Talk:Pi

Please add new comments at the end of the page.

• Archives: Archive 1 | Why approximate pi? debate | Archive 2

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. π 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 π. --Macrakis 18:02, 31 October 2005 (UTC)

In Euclidean space, the ratio between the circumference and the diameter of a circle is always π. In a curved space, this ratio varies, depending on how large the circle is. However, even in a curved space the number 3.14… 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…. Intuitively, this is because the curvature of the space vanishes if you look very close. -- Jitse Niesen (talk) 18:32, 31 October 2005 (UTC)

Least accurate approximations

I just wonder, do we really need the subsection Pi#Least accurate approximations 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)

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 [1] 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 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)

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 $\pi$ (<big><math>\pi</math></big>).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 π 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)

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 π rather than 2π 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)

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)

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. [2] [3] [4] 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)

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

[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 π anywhere in Wikipedia. What π is, is certain mathematical relations, such as sin(π)=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 π 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 γ? 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 _vote^talk 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)

• 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.

I'll revert back to my version. Melchoir 05:18, 15 January 2006 (UTC)

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 π. 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, π 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 π 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 π=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)

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)

I did that with my calculator as well, except I just used the fraction 4354121751/1385959999 and got 3.141592654 on my calculator, too.

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)

External Links

The link for pi to a million places is no more, and it links to a porn site. Frogan 06:16, 20 February 2006 (UTC)

So.... why did you remove it? Melchoir 06:20, 20 February 2006 (UTC)

Because ... it ... wasn't ... offering ... pi ... to ... a ... million ... places. Frogan 06:48, 21 February 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 π 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.