, but why punish myself by making it harder to scan lines? Already I've got more characters per line than a print typesetter would ever allow. More relevantly, though, we have to think of all the poor civilians on 1024. Melchoir 00:43, 11 January 2006 (UTC)

Does anyone think creating an article "Digits of Pi", with 10,000 digits or so, is approporiate? Maybe we could also leave 50 digits in the introduction of this article, and adding a section with more digits. --Meni Rosenfeld 16:23, 12 January 2006 (UTC)
 * Why? Melchoir 16:54, 12 January 2006 (UTC)

It would be nice to know. I think that given the amount of information about pi in this article, there should also be some words (or numerals) regarding what pi really is. Linking to other sites is great, but there should probably be more information within WP. I think I will create such an article unless there is a strong objection. --Meni Rosenfeld 18:09, 12 January 2006 (UTC)

Object There is really little point in showing large numbers of digits of &pi; anywhere in Wikipedia. What &pi; is, is certain mathematical relations, such as sin(&pi;)=0. The numerical value is less interesting. Fifty digits is much more than enough for any practical application (science, engineering), and no number of digits is enough to resolve any of the deep mathematical issues. Sometimes people use &pi; as a source of pseudo-random digits, but there are better ways to do that nowadays and WP isn't supposed to be a library of mathematical subroutines. Pointing to outside sources is just fine for large numbers of digits. Would you also suggest that WP should have 10,000 digits of e? Of sqrt(2)? Of &gamma;? etc. etc. etc.? --Macrakis 18:33, 12 January 2006 (UTC)

Object Yes, it's nice to know, but humanity already knows the first few thousand digits of pi, and we've already linked to them. Let's not kid ourselves: the absence of information from Wikipedia does not make it less real, or necessarily any harder to find. In the opposite direction, Wikipedia is not an indiscriminate collection of information. The digits of pi do not demand an article that anyone can edit, and they are not encyclopedic in the sense that the proposed article would forever be a one-sentence substub. The digits of pi don't belong in either half of the Wiki-pedia.

Why do I care? Because the digits of pi don't tell you anything about "what pi really is". That's what this article is for, and if you feel it's insufficient, then it needs more discussion, not more digits. I could create the article "3.14 followed by 10,000 random numbers", and it would be equally enlightening. Melchoir 18:43, 12 January 2006 (UTC)


 * Okay okay, objection sustained. --Meni Rosenfeld 19:36, 12 January 2006 (UTC)
 * Well, it's good that we aired this all out. Before you made your suggestion, I actually considered the idea, but I privately dismissed it. Maybe all the talk will put the issue to rest. Melchoir 19:41, 12 January 2006 (UTC)

For There should be a "More Pi" (or something) section at the bottom of the article that includes several hundred digits. This way the beginning of the article is kept tidy while you still have all of the information. And these digits of pi are important ... if somehow all other works in the world are destroyed along with all computers, but some printout of this page remains, the survivors will need to know the precise value of pi. --Cyde Weys votetalk 20:27, 12 January 2006 (UTC)

I do hope you are joking -- hard to tell when communicating online, with someone you don't know. --Macrakis 20:52, 12 January 2006 (UTC)

For  although I admit infint digits do not serve anything ,the external links's digits are diifficult to view ,and this article being So large(and spun off another article) ,we could for the completness of it have a few thousand digits articles Pi value. unlike e ,whic is used to simplify mathematical calculations and is not really needed, pi's value is of real use. No harm will be done by creating such an article.-- Procrastinating@ talk2me 10:32, 29 January 2006 (UTC)


 * No, pi's value past the first handful of places is of no real use. The section at the bottom of the article is already too long; I won't allow it grow longer. Melchoir 10:20, 23 February 2006 (UTC)

I just reverted 10,000 digits from the article. Per this discussion, it seemed like too much. --Hansnesse 21:17, 25 February 2006 (UTC)

Cubits
First of all, let me say that I'm grateful for the anonymous contributions to the history section. I've always thought that Nehemiah misses the point of quoting numbers with limited precision. However, I really think the anons are conflating two separate issues:
 * In the Biblical passage saying "ten cubits" and "thirty cubits", the intended first-uncertain-digit is either the ones place or the one-tenths place. Even if we assume the latter, we get a range consistent with the true value of pi. This is a valuable insight.
 * See discussion below. Also note that the ancient Hebrews did not have a "one-tenths place" -- decimal fractions came much later. --Macrakis 03:12, 19 January 2006 (UTC)

I'll revert back to my version. Melchoir 05:18, 15 January 2006 (UTC)
 * The meaning of "cubit" is itself uncertain. However, there is no reason to assume that the length of a cubit changes within the sentence, so the exact length is irrelevant; it cancels. Furthermore, even if the cubit does change within the sentence, there is no indication of the amount by which it changes. So phrases like "maximum reasonable precision" are wishful thinking.

From the anon:  The reason for noting the imprecision of cubits was to counter the argument that one of the measurements should be read as exact. If the cubit *were* defined universally and exactly, one might assume a dimenson was built to that spec, instead of simply measuring approximately that many cubits. (It'd be analogous to a "10-meter diving board", which doesn't simply coincidentally measure approximately 10 meters; it's specifically built to be as close to 10 meters as possible.)

That said, I don't think it's a big enough deal to revert back, as the shorter passage also makes the main point and I haven't seen anyone here actually raise the objection the "not precisely defined" sentence was intended to counter.

-- Anon (JMO from a wireless conn.)

Why 1 Kings doesn't belong here
I don't think that the 1 Kings passage and its discussion by Nehemiah belong in the Pi article. At best, they belong in the History of Pi article, but perhaps not even there. Here's why.

The 1 Kings passage itself is not good evidence of knowledge of the value of &pi;. The figures given are round numbers, and I see no reason to expect that they'd be accurate measurements rather than just impressionistic estimates: the specific numbers just tell the reader that it's a very big vat -- a common practice in ancient texts. Applying modern engineering assumptions about "significant figures" is completely anachronistic. For that matter, who says it was precisely circular? Nehemiah's exegesis is tendentious and questionable. The assumptions about the diameter being measured outside the thickness of the vat and the circumference inside its thickness contradict both the text and common sense: it is much more sensible to measure the outside circumference with a rope than to try to measure the inside circumference (how would you even do that?). The analysis also assumes specific values for cubits and hand-breadths which don't correspond to the values documented in cubit and especially not to the ratio of hand-breadths and cubits, which was normally an exact integer (5, 6, or 7). By the time of Nehemiah, &pi; was known rather accurately, so it seems he worked backwards to make the 1 Kings text give the right answer.

