Talk:Pi

Pi in science fiction literature

Every now and then I run into a science fiction novel that supposes the value for pi can vary according to a gravitational constant, or a local "curvature" in the universe. Um, I don't think so, but it is getting kind of predictable that this sort of thing keeps popping up in science fiction literature.

The main article could be improved if somebody put a link in there, connecting it to another Wiki article about Pi in science fiction literature. For instance, The Infinite Man by Daniel F. Galouye is one such novel that uses this as an essential part of its plot. His story proposes that computers using standard calculations, according to a standard formula, suddenly start spitting out a different sequence of decimal digits, because the whole universe starts changing its density levels, apparently in response to a supreme being deciding to change the amount of mass in the universe.

It isn't my purpose to argue against one plot in support of another, in terms of science fiction literature employing plausible plot lines, merely that this kind of thing apparently keeps happening, and among different writers around the world. Science fiction authors keep arguing that the formulas for calculating pi, as applied, produces results that are consistent with observable data. Dexter Nextnumber (talk) 07:50, 1 January 2010 (UTC)

Perhaps in the open questions part of the article would be a reasonable place to place this type of conjectural suggestions of variant values for Pi. Even though they are not really open questions it is the place where the case might be explored. It is certainly interesting to imagine what other universes might be like if they had sufficiently different conditions that their values of Pi could be unique. What would it mean if Pi<1, or Pi=1, or Pi=Infinity? What would it mean if Pi were not a constant? What would it mean if Pi could change its sign? —Preceding unsigned comment added by 76.11.118.129 (talk) 03:41, 21 February 2010 (UTC)

As π is a mathematical (not physical) constant, it does not depend on the physical properties of the universe, it depends on logic. It is defined in terms of idealized mathematical objects. You may be thinking of a different constant such as c or G or perhaps Λ. You can't change the value of π unless you redefine circles, spheres, sines and cosines, complex numbers, etc. It sounds like the book is more fiction than science. Ropata (talk) 04:46, 20 March 2010 (UTC)

Pi is a mathematical constant, yes. In Euclidean space, it is the circumference-to-diameter ratio of a circle. In curved space, this ratio, which could be interpreted as "pi", would be different (e.g. the equatorial circle in Riemannian geometry has a ratio of 2). However, since computers don't calculate pi by measuring circles, their numbers shouldn't change. —Preceding unsigned comment added by 174.47.110.67 (talk) 19:51, 9 April 2010 (UTC)

If you can find a reliable (non fiction) source for these speculations, they could possibly be added to the "open questions" section. But it looks a lot like WP:OR to me. Ropata (talk) 13:27, 23 April 2010 (UTC)

Supposing that in curved space and riemannian geometry the smoothness of the manifold in question is included, then yes, the ratio of circumference to radius may vary. But in the limit of very small radii, the local view of the curved space becomes—by smoothness—indistinguishable from euclidean space, so the ratio goes under this limit back to the well-known value of pi.--LutzL (talk) 14:35, 23 April 2010 (UTC)

I was going to comment on the introductory classification of pi as a "mathematical and physical" constant, and this talk section fits right in. I thought these were exclusive categories. As Ropata explained, pi is mathematical and not physical. If someone notable uses these words differently, I propose that a citation be requested. (Collin237) —Preceding unsigned comment added by 166.217.168.155 (talk) 13:57, 22 July 2010 (UTC)

Definition using the circle

While this is historically the correct way, and quite possibly the way the article should go, it is also dangerous, because it gives the layman the wrong impression. It is much more fruitful to consider pi an abstract constant (possibly defined through exp(i*pi)=-1), which happens to also give a certain relationship in a circle.