So it doesn't make sense to use these numbers either to 'prove' that the Hebrews were terrible mathematicians who thought that &pi; was 3 or fabulous mathematicians who were far ahead of their time and thought it was 355/113). The section does not belong here.  --Macrakis 03:09, 19 January 2006 (UTC)


 * I agree that Nehemiah makes no sense, and okay, sig figs are an anachronism here. The main point with the latter is just that given reasonable assumptions about the imprecision of the language, 3.14 isn't ruled out. I think it's worth mentioning precisely because you so often hear "Bible says pi is 3!!!11!1". Melchoir 04:34, 19 January 2006 (UTC)
 * This is why a reasonable account of 1 Kings should stay in the article. If it goes, anons and newbies will keep putting in (usually mistaken) versions. We had enough of this with the Indiana affair, lower down, until someone combined an on-line source with Beckmann to give the present, stable, text there. Septentrionalis 06:57, 19 January 2006 (UTC)
 * Actually, I prefer Macrakis' version; as he points out, using the inner circumference is nonsense, and it misses the point by insisting on more precision than the author intends or the reader should expect. Melchoir 07:03, 19 January 2006 (UTC)
 * After reading Melchior's first answer (04:34), I did some quick Web research and realized he was right about the "Bible says &pi;=3" problem--I didn't realize it was so widely discussed. In my edit after that, I expressly mentioned "other commentators" and (intentionally unspecified) "auxiliary hypotheses" because the inner circumference is not the only way to force the "right" answer -- another commentator (for example) reads the text to mean that the vessel was everted at the top, with the diameter being measured across the wide, everted part, and the circumference around the smaller body. But I agree that Sept's language is crisper. --Macrakis 07:29, 19 January 2006 (UTC)

Please cleanup digit overload
Someone pasted in an insane quantity of digits, and on my browser the sequence doesn't even start with 3.14...and also breaks out of its formatting box. With all the links, no reason to clog up the page with thousands of digits, so can someone please cleanup? This is an important article so I'm scared to mess with it myself.Ben Kidwell 18:41, 26 January 2006 (UTC)
 * Got it. Melchoir 19:22, 26 January 2006 (UTC)
 * Can you please

or or Jclerman 01:53, 1 March 2006 (UTC)
 * Put a maximum size of text to be entered
 * Block the IP number of the guy that puts the zillion digits
 * Both !

Did I find pi?
It appears that I have found a simple way to approximate pi to at least 9 (and likely at least 10) significant digits despite the fact that I am a high school student whose worst subject is math. One day recently, I was curious what my calculator would do if I were to ask it to take .5 factorial. Then, for no particular reason, I had it square the answer and then multiply it by 4. The screen, which shows no more than ten digits of a solution, read 3.141592654. Could someone who knows enough about pi please convince me that 4(.5!)^2 is at least probably not it? I suggest you get right on it as my head is growing at a rate that suggests it may explode at any moment. Ev-Man 18:00, 28 January 2006 (UTC)


 * The factorial function is usually defined only for nonnegative integers. For other values z, z! is either left undefined or defined to be Gamma(z+1), see Gamma function.  [This makes sense because z!=Gamma(z+1) is also true for nonnegative integers.]
 * By this definition, (0.5)! = Gamma(1.5) = 0.5*Gamma(0.5)= 0.5*square root of pi. So indeed  4(.5!)^2 = pi.  But this is not a method for computing or approximating pi, because the usual method for computing n! works only for natural numbers n. --Aleph4 18:31, 28 January 2006 (UTC)
 * The ancient roman 22/7 is 99.959% accurate ,isn't that more simple ? that's how I actually calculate most things in my head most of the time.-- Procrastinating@ talk2me 20:47, 28 January 2006 (UTC)
 * I understand now. Thanks for shrinking my head back to its original size.Ev-Man 21:53, 28 January 2006 (UTC)
 * Well, I do think a job well done, however! I have been told that Stephen Smale discovered some interesting properties of fractals, just by playing around on a calculator.  And indeed, it is pretty cool. I did not see an expresion of the gamma function for pi until well into my math degree in college.  Good work!  --Hansnesse 01:59, 1 March 2006 (UTC)
 * I did that with my calculator as well, except I just used the fraction 4354121751/1385959999 and got 3.141592654 on my calculator, too.
 * It's a branch of math called "experimental mathematics". We used to have summer schools on chaos (Los Alamos, Santa Fe, etc) including it, around the mid 1980s. Jclerman 02:57, 1 March 2006 (UTC)

Table of different approximations of pi
The Spanish wikipedia has a pretty nifty little table that depicts various historical approximations of pi. Could someone else take a look and see if it is worth translating into English?
 * Well, there's already a comprehensive table at History of Pi. Melchoir 06:21, 31 January 2006 (UTC)

Pi = 3
I just reverted an edit to the Prof. Frink quote in the "Fictional references" section. A quick google search seemed to show that the original is correct, but I wanted to throw it open for discussion if others know differently. Thanks, --Hansnesse 17:46, 21 February 2006 (UTC)

Question about Pi
I have a question which someone more informed about math may want to answer in the article. It is obviously not possible to measure the actual ratio of a circle's circumference to its diameter to millions of significant digets. Our measuring tools are not that precise. So, how do we know that the mathematically calculated value of pi is actually the ratio that exists in the real world? Even if you decide not to put this information in the main article, I would like to find out the answer to satisfy my own curiosity.
 * The quick answer is: It almost certainly isn't. Space isn't flat. Septentrionalis 06:05, 27 February 2006 (UTC)
 * There are two answers I can think of. (edit conflict with above, and I agree)
 * First, regardless of measuring tools, there are no perfectly circular physical objects. The ratio of circumference to diameter of an object obviously depends on its shape, and all we can say is that the closer an object gets to being perfectly circular, the closer that ratio gets to pi.
 * Second, pi is defined within Euclidean geometry, which is only an (extremely good) approximation to physical space, and that approximation itself breaks down on very large or very small scales. Given that, there is no conceivable way of "measuring" pi to millions of digits.
 * If you want a slogan, how about this: real numbers do not exist in the real world. This is fortunate for mathematicians; they have no competition! Melchoir 06:10, 27 February 2006 (UTC)
 * I think the point is also, that whatever our assumptions are about the physical universe, we can, using mathematical calculation, get results as precise as we wish regarding the properties of this universe (for example, the ratio of cirumference to diameter). The value of Pi described in this article can be shown to be correct for the assumptions of euclidean space and perferct circular shape - For other assumptions, other values can be obtained. -- Meni Rosenfeld (talk) 12:09, 27 February 2006 (UTC)


 * Originally, of course, geometry was defined as a practical system for measuring fields, calculating volumes, etc. In that context, it is not possible to measure things to more than 10-20 digits of decimal precision. However, over time, geometry in particular and mathematics in general have become abstract systems with their own internal logic.  These systems are used by physicists and engineers to model the physical world and, as one paper put it, are "unreasonably effective" there ("The Unreasonable Effectiveness of Mathematics in the Natural Sciences").  But the 1000000th digit of &pi; does not belong to physics, but to pure mathematics. --Macrakis 14:00, 27 February 2006 (UTC)

Thanks to all for the quick response to my question. As I understand it from your answers, pi is a mathematical construct derived from a geometrically pefect circle in euclidian space, and is not based upon physical measurements of real objects. My follow up question is "How was the formula for calculating the digits of pi arrived at?" I assume that there must be some sort of mathematical "description" of a perfect circle which is used to derive the formula, but how do you describe a perfect circle in math without using pi? Thanks in advance for your help with this.


 * The definition of a perfect circle is very simple: given a center point C in a plane P, and a radius r, it is all the points which are distance r away from C in the plane. You can derive formulae for circumference, area, etc. using the definition of Euclidean distance and calculus.  Calculus often gives you results in the form of infinite series, which you sum to calculate many digits; some series are better than others for calculation. --Macrakis 22:22, 27 February 2006 (UTC)

OK, we are closing in on the answer now. Macrakis states "you can derive formulae for circumference, area, etc. using the definition of Euclidean distance and calculus." I understand that diameter is 2r, so that part is easy. How do you derive the circumference without using pi, when the only starting data is r? I don't understand how "the definition of Euclidean distance and calculus" gives you this information. I'm not trying to be difficult, I'm just trying to understand. Thanks.


 * Conceptually, the simplest way is to imagine the circle being surrounded by a regular polygon with more and more sides. As the number of sides gets larger, the accuracy of your approximation improves.  (You can also draw the largest polygon that fits inside the circle to give a lower bound.)  If you're interested in this, you should study more math.  WP isn't really set up to give one-on-one tutorials like this. --Macrakis 01:47, 28 February 2006 (UTC)

That last explanation is very helpful, and I appreciate it. At the beginning of this topic, I suggested that the answer to my question might be appropriate for inclusion in the article. Sometimes when experts are writing an article, they fail to address issues which they think are too obvious to be addressed, but that a lay reader would appreciate having explained. I leave it up to others to decide whether a section in the article should be written to concisely explain how pi is derived, and why it does not necessarily describe a property of the physical universe.

Perhaps the article Length of an arc should be more widely advertised? The approximation of pi by regular polygons is, IIRC, of historical interest, so that might be expanded upon in this article. Melchoir 03:04, 28 February 2006 (UTC)

By the way, if you haven't figured it out already, there are ways besides measuring to find the value of pi.

The Joy of Pi
Melchoir, are you sure the link to this book qualifies as spam? I would think an article should refer to books about the subject. Perhaps it should be placed in "References" instead? -- Meni Rosenfeld (talk) 07:28, 4 March 2006 (UTC)
 * There were two links to a website with little content and whose purpose is to sell a book; my conscience is clean. The dearth of references in this article is, of course, a big problem. If anyone has access to the actual book and would like to use it to verify the article, that would be awesome. Until then, I think it would be misleading to put it in "References". Melchoir 07:39, 4 March 2006 (UTC)

Well, I happen to have that book. So what you are saying is that it will be a good idea for me to check that the information in the article and in the book match, and if so, include it in the references? -- Meni Rosenfeld (talk) 08:41, 4 March 2006 (UTC)
 * Awesome! Please do. In an ideal world, you would have enough time and energy to seek out specific parts of the article and tag them with inline citations as described at Citing sources. But that would be a really tedious task, and I'll stop just short of asking you to do it. (I think there are much easier ways to start verifying the article; a good first step would be to split out the sections according to Summary style.) Just checking a couple of things and adding the book as a reference will already be a big improvement. Melchoir 08:57, 4 March 2006 (UTC)

I'll see what I can do. Could take a while though. -- Meni Rosenfeld (talk) 09:05, 4 March 2006 (UTC)

Pi day
Given Wikipedia's rise in popularity since last year, I anticipate an unprecedented rash of vandalism to this article on March 14. It will be tempting to semi-protect the page, but we probably shouldn't. Just saying. Melchoir 19:37, 4 March 2006 (UTC)


 * WP:SPP: Note to Administrators: semi-protection should only be considered if it is the only option left available to solve the problem of vandalism of the page. In other words, just like full protection, it is a last resort, not a pre-emptive measure. Arvindn 22:09, 4 March 2006 (UTC)
 * I'm definitely against protecting pages unless it's absolutely necessary. This page is on a lot of people's watchlists, so unless the vandalism is coming every minute, and is extremely offensive (pictures of dead people or whatever), then protection is not necessary.  I really don't anticipate vandals being all that attracted to Pi. -lethe talk [ +] 22:15, 4 March 2006 (UTC)

Corporate pi?
In the trivia section, is there a particular reason why "A9.com" is in bold while "amazon.com" is in italics? Or why the entry should be prefaced by "Corporate pi:" at all? Clark Kent 04:49, 5 March 2006 (UTC)
 * So go ahead and fix it! Melchoir 05:38, 5 March 2006 (UTC)

Digits of Pi
How can a program such as Wolfram Mathematica calculate pi to 1*10^7 digits of pi. What formulaass ar ussedd?--72.36.198.186


 * Mathematica uses the Chudnovsky formula,
 * $$ \frac{1}{\pi} = 12 \sum^\infty_{k=0} \frac{(-1)^k (6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 640320^{3k + 3/2}}.$$
 * In principle, all you have to do to calculate &pi; with this formula is adding up terms until you have enough correct digits. In practice, many tricks are used, so the answer to "how a program can..." depends on how detailed an explanation you're looking for. Do you have any programming knowledge? You'll find code for a simple program to calculate &pi; here (using another formula, Machin's). Fredrik Johansson 21:25, 6 March 2006 (UTC)
 * Thank you. This has clarified things alot.  I wonder how many iterations of that formula the computer has to go throuhg to calculate something like 1000000 digits of pi.--72.36.198.186
 * According to MathWorld, 14 digits are added per term. Fredrik Johansson 10:19, 7 March 2006 (UTC)

And you don't have to trust mathworld, you can get a very rough estimation of the kth term:
 * $$12 \frac{(-1)^k (6k)! (13591409 + 545140134k)}{(3k)!(k!)^3 640320^{3k + 3/2}} \approx \frac{(6k)!}{(3k)!(k!)^3 640320^{3k}} \approx$$
 * $$\frac{(6k)^{6k}e^{-6k}}{(3k)^{3k}e^{-3k}k^{3k}640320^{3k}} = \left(\frac{6^6 e^{-6}} {3^3 e^{-3} 640320^3}\right)^k \approx (10^{-16})^k$$