I would advice that, at a minimum, the introduction stresses that the "traditional" definition is a historical left-over and ultimately only a secondary characterization of pi. 188.100.196.8 (talk) 00:26, 7 January 2010 (UTC)

Are you sure? I think an analytic definition, while perhaps more rigorous, is still secondary to the very basic properties of circles. Ropata (talk) 04:53, 20 March 2010 (UTC)

Manually collapsing WP:OR
The following discussion has been closed. Please do not modify it.
Polygons inscribed in a circle A simplest way to calculate pi is to observe polygons (polygons from three sides, to polygons increasing by multiple of two) inscribed in a circle and watch the height and the base of the sides of the polygons and use the theorem of Pythagoras to find the degree of the angles. The more sides there are in the polygons and the less the degree of the angle of the triangles. Since the angles start with 60 degree and diminish by multiple of two and the sides increase by multiple of two we have an equation: Sin (60/2^x) * 2^x *3=pi $\pi =(\sin(60/2^{x})(2^{x})(3))\,$ $\ (\sin A)/(\cos C)=1\,$ $\ (\sin 30)/(\cos 60)=1\,$ $\pi =(\sin(180/2^{x})(2^{x})\,$ Angles of triangles of polygons. 30+90+60,---------60/30=2 15+90+75,---------75/15=5 7.5+90+82.5,-------82.5/7.5=11 3.75+90+86.25,------86.25/3.75=23 1.875+90+88.125---- 88.125/1.875=47 From 2 to 5=3 From 5 to 11p=6 From 11 to 23 =12 From 23 to 47 =24 ……Twentythreethousand (talk) 20:57, 11 January 2010 (UTC) $\ (60/30=2)...(90/30=3)...(90/60=3/2)\,$ $\ (75/15=5)...(90/15=6)...(90/75=6/5)\,$ $\ (82.5/7.5=11)...(90/7.5=12)...(90/82.5=12/11)\,$ $\ (86.25/3.75=23)...(90/3.75=24)...(90/86.25=24/23)\,$ Twentythreethousand (talk) 00:25, 15 January 2010 (UTC) you can check what it looks like on a graph with radians and degrees and the graph is a constant on pi and on 180. you can make a graph with this equation.Twentythreethousand (talk) 00:06, 22 January 2010 (UTC) $\pi =(\sin(6/999999999......))*3\,$ $\pi =(\sin(60/x^{k})(x^{k})(3))\,$ Twentythreethousand (talk) 19:30, 31 January 2010 (UTC) $\pi =(\sin(6/100000000......))*3\,$ $\ 0.6--90--89.4----90/0.6=150---89.4/0.6=149---90/89.4=150/149\,$ $\ 0.06--90--89.94----90/0.06=1500---89.94/0.06=1499---90/89.94=1500/1499\,$ $\ 0.006--90--89.994---90/0.006=15000---89.994/0.006=14999--90/89.994=15000/14999\,$ $\ 0.0006--90--89.9994--90/0006=150000---89.9994/0.0006=149999---90/89.9994=150000/1499999\,$ $\pi =(\sin(0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000.......18)*10^{n})\,$ $\pi =(\sin(0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000.......6)*3)*10^{n}\,$ Twentythreethousand (talk) 01:13, 2 February 2010 (UTC) $\pi =(\sin(1/10^{n}*18)*10^{n})\,$ 1degree,0.1degree,0.001degree,0.0001degree,$1/10^{n}degree\,$ Twentythreethousand (talk) 16:24, 12 February 2010 (UTC) May I ask what this has to do with improving the article? We know $\pi =180\lim _{x\to 0}{\frac {\sin x^{\circ }}{x}}.$ — Arthur Rubin (talk) 17:24, 12 February 2010 (UTC) dear Arthur Rubin you said you know,but your equation is not even in the article and what I have stated in this discussion group is not hard trigonometry and not even hard integral calculus $\pi .