This means that each term is roughly 10^16 times smaller than the one before, so each term gives you roughly 16 additional digits. -- Meni Rosenfeld (talk) 10:48, 7 March 2006 (UTC)
 * You missed a factor of e-3k for the second factorial in the denominator. Include it and you get
 * $$\left(\frac{6^6}{3^3 640320^3}\right)^k,$$
 * so the factor is about 1.5 &middot; 1014. Fredrik Johansson 11:43, 7 March 2006 (UTC)

Right. That explains why I got a different result. Thanks for pointing this out. -- Meni Rosenfeld (talk) 17:49, 7 March 2006 (UTC)


 * This is a really interesting formula. I was surprised that the exponential conversion of this thing adds 14 more digits to the number with each additional term. That said, I have several questions:
 * 1.Are there formulas for PI that converege faster than this?
 * 2.How efficient is this formula? My question is, how many cpu cycles a computer has to complete to create one iteration? Are there any formulas that are more processor efficient than this? --BorisFromStockdale
 * There are basically two categories of useful formulas for &pi;: series that add a constant number of digits per term (such as this one), and iterations that multiply the number of correct digits in each step (such as the Borwein algorithms). In theory, any method with better than constant convergence will beat a linear series for a large enough computation. In practice, however, the Chudnovsky series is faster for reachable amounts of digits. The reason is basically that each step requires only multiplication and addition, whereas the iterations involve expensive square roots and divisions in each step. The world record computation was done with a Machin-like formula and the fastest PC programs (such as PiFast) use Chudnovsky's series. According to this page, $$O(n \log(n)^3)\,$$ CPU cycles are needed to compute n digits with Machin's formula; Chudnovsky's series probably has similar time complexity, but I don't know the details. Fredrik Johansson 09:36, 9 March 2006 (UTC)

Role in physics equations
All the physics equations listed in the article show PI in a product or division with a physical constant, or referring to chosen measuring units. Thus, it's no significative the appereance of PI there. For example, the quantity $$ G \cdot \pi $$ can be defined as a universal constant itself, and so pi would dissapear. This is more a matter of the units and constants chosen, in all those cases. Probably, there are better equations to write as examples.
 * But if you defined G &middot; &pi; as the fundamental constant G*, those equations involving G alone would involve G*/&pi;. and &pi; would reappear. The point would be the same. Septentrionalis 01:53, 9 March 2006 (UTC)
 * But the only way to pass between those two different constants is to do a spherical integration (the way you do when you pass from Gauss's law to Coulomb's law). So it's really true that the π in those equations has little to do with the physical constants, and is rather an artifact of the fact that the equations are written in a spherically symmetric form. 66.188.137.39 01:47, 26 March 2006 (UTC)

"You are so stupid" in properties of pi?
From the properties section:

"Because the coordinates of all points that can be constructed with ruler and compass are constructible numbers, it is impossible to square the circle, that is, it is impossible to construct, using ruler and compass alone, a square whose area is equal to the area of a given circle. If you don't know that you are so stupid!"

Just as some random guy looking at the article, that doesn't seem too professional. I'll leave the editing to someone else though.

Edit: didn't realize it was pi appreciation day, was just going through a textbook in preparation for a test and curious as to wikipedia's pi page. Someone probably snuck it on here today.


 * Thanks for spotting it. It was, as you guessed, vandalism. Wikipedia gets lots of attempts at vandalism, most of which is reverted quickly.  In that case, it was removed in 7 minutes, which is a little longer than ideal.  For more on fighting vandalism, see WP:VAND.  Thanks again, --TeaDrinker 18:19, 14 March 2006 (UTC)

History of Pi
This article says "As early as the 20th century BC, Babylonian mathematicians were using π=25/8" but in the history of pi article it says that the babylonians started using 25/8 in the 19th century, I didn't want to change anything because I don't know which is right but someone who knows should. William conway bcc 22:51, 14 March 2006 (UTC)\
 * That's the difference between two theories of Babylonian chronology. We're lucky there's only a century difference. Leave it alone, as a warning to the careful reader. Septentrionalis 00:36, 15 March 2006 (UTC)

Here's another inconsistency: this article says π stands for περιφέρεια, history of pi says it stands for περιμετρος (sic). -- EJ 23:17, 14 March 2006 (UTC)


 * As for the Greek, neither article gives an inline citation, so it's impossible to know which, if either, is right. As for the history, I think we should defer to the more specialized article, so I'll change Pi. Melchoir 00:13, 15 March 2006 (UTC)
 * The second should in any case be perimetron. Septentrionalis 00:36, 15 March 2006 (UTC)


 * Earliest Uses of Symbols for Constants says: "The first person to use &pi; to represent the ratio of the circumference to the diameter (3.14159...) was William Jones (1675-1749) in 1706 in Synopsis palmariorum mathesios. It is believed he used the Greek letter pi because it is the first letter in perimetron (= perimeter)." The Oxford English Dictionary says that pi is used "in Math. to express the ratio of the circumference or periphery (περιφέρεια) of a circle to its diameter." -- Jitse Niesen (talk) 09:44, 15 March 2006 (UTC)

Irrationality of Pi
In the properties section, it is written:

pi is an irrational number; that is, it cannot be written as the ratio of two integers, as was proven in 1761 by Johann Heinrich Lambert.

The proof that pi irrational is thousands of years old. The Pythagoreans knew it, and I'm pretty sure it's in Euclid's Elements as well. I edited it but someone keeps reverting it back. Nan Yang 17:13, 16 March 2006 (UTC)
 * Where have you heard it was known to the pythagoreans? This isn't true. Perhaps you're confusing it with $$\sqrt{2}$$? -- Meni Rosenfeld (talk) 18:16, 16 March 2006 (UTC)


 * Yes, I have definately confused it with root 2. My apologies.Nan Yang 05:46, 18 March 2006 (UTC)

thousand digits
I am not able to spot who put again 1000 digits of pi on this page. I think earlier discussion concluded in that this is of no use on this page.

If s.o. else agrees, please delete this chunk of digits from the section "Numerical approximations".

Numerical approximations
This section would merit a page on its own. Maybe I'll give it a try.

(The pi page is so huge I don't even dare to edit the preamble with the statement "for more digits, see the links below" which is not really appropriate. The OEIS page cited just before however gives useful links - I would prefer referring to this.) &mdash; MFH:Talk 21:57, 16 March 2006 (UTC)

=> see Talk:History_of_numerical_approximations_of_&pi;

still a mess
This article is still a mess. Starting from the introduction: Too long, much irrelevant suff (for a "zeroeth section"), many things said twice (Euclidean definition...), others not at all. The "precise" definition should go into a first subsection. A rough approximation (3.14) should be given at the start, etc. etc. &mdash; MFH:Talk 16:38, 21 March 2006 (UTC)

very young
I am about 10 years old and need a formula for pi that is as simple as possible. I have been loking for it ever since I learned about pi. Also, I think my IP address is shared with about 10 other people. I had nothing to do with that pi thing. I hardly noticed that. —Preceding unsigned comment added by 64.131.43.6 (talk • contribs) 22 March 2006, 02:59 (UTC)


 * Hmm... I guess it depends on what you're aiming for by "simple". What purpose do you have in mind? Melchoir 03:12, 22 March 2006 (UTC)
 * Like Melchoir suggested, you should be clearer about what precisely you are looking for. The article already contains many formulae for &pi;. However, here are a few suggestions: If you're looking for an approximation, then 355/113 is correct for 7 digits. You can also try this iterative method: Take a scientific calculator, make sure it's set on "radians" (and not degrees), type "3", and then repeatedly calculate "Ans + Sin (Ans)". Each iteration will triple the amount of correct digits. -- Meni Rosenfeld (talk) 12:31, 22 March 2006 (UTC)


 * You can also use : &pi; = 4 arctan(1) (where arctan is "tan-1"), i.e. type "1", "tan-1" (in RAD mode), and multiply by 4.
 * However, knowing kids, I find it somehow suspicious that you say "very young" and "I'm about 10 years old" - usually kids of that age are very precise concerning their age... &mdash; MFH:Talk 14:33, 22 March 2006 (UTC)

What I mean is something you can do by hand. I want it to be exact to at least hundreds of decimal places. And only kindergaren age kids do that.64.131.43.6 22:17, 22 March 2006 (UTC)
 * By hand? This could take a while, I guess dozens of hours. But here's a suggestion: Calculate:
 * $$\frac{1^2}{4*6} + \frac{1^2*3^2}{4*6*8*10}+\frac{1^2*3^2*5^2}{4*6*8*10*12*14}+\cdots$$
 * Add 1 to the result, and multiply by 3. Note that you don't have to calculate each term from the start: After finding, for example, the 2nd term, multiply by 52 and divide by 12 and 14 to get the 3rd term.
 * By calculating 160 terms, you'll have &pi; correct to 100 digits. Of course, you'll have to calculate each term up to, say, 105 digits. -- Meni Rosenfeld (talk) 10:11, 23 March 2006 (UTC)
 * Of course, there are formulae that can allow you to calculate it a lot faster, but they're a bit more complicated. Do you intend to actually perform the calculation (which will be very long in either case), or just interested about the possibility? -- Meni Rosenfeld (talk) 17:12, 23 March 2006 (UTC)


 * I think your conception of what kindergarden age kids do is very funny.
 * Are you supposed to calculate "at least hundreds(!) of decimal places" in your head, without calculator?
 * Then you should also know how to take square roots. (e.g. by iterating r -> (r + x/r)/2)
 * Jon Borwein's slides "Life of Pi" (see links at bottom of page) gives you formulae involving only square roots which gives you 97 digits in 3 steps (and 400 more in the 4th step). (He used it to get a trillion digits in 20 steps; every step involves calculating one 4th root, equivalent to taking 2 square roots. Unfortunately, his computer made errors when calculating square roots...) &mdash; MFH:Talk 19:54, 23 March 2006 (UTC)

The first 103 are available at http://en.wikipedia.org/wiki/Pi#Numerical_value. What are you using it for? He Who Is 21:06, 16 June 2006 (UTC)

sorry for many edits
I'm sorry for a series of subsequent edits to the top section of pi. I think that the several equivalent definitions should go into a separate subsection. It took me about 4 hours to change the formulations in a satisfying way. Unfortunately, when I finally saved it, I had to notice that the table of contents (which I could not see in the previews) interfered with the display of the first two images.

I made some fixes to the problem, but I'm still not very happy with the current state. I would like to have the circle displayed a bit earlier (I initially put it jut before the ==Definition== which looked quite nice, but only without the T.O.C.). To get an idea of what I tried to get, consider the featured article on &pi; on German Wikipedia. &mdash; MFH:Talk 18:15, 22 March 2006 (UTC)

Digits
Could somebody check the first 1,000,000 digits of pi found on this web site? They were created by Mathematica (Timing[Export["pi1.txt", N[π, 1000000], "List"]]). They are put into nice ,TXT files.
 * Should this link be included on the main article? --BorisFromStockdale 04:28, 23 March 2006 (UTC)
 * It doesn't look like a real site. Is this on your personal computer? My browser can't load it. Perhaps your router doesn't allow access. In any case, I don't think a page on someone's personal computer is appropriate for inclusion in an article. -- Meni Rosenfeld (talk) 10:16, 23 March 2006 (UTC)
 * Sorry, my web server pc got shut down. It should be up now...--BorisFromStockdale 14:41, 23 March 2006 (UTC)


 * I agree with Meni Rosenfeld: I don't think a page on someone's personal computer is appropriate for inclusion in an article. The OEIS page for Pi's decimals has enough references for any number of wanted digits. &mdash; MFH:Talk 19:05, 23 March 2006 (UTC)
 * I also agree with you that the site should not be included in it's current form, it is my site and I am still working on it. I would like to comment on your statements about personal computers.  Many people host web pages from their home PC's.  For example, if you have a broadband connection supporting 40KB/s upload you can freely host static text web pages and pages with small file sizes.  Many people use Apache for this or SimpleWWWServe.  After they do this, the page can be accessed wia IP adresses.  People then can register their domain names for money and make the DNS web servers redirect traffic to their home PC's iP adress.  Anyway, what I want to say is that even if the web page domain name is not registered and appears as an IP adress, that does not mean that the page is inferior...--BorisFromStockdale 23:06, 23 March 2006 (UTC)
 * Of course, appearing as an IP address doesn't make a page infrerior, but it just doesn't look very proffesional. I don't think it's the kind of thing we'd want to link to from an article. If you register a domain name and improve the design, I'll support this link. -- Meni Rosenfeld (talk) 10:33, 24 March 2006 (UTC)
 * Ok, I am working on it. This was just the first trial version of the web sitte. I will revise it over the weekend and also next week.  I was thinking of adding more constants to the site such as GoldenRatio and others...--BorisFromStockdale 20:01, 24 March 2006 (UTC)