$ If the calculator machine allowed an irrational number without any increase or a decrease of the number which is a straight line and a measure of a distance that require only two or three digits,what's the use of calculating pi to the billions of digits.Twentythreethousand (talk) 18:09, 13 February 2010 (UTC) File:Radianconstant180.jpg Perhaps it should be in the article, but it's a trivial consequence of: $\lim _{x\to 0}{\frac {\sin x}{x}}=1$ and 180 degrees is π radians. The latter probably should be somewhere in the article. (Actually, it is, in the infobox, and in a picture caption.) — Arthur Rubin (talk) 19:13, 13 February 2010 (UTC) $\lim _{x\to 0}{\frac {\sin x}{x}}=1$ x can not equal to 180 in this case.It's 0.174.119.27.38 (talk) 19:55, 13 February 2010 (UTC) You can believe what you want, but List of trigonometric identities#Calculus has the limit I wrote, and it's unlikely you will be able convince people otherwise. — Arthur Rubin (talk) 20:21, 13 February 2010 (UTC) the derivative would be the inverse of a number.If in radians pi equals to 0 and 180 the same and we're using 1 and 0 there not much difference with degrees.You have three colors in a magnetic fields and one color has an opposite or inverted color of the other.Both proof are the same.Twentythreethousand (talk) 21:27, 13 February 2010 (UTC) one other thing Plato the republic and criticism the major statement by Charles Kaplan about the creator and the imitator there was a movie called Coming to America that was made relating to the book.For the last generation.I am not the creator of math.We all live in a circle. —Preceding unsigned comment added by Twentythreethousand (talk • contribs) 18:39, 14 February 2010 (UTC) New Interesting Formula I suggest adding formulas 1.1 and 2.13 from http://iamned.com/math/infiniteseries.pdf to the main article They are interesting —Preceding unsigned comment added by 71.139.200.147 (talk) 06:14, 17 January 2010 (UTC) $\pi 2^{10}{\sqrt {3}}=\sum _{k=0}^{\infty }{\frac {1}{9^{k}{\tbinom {8k}{4k}}}}\left({\frac {5717}{8k+1}}-{\frac {413}{8k+3}}-{\frac {45}{8k+5}}+{\frac {5}{8k+7}}\right)$ $\pi ={\frac {\sqrt {3}}{60}}\sum _{k=0}^{\infty }{\frac {(2k)!(130k+109)}{({\frac {7}{6}})_{k}({\frac {11}{6}})_{k}(-1296)^{k}}}$ Extremely Accurate Approximation $\pi -7.66*10^{-63}\approx \ {\frac {4{\sqrt {3z(5+g)}}}{9}}\left({\frac {-{\sqrt {89}}}{g^{2}(5+g)}}\left({\frac {9(10-g)^{2}}{4z}}+{\frac {1}{5}}\right)+{\frac {827}{5}}\right)^{-1}$ ${\begin{array}{lcl}z=9(5+g)^{3}-(10-g)^{3}\\g={\sqrt[{3}]{500+53{\sqrt {89}}}}\end{array}}$ —Preceding unsigned comment added by 67.161.40.148 (talk) 05:44, 19 January 2010 (UTC) So, you managed to get 63 significant digits of pi by a complicated formula with 80 symbols. Well, guess what: I can do away with only 64 symbols in a much easier way. I leave it as a simple exercise to the reader. — Emil J. 11:06, 19 January 2010 (UTC) For those like Finell who do not get it, the solution is "3.14159265358979323846264338327950288419716939937510582097494459". — Emil J. 11:51, 19 January 2010 (UTC) The often quoted ramanujan approximation uses 13 digits to get 10 places: http://mathworld.wolfram.com/images/equations/PiApproximations/Inline49.gif there's a bunch of them here: http://mathworld.wolfram.com/PiApproximations.html The only really good one is http://mathworld.wolfram.com/images/equations/PiApproximations/Inline77.gif but it's a coincidence due to the continued fraction expansion of pi^4 To me the problem with the MathWorld's "Pi Approximations" page is that most of them seem to be mathematical coincidences. Even when there is a deeper mathematical reason for the approximation, it may still be a long way from a practical method for computation.--RDBury (talk) 13:57, 20 January 2010 (UTC) @RDBury From the work I;ve done those approximations are either coincidences or in the case of Ramanujan derived using elliptic integrals. All expressions that don't involve logarithms are constructable, but obtaining the approximation probably done though trial and error via a computer without an underlying theory. As for computation, you wouldn't use a pi approximation, but a pi formula. —Preceding unsigned comment added by 67.161.40.148 (talk) 16:25, 20 January 2010 (UTC)

Einsten the first to explain river meandering?