'''I have made several small revisions to the web site and have moved it to another computer. The site should be currently and permanantly up(I had some small previous problems that have been resolved). How about including it in the article now? In my oppinion the site is very clear and consice. If you have any suggestions on improving it further, please leave a comment here. Otherwise, let's add it...'''--BorisFromStockdale 03:51, 26 March 2006 (UTC)

As a web administrator, I would say that the site must be on a dedicated server that is going to be available and reliable. Otherwise, the linkrot team will eventually notice that it is an unreliable server and they will remove the link. - Corbin Simpson 04:06, 26 March 2006 (UTC)


 * As far as I know I can keep it reliable... My broadband connection has a static public IP adress, and my computer is always on...--BorisFromStockdale 04:14, 26 March 2006 (UTC)
 * By the way, what exactly is the linkrot team? --BorisFromStockdale 04:17, 26 March 2006 (UTC)


 * Your call. I won't change it either way. Dead_external_links is where people fight linkrot. - Corbin Simpson 06:23, 26 March 2006 (UTC)


 * Impossible to connect to this web server at present. &mdash; MFH:Talk 01:20, 1 April 2006 (UTC)


 * Still doesn't work!172.205.150.191 08:50, 1 May 2006 (UTC)

Between 3 and 4
Come to think of it, what in the world is the last item in the current Trivia section talking about? Melchoir 21:36, 24 March 2006 (UTC)
 * A hexagon has length three times its diameter, which is the diameter of the circumscribed circle. A square has length four times the diameter of the inscribed circle. Polygons with more sides lie between these. (Rather than fixing it, I took it out.) Septentrionalis 21:52, 24 March 2006 (UTC)
 * Oy, good call. Melchoir 21:58, 24 March 2006 (UTC)


 * At least a certain User:205.200.124.113 with a bit too much of "true wikipedia spirit" (but unwilling to follow the link to unit disc...) understood it some unintended way. I put it back with slight change of wording and more references.&mdash; MFH:Talk 22:03, 27 March 2006 (UTC)

Featured article?
I think this is a very good article - at the very least it should go on the list of Good Articles. However, would there be any objection to me putting this foward as a featured article candidate? (Has it been already?) CloudNine 18:44, 25 March 2006 (UTC)
 * There's nothing wrong with nominating for FA, but I have to predict that it'll fail for being poorly cited. Also, it hasn't had a peer review. GA is a good idea, though. Melchoir 22:04, 25 March 2006 (UTC)
 * Sorry, but this is one of the worst mathematics articles in Wikipedia. It's basically a list of random facts, littered with unimportant trivia mixed in among the glaring omissions. In addition to its failure to describe important concepts and developments (it instead lists formulas that are consequences of them), I have spotted several statements that, if not factually incorrect, are directly misleading. And what's the deal with all the duplication of content in History of numerical approximations of π and Chronology of computation of π? They are sure signs that this article needs to be rewritten from scratch by someone with a clue. Fredrik Johansson 22:36, 25 March 2006 (UTC)
 * If anybody is serious about upgrading this to FA, go here for some fine examples. - - - Papeschr 04:03, 26 March 2006 (UTC)


 * I agree that this article is rather in bad shape. The result of duplication stems from the fact that History of numerical approximations of π was created recently since this subject took up more than 1/2 of the Pi article, and I did not yet dare to delete all/most/the adaequate parts of the old text here. Please be bold (I didn't want to mae too severe changes all on my own.) I think the "History" and "Num.approx." sections here should contain the main cornerstones resp. basic ideas, and should be developed elsewhere. (Maybe all "history of..." should have gone to "history of pi" and there should be rather a separate page on numerical approximations of pi.) &mdash; MFH:Talk 22:12, 27 March 2006 (UTC)
 * There's a history of pi as well? This is getting worse. Fredrik Johansson 06:45, 28 March 2006 (UTC)


 * It is worse. But you can help! And, imho, the existence of a history of pi page is largely justified, since the pi page could be overfull even if one would only put a link to each possible subject that could be addressed there. It is not justified that the "History" aspect takes up 1/2 of the article, there are so many things worth mentioning.
 * And also, a page about the mathematical theory/-ies about numerical approximations of pi, separate from pi and from history of pi, is also justified.
 * At present, the main difficulties in work on this section are:
 * to make a good choice of "history milestones" deserve being mentioned here
 * try to delete as much details as possible from the "numerical approximations" section, leaving meaningful but concise summaries about the key ideas.
 * Maybe move the history of numerical approximations of &pi; page to numerical approximations of &pi;, while waiting for the splitting up into (a) history of numerical approximations of &pi; and (b) mathematical theories for numerical approximations of &pi; (while digits of &pi; has yet another important function: (1) to have a separate place where the "millions of digits vandalizers" can paste their stuff, and (2) where people who are just interested in finding digits of &pi; in various formats can look for that.) &mdash; MFH:Talk 15:27, 29 March 2006 (UTC)
 * This chopping-up does no good except causing further duplication of content and making the large-scale structure harder to manage (it's evidently bad already). My recommendation would be to rewrite this article from scratch, in the style called "prose" instead of bullet-point, and then deciding what would be the best way to organize the details. But I don't currently feel up for it myself, and don't control others. Fredrik Johansson 16:08, 29 March 2006 (UTC)
 * I agree that the "cleanup" so far in the history section is not good at all. You are right, it should be written in "prose". But much deserves being told in detail, somehow grouped together, but not on the main page: I think the existence of the history of pi page is justified. And I think a separate page on numerical approximations of pi could be justified also. I'm pretty sure that with a mush shorter "History" and "Numerical approximations" section, the article would quickly be in a much better shape. &mdash; MFH:Talk 01:27, 1 April 2006 (UTC)
 * Why don't we find someone who speaks both German and English and have them convert the german page, which is most impressive? 16:24, 08 April 2006 (UTC)

Dead link?
I was not able to access this external link: "π available in various lengths, up to 4.2 billion digits" in the main article? --BorisFromStockdale 06:46, 28 March 2006 (UTC)
 * never mind, it's back up--BorisFromStockdale 06:48, 28 March 2006 (UTC)


 * Although could you please tell me exactly where the digits are stored on that ftp page? I have trouble accessin the folders. --BorisFromStockdale 06:51, 28 March 2006 (UTC)

Pronunciation
Pi is not pronounced with the dipthong "ie" in the english, "pie." The pronunciation of the greek spelling Pi Iota is disputed, but it was with near absolute certainty either the sound represented in the IPA ([]) as i, "ee," or as I, as the sound in "it" Thanatosimii 04:05, 29 March 2006 (UTC)

agreed but: In greek, I was taught 'Pee' But of cource math class it is 'Pie' and that is proably what the article implies Minnesota1 04:09, 29 March 2006 (UTC)