The text currently says that Einstein was the first to suggest that rivers have a tendency towards an ever more loopy path because the slightest curve will lead to faster currents on the outer side, which in turn will result in more erosion and a sharper bend. He may well have been the first to discover the connection with pi but I cannot believe he was the first to explain the process, even though the cited source claims this. Martin Hogbin (talk) 18:44, 30 January 2010 (UTC)

Economics

Strangely enough π is also used in economics to represent profit. l santry (talk) 16:11, 4 February 2010 (UTC)

Computation in the Computer Age

The ploufe formulas need to go. You wouldn't use them to actually compute pi. They don't seem to fit in with the overall flow of the article. —Preceding unsigned comment added by 67.161.40.148 (talk) 05:38, 17 February 2010 (UTC)

Furthermore, the physicist using 39 digits to draw a circle of known universe is highly ambiguous, fully unsourced, and seems to be one of those 78% of all statistics that are made up. —Preceding unsigned comment added by 71.180.59.107 (talk) 05:15, 24 March 2010 (UTC)

New chapter to Pi

I think adding a chapter named "computing pi" addressing historical and computational aspect of this number would have a stand in this article. As it's been a difficult topic for a long time in history. Also I noticed that it's been already addressed in other articles like,

Computation of π

In one of his numerical approximations of π, he correctly computed 2π to 9 sexagesimal digits.[9] This approximation of 2π is equivalent to 16 decimal places of accuracy.[10] This was far more accurate than the estimates earlier given in Greek mathematics (3 decimal places by Archimedes), Chinese mathematics (7 decimal places by Zu Chongzhi) or Indian mathematics (11 decimal places by Madhava of Sangamagrama). The accuracy of al-Kashi's estimate was not surpassed until Ludolph van Ceulen computed 20 decimal places of π nearly 200 years later.[1] in the Kashi's article. Repsieximo (talk) 19:45, 14 March 2010 (UTC)

See Pi#History. Ropata (talk) 04:58, 20 March 2010 (UTC)

pronounciation

why not writing something about pi's pronounciation ? (i am french, we pronounce it like pea) —Preceding unsigned comment added by 77.200.68.70 (talk • contribs) 17:29, March 14, 2010

It is pronouncedin the United States like the singlular noun pie. —Preceding unsigned comment added by 66.30.185.201 (talk • contribs) 19:26, March 14, 2010

I'm fairly sure that's true in the entire English-speaking world. Even people who say "psee" and "ksee" still say "pie", because otherwise, how would you distinguish from the Latin letter P? --Trovatore (talk) 20:20, 14 March 2010 (UTC)

Minor semantic error

{{editsemiprotected}}

There is a minor error in the section titled "Decimal Representation", third paragraph, first sentence. It says, "Because π is an irrational number, its decimal representation does not repeat, and therefore does not terminate." This does not make sense because repeating and terminating are mutually exclusive concepts. A number must either repeat or terminate. It must do one or the other and it cannot do both. I would suggest rewriting this to say "Because π is an irrational number, its decimal representation does not terminate, and therefore repeats indefinitely."—Preceding unsigned comment added by Fkento (talk • contribs) 14:15, 15 March 2010 (UTC)

I won't remove the edit request, but "terminating" decimals are often considered to be "repeating" with all 0s or all 9s at the end. — Arthur Rubin (talk) 14:24, 15 March 2010 (UTC)

(e/c) The reformulation does not make sense, the fact that the decimal representation does not terminate does not imply that it repeats, it fact, the whole point of the sentence is that the decimal representation of π does not eventually repeat. The original statement is correct, since termination of the decimal representation of a number means the same thing as the decimal representation ending with repeated 0.—Emil J. 14:26, 15 March 2010 (UTC)

Yes, you are correct. I realized my mistake a few hours later but not soon enough to delete the comment. You can remove the edit request if you so desire. Thanks Fkento (talk) 18:45, 15 March 2010 (UTC)

Delations

A bunch of stuff has been deleted uncessarily from he pi discussion pages— Preceding unsigned comment added by 67.161.40.148 (talk • contribs)

Do you mean this junk? Or are you referring to the material archived in January? Mindmatrix 14:49, 24 March 2010 (UTC)

Edit request

{{tn| The value of PI was first calculated by an Indian mathematician Budhayan, and he explained the concept of what is known as the Pythagorean Theorem. He discovered this in the 6th century, which was long before the European mathematicians.

Amitsinghsodha (talk) 05:03, 26 March 2010 (UTC)

You must supply references to reliable sources for verification.  Chzz  ►  06:52, 26 March 2010 (UTC)

 Not done

"See": Budhayan aka Baudhayana here in Wikipedia - with a number of other references from a Google search. Btw, these pages for variations of his name need to be consolidated

Robert Pollard (talk) 20:17, 5 May 2010 (UTC)

{{tn| Please remove repetitive information from the following consecutive sentences:

Both Legendre and Euler speculated that π might be transcendental, which was finally proved in 1882 by Ferdinand von Lindemann.

The transcendental nature of π was proved by Ferdinand von Lindemann in 1882.

Robert Pollard (talk) 17:50, 5 May 2010 (UTC)

Numerical approximations

In the section "Numerical approximations", it reads:

The approximation 355⁄113 (3.1415929...) is the best one that may be expressed with a three-digit or four-digit numerator and denominator; the next good approximation 103993/33102 (3.14159265301...) requires much bigger numbers, due to the large number 292 in the continued fraction expansion.

But 103933/33102 is NOT the next good approximation, because:

${\begin{array}{rcl}{\frac {355}{113}}-\pi &=&+2.667641890\cdots \times 10^{-7}\\{\frac {52163}{16604}}-\pi &=&-2.662132574\cdots \times 10^{-7}\\{\frac {103993}{33102}}-\pi &=&-0.005778906\cdots \times 10^{-7}\\\end{array}}$

Thus, 52163/16604 is closer to $\pi$ than 355/113. Since both the numerator and denominator of this are smaller than 103933/33102, the latter cannot be the next good fraction.

If what "good" means here is the number of correct decimal places, then compare:

${\begin{array}{rcl}{\frac {355}{113}}&=&3.141592\,920353\cdots \\{\frac {86953}{27678}}&=&3.141592\,600621\cdots \\{\frac {103993}{33102}}&=&3.141592\,653011\cdots \\\pi &=&3.141592\,653589\cdots \\\end{array}}$

Again, there is a fraction, namely 86953/27678, which is correct to more decimal places than 355/113, but has numerator and denominator both smaller than 103993/33102. So, again, this latter fraction cannot be the next good fraction.

The explanation in the Wiki page reads:

..., due to the large number 292 in the continued fraction expansion.

That's the culprit. Continued fraction is not the sole method of finding fractions close to $\pi$. The "better" fractions that I give above were found using Stern-Brocot tree.