 * What is in question here is not how the Greek letter is pronounced in Greek or when discussing its use to write words from the Greek language. The article is concerned with how the letter is pronounced by mathematicians when they speak in English about Greek letters used as mathematical symbols. In that context, pronouncing it as "pie" is universal. Henning Makholm 10:05, 29 March 2006 (UTC)


 * I agree. Even more, I think that this very good point could merit being clearly emphasized in the article ("the symbol pi standing for ... is pronounced 'pie', in English, when referring to this constant, regardless of (a maybe missing concensus about) the pronounciation of this greek letter in other contexts" ) &mdash; MFH:Talk 16:18, 29 March 2006 (UTC)
 * I trust this clarification will be acceptable. Please note that I have avoided the OT question of what the ancient pronunciation of π was. Septentrionalis 16:58, 29 March 2006 (UTC)


 * A try to justify the pronounciation has reappeared, to avoid an endless editing conflict, I put a HTML comment next to it: "only state the fact, no try to justify".
 * Indeed, the modification read

following the usual convention for pronunciation of Ancient Greek in English; the Modern Greek pronunciation of π differs. There is no information about this convention on the page Ancient Greek, and we don't talk about the Modern Greek pronunciation, but about the English pronounciation. (In all other languages (French, German, Japanese, Chinese, Russian....) it is pronounced /pi/ (i.e. pee for those who prefer). (Yes, even in Russian, even though the cyrillic alphabet has the same letter which is not pronounced like this.) &mdash; MFH:Talk 21:05, 30 March 2006 (UTC)


 * I would prefer it if we said /paɪ/ instead of "pie". IPA is a pretty uniform standard here on wikipedia. -lethe talk [ +] 21:37, 30 March 2006 (UTC)
 * Use both; everyone using this encyclopedia reads English; most of them speak it. Neither is true of IPA. Septentrionalis 06:34, 31 March 2006 (UTC)
 * Now that I check the OED for the above claim, I see this is wrong. Both British and American pronounce pi like pie, but the British pronunciation is /pʌɪ/ for both. Allowing for the regular difference between English dialects, this is a conventional (and uniform) pronunciation for the Greek letter. I shall alter the article accordingly, until a speaker of some other English dialect objects, and I doubt they will. Septentrionalis 06:49, 31 March 2006 (UTC)


 * Lethe, I totally agree with you about IPA in general, but in cases like this where the pronunciation is identical to another English word, I don't see a problem with just saying that. Pi is pronounced like pie. No need to have a big debate about it. —Keenan Pepper 23:28, 31 March 2006 (UTC)
 * Well, I have a rebuttal for you, but your last comment makes me think that you don't want to debate the issue. Is it so?  -lethe talk [ +] 23:34, 31 March 2006 (UTC)


 * Haha, no, go ahead! —Keenan Pepper 23:43, 31 March 2006 (UTC)
 * Well, as far fetched as it may seem, what about people who can read English, but not speak it? What good does it do to tell them other English words?  What about funny dialects, what about homophones?  Anyway, the only reason not to include IPA is the learning curve associated with it, but that's mitigated simply by including also the English word.  Surely you don't object to that situation? -lethe talk [ +] 00:08, 1 April 2006 (UTC)


 * Good points. So... what exactly is the disputed tag about? —Keenan Pepper 00:30, 1 April 2006 (UTC)
 * The Oxford pronunciation is not /paɪ/ either for 'pie" or for the subject of this article. Septentrionalis 03:40, 1 April 2006 (UTC)


 * I think from the "I shall alter the article accordingly..." on, the point has once again be misunderstood (although this seems only possible if the phrase has not been read): we do NOT speak about the pronounciation of the greek letter, but we speak about the pronounciation of the mathematical constant. AFAIK, also British mathematicians say "pie". Maybe I'm wrong on this and thus what you talk about, but then the parenthesis you added is ambigous. This should be made clear. So let's ask the question clearly: Do British mathematicians pronounce this constant "pie" or "pee" ? (and please, if there is 0.1 % of British mathematicians that have an "Ancient Greek" background which motivates them saying "pee" in contrast to all others, then we should ignore them here since we talk about common usage in English. &mdash; MFH:Talk 01:09, 1 April 2006 (UTC)


 * IMHO it is not reasonable to say that the constant has a prononciation at all. The word which is being pronounced is the name of the symbol which is used for the constant.  The fact is that the name of that symbol is consistantly pronounced one way in a whole host of related contexts, and that this pronounciation is different from the way the name of the symbol is pronounced in other contexts.


 * This article currently states: ' "When referring to this constant, the symbol π is always pronounced like "pie" ". '


 * I wonder, has the author of this sentance been present at every utterance of the word in question since the beginning of time?


 * It is not the place of an encyclopedia to order people how they must pronounce a word, but to describe the way in which they do.


 * I propose replacing the entire disputed paragraph with the following:


 * The english name of the Greek letter π is written in the latin alphabet as pi. In the context of mathematical symbols this is usually pronounced /IPA/ like the english word "pie".  This is different from in linguistic contexts, where it is pronounced /IPA/ like "pee".


 * (with the correct IPA substituted)


 * TomViza 17:16, 11 April 2006 (UTC)
 * The assertion about linguistic contexts is both off-topic and disputable.
 * The English and American pronunciations of π (and "pie") have different IPA representations.
 * No one is being prescriptive, merely descriptive.
 * Please do not. Septentrionalis 21:53, 24 April 2006 (UTC)


 * I don't think it is the job of this article to make claims about how linguists pronounce &Pi;. Also, "is always pronounced like "pie"" is a desctiption of the way people do pronounce it. Henning Makholm 17:51, 11 April 2006 (UTC)


 * You missed the point. We are not talking about the pronounciation of &Pi;. We are talking about the pronounciation of 'pi'.  One cannot pronounce a symbol.