219.79.176.121 (talk) 15:36, 21 April 2010 (UTC)

Well, continued fractions do determine all the best rational approximations, but one has to do it properly. The criterion is described at Continued fraction#Best rational approximations. In particular, the next best rational approximation to π after [3;7,15,1] = 355/113 should not be [3;7,15,1,292] = 103993/33102, but either [3;7,15,1,147] or [3;7,15,1,146]. Now, the latter indeed gives 52163/16604, in agreement with what you found.—Emil J. 16:00, 21 April 2010 (UTC)

And, according to the last paragraph of that section, the (continued fraction) convergents to π are best approximations in an even stronger sense: n/d is a convergent for π if and only if |dπ − n| is the least relative error among all approximations m/c with c ≤ d; that is, we have |dπ − n| < |cπ − m| so long as c < d. — [Unsigned comment added by Arthur Rubin (talk • contribs) 16:40, 21 April 2010 (UTC).]

On average, the number of significant places of the "best" approximation will be close to the sum of the digits of the numerator and the denominator of the approximating fraction. This can be understood as reasonable by thinking of throwing darts so they "stick" in a line 1 unit long. If there are 10000 darts then the average distance between pairs of darts is going to be 1/10000. Likewise when you think of the number of choices of possible fractions using arbitrary numerators and denominators, the estimate is simply the product of the numerator times the denominator, thus giving us a rough estimate of what to expect. This works very well except we now have the problem that 355/113 is more accurate than we would usually find for the number of digits. This is easily explained by the dart analogy because occasionally the darts will strike considerable closer to each other than what is average, and that is exactly how the 292 comes up. As the digits of Pi seem to be more or less random I'm sure a good probabilistic analysis of the likelihood of the 292 coming up would not be any earth shaking profundity.

What the article calls "Rational Approximations", are derived directly from what the article calls "continuing fraction" (I prefer to think of these as the terms of a continuing fraction, they are a series, not a fraction). In fact, given the terms of a continuing fraction series as far as it has been calculated, along with the residue left over from deriving the terms thus far, we have the complete and "lossless" description of PI because one can be exactly derived from the other in either direction (e.g. they contain exactly equivalent information).

Without proving the rational approximations derived from the continuing fraction series of Pi produce the best approximations of Pi, it is easy to show that it is reasonable that they are. In particular, any candidate fractional approximation of Pi that is not equal in value to any of the approximations of Pi derived from continuing fraction series of Pi, must itself have its own continuing fraction series. That series will be different from the continuing fraction series of Pi and if that series is extended in attempt to approximate Pi, it will fail to do so because it must converge to a different value than Pi. This is because process is reversible and if it approximates Pi it would exactly produce the unique continuing fraction series of Pi, contradicting the condition which said it was not derived from the continuing fraction series of Pi.

Stronger arguments can be made, but this one is more fun.

99.22.92.218 (talk) 10:35, 30 April 2010 (UTC)

Pi in a different universe

I've often seen the assertion that "in a different universe, pi would have a different value". It's nonsense, of course, and this fact is briefly alluded to in the article (in the "Physics" section):

Although not a physical constant, π appears routinely in equations describing fundamental principles of the Universe ...

It might be helpful to expound on this in further detail in the article, drawing a more blatant distinction between physical and mathematical constants. — Loadmaster (talk) 01:26, 14 May 2010 (UTC)

This could be an interesting aside, possibly drawing from Philosophy of mathematics, and some other comments from this talk page: Talk:Pi#Pi_in_science_fiction_literature. Is Pi an inherent property of reality or something imagined by the human mind? It seems quite useful anyway ... The Unreasonable Effectiveness of Mathematics in the Natural Sciences. -- Ropata (talk) 06:22, 14 May 2010 (UTC)

I would say that pi is not an inherent property of reality, unless you're willing to include abstract mathematic concepts as part of reality. Pi is an abstract idea based (initially) on geometric concepts (independent of any physical reality), and (later) on analytic geometry, complex algebra, etc. That being said, the value of pi does occur in certain physics equations that describe fundamental properties of (our particular) universe. — Loadmaster (talk) 23:28, 17 May 2010 (UTC)

Pi's digits

3.

1415926535 8979323846 2643383279 5028841971 6939937510
5820974944 5923078164 0628620899 8628034825 3421170679
8214808651 3282306647 0938446095 5058223172 5359408128
4811174502 8410270193 8521105559 6446229489 5493038196
4428810975 6659334461 2847564823 3786783165 2712019091
4564856692 3460348610 4543266482 1339360726 024914127
7245870066 0631558817 4881520920 9628292540 9171536436
7892590360 0113305305 4882046652 1384146951 9415116094

You forgot a 3 in ...412737245... I think 50 decimals in Pi#Decimal representation is enough. PrimeHunter (talk) 19:48, 17 May 2010 (UTC)

Hope you don't mind, I redid the digits in groups of ten to make the point more clear. -- Glenn L (talk) 01:57, 20 May 2010 (UTC)

heres one million decimals: http://robin1232.110mb.com/pi.html —Preceding unsigned comment added by 77.251.99.248 (talk) 12:47, 5 August 2010 (UTC)

Formatting

I've rearranged the images a bit to try and improve the format. Previously, there was a lot of white space in the text, some text was blocked out by images, and the images at the top of the article looked a bit ugly. I also added some info about the Old Testament.Anythingyouwant (talk) 05:00, 20 May 2010 (UTC)

Old testament

I have reverted the bare claim that the Old Testament claims pi equals 3, but I agree that the issue should be dealt with (surprised it isn't already — should look through the history and see if it's been removed at some point). What it actually says is that some king (I think it was) made a "molten sea" ten cubits across, and thirty cubits did compass it round about, something like that. To get from there to "pi equals three" involves several questionable steps of logic. --Trovatore (talk) 05:05, 20 May 2010 (UTC)

I've added more detail, per the cited source.Anythingyouwant (talk) 05:09, 20 May 2010 (UTC)

Yes, that reads much better; thanks. --Trovatore (talk) 07:04, 20 May 2010 (UTC)

I have heard the following mishna, which I think is worth finding a notable quote of if you can:

The usual word for "length" is קו, which has a Gematria number of 106. However, in this passage, the word is קוה, which has a Gematria number of 111. So this suggests a value of 3 × 111 ÷ 106, which gives the value 3.1415 to four decimal places. (Collin237) —Preceding unsigned comment added by 166.217.168.155 (talk) 14:23, 22 July 2010 (UTC)

Image at top

I see that there is some disagreement about what image should go at top. I like it this way, with a large Greek letter pi at the top. What do others think? The table looks kind of ugly, and if you go to the link I just gave, you'll see that the table is broken up into two pieces, each located lower down in the article (one is in the section on "Estimating pi" and the other is in the "See also" section).Anythingyouwant (talk) 10:07, 20 May 2010 (UTC)

I moved the infobox back to the top of the article. This is consistent with its placement in other mathematical constant articles, such as Euler–Mascheroni constant and Plastic number. The whole point of an infobox is that it provides easy access to summary information - if it is hidden half-way down an article, that defeats its purpose. As for the giant letter pi image, I thought it was ugly, intrusive and uninformative - we all know what the letter π looks like, so what was the point of a giant 350px image ? I much prefererd the (now removed) rolling circle animation. But let's see what other editors think. Gandalf61 (talk) 10:23, 20 May 2010 (UTC)

3. 1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 3809525720 1065485863 2788659361 5338182796 8230301952 0353018529 6899577362 2599413891 2497217752 8347913151 5574857242 4541506959 Pi to 1120 digits was first obtained using a gear-driven calculator in 1948, by John Wrench and Levi Smith. This was the last, best estimate before electronic computers took over.[FN] FN: Wrench, John. "The evolution of extended decimal approximations to π", The Mathematics Teacher, volume 53, pages 644–650 (1960).

Pi is a much higher-profile concept, and is studied at a much earlier age, than Euler–Mascheroni constant and