 * The reason I included the other pronounciation is because saying "this is sometimes pronounced thus" begs the question of how else it might be pronounced. It is not really relevant, but it is something that it is likely that a reader might want to know.  The alternative is to simply say "this is pronounced thus", which is not universally true. TomViza 15:20, 12 April 2006 (UTC)


 * Unfortunately, you have succeded in implying that it is different in other contexts, which is precisely the dispute we are trying to avoid. Let me try again. Septentrionalis 03:40, 1 April 2006 (UTC)

Top image
The iamge of the large π was just moved from left to right with the edit summary "Image should not be on the left". This seems brusque; for Heaven;s sake, why not? Septentrionalis 01:40, 30 March 2006 (UTC)


 * It made it look pretty bad, at least on Firefox in GNOME. —Keenan Pepper 02:07, 30 March 2006 (UTC)

TODO: How to get this to a featured article
This is an article that can be reorganised into a featured article. Raising points on discussion: this should be our goal, so where shall we start? —Preceding unsigned comment added by Natalinasmpf (talk • contribs) 22:49, 31 March 2006


 * Choose "milestones" for the section "history", and put everything else into history of pi
 * Choose "key ideas" of the section "Numerical approximations", and put everything else into history of numerical approximations of &pi; (if you want, rename this to [[numerical approximations of &pi;]])
 * Choose some more pictures illustrating various issues (one in the history section, e.g....)
 * Look at the featured versions in other languages (just look at the layout, size of sections, no matter what the text is about)
 * (...) [ continue putting here other ideas ] &mdash; MFH:Talk 01:16, 1 April 2006 (UTC)
 * Check out this featured article on Pi from the German Wikipedia for a beautiful example of what this article could become. It also has numerous relevant images.
 * I just went over to de.wikipedia.org/ and asked our German comrades for help with this!
 * Also, here's a Babelfish translation of the Kreiszahl page that should help monolingual contributors... ~ Papeschr 13:28, 4 April 2006 (UTC)

Childhood's End
I endorse anon rm of:


 * "Childhood's End" -- science-fiction novel by Arthur C. Clarke (1953). In the novel, a race of aliens that visits Earth mentions discovering a pattern within the digits of π. They indicate that they do not know the meaning of the pattern, but have devoted much effort to uncovering it. They speculate that the pattern could only have been placed there by the creator of the universe.

I am unable to verify this plot point via web and have not a copy handy. I will entertain counterargument. John Reid 00:12, 3 April 2006 (UTC)


 * If users start removing sourced claims they cannot readily verify, then surely Wikipedia will soon consist of only unsourced claims! Lambiam Talk 01:03, 8 April 2006 (UTC)
 * But I think John Reid is right; that's from Contact by Sagan. Septentrionalis 23:07, 8 April 2006 (UTC)
 * Seconded, I remember that point from Contact. On the other hand, if I remember correctly: In Childhood's End, the chief Overlord lets slip that his task as adminstrator of Earth is just a temporary assignment, on loan from a civilian job. One of the human characters (the UN secretary-general?) gets the vauge impression that he is "something like a mathematics professor". That, and the general secrecy of the Overlords, seems inconsistent with them disclosing a hidden-message-in-pi project elsewhere in the novel. Henning Makholm 23:32, 8 April 2006 (UTC)

Formula by 64.59.233.88
has added the formula $$\frac{\pi^2}{8}=1+\frac{1}{9}+\frac{1}{25}+\frac{1}{49}+\cdots$$. In my opinion it is a trivial consequence of the formula $$\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots = \frac{\pi^2}{6}$$ which appears above, and should be removed. Any objections? If no one objects, I will remove the formula. If we do decide to keep it, then we should also add more important formulae such as $$1 - \frac{1}{3^3} + \frac{1}{3^5} \cdots = \frac{\pi^3}{32}$$. -- Meni Rosenfeld (talk) 18:31, 6 April 2006 (UTC)


 * Is it trivial that the reciprocal even squares account for a fourth of the whole series? In any case, there are too many disjointed formulae on the page, and removing obscure ones has my approval. Henning Makholm 20:34, 6 April 2006 (UTC)


 * I agree it's trivial and I removed the formula. I will also AfD the new article A property of PI. -- Jitse Niesen (talk) 03:29, 7 April 2006 (UTC)

Henning: Yes, it is. Think about it - if you multiply each term by 1/4, you'll be left exactly with the reciprocals of the even squares. -- Meni Rosenfeld (talk) 07:49, 7 April 2006 (UTC)
 * Well, duh! Henning Makholm 09:05, 7 April 2006 (UTC)

While we're at it, how about a comprehensive article "List of formulae involving Pi", including this formula and many others? If not on Wikipedia, is there a sister project where such an article would be appropriate? -- Meni Rosenfeld (talk) 08:07, 7 April 2006 (UTC)
 * I think such a list page would be a good idea. First we'll have to battle over whether to call it "formulas" or "formulae" :-) -lethe talk [ +] 08:12, 7 April 2006 (UTC)

List of formulae involving Pi
Why battle first, when we can do it later? :) See List of formulae involving Pi and Talk:List of formulae involving Pi. -- Meni Rosenfeld (talk) 09:25, 7 April 2006 (UTC)

Pi/Unrolled
I dont understand the purpose of the 'unrolled' subpage. The use of subpages at all is not standard practice on Wikipedia. If it is just about the word 'unrolled' in terms of pi, then maybe it should be moved to Wiktionary? Other information that might be relevant to pi itself should probably be merged into the pi article. Thoughts? Remy B 08:39, 8 April 2006 (UTC)
 * Actually, since it mostly concerns an obsolete idea of Euclid's, perhaps History of π would be better? Melchoir 09:12, 8 April 2006 (UTC)
 * The animation is sort of cute, but the claims about Euclid and ancient Greek mathematics are somewhat at odds with what my source (V. J. Katz A History of Mathematics) say. Archimedes explicitly considered the circumference of a circle as a length, and bounded its ratio to the diameter between 223/71 and 22/7, and it was known very early on (Archimedes gave explicit proof) that a rectangle with sides equal to the diameter and the circumference is exactly four times the circle's area. It would be trivial to the Greeks that if you can square the circle, a straight line equal to the circumference can easily be constructed. It is true that Euclid did not consider the ratio between curved and straight lines in the Elements, but that was because he was writing an, ahem, elementary textbook, not because he thought there would be anything inherently meaningless in such a ratio. There just were no results on such curved lines that could be presented with the elementary vocabulary Euclid restricted himself to. Henning Makholm 12:11, 8 April 2006 (UTC)

I have inserted prod, which proposes it for deletion. It is out of place, and in error on two points (marked). Septentrionalis 23:05, 8 April 2006 (UTC) ....................................... Please discuss on page Talk:Pi/Unrolled. Lambiam Talk 06:24, 11 April 2006 (UTC)

?
Lets keep islam out of it. We call 1940's Van Braun rocketry as 'German', not Nazi. Same as Persian. 23:47, 19 April 2006 by 


 * Please remember to sign your posts on talk pages. Typing four tildes after your comment ( &#126;&#126;&#126;&#126; ) will insert a signature showing your username and a date/time stamp, which makes it clear who said what, and when. Thank you. You might also like to add more context to your comment. John Reid 04:17, 20 April 2006 (UTC)

Vandilism
I don't know where to report this, but the Pi page has been vandilized terribly, look into Properties for starters.
 * Thanks, I think I've fixed it. Melchoir 20:54, 24 April 2006 (UTC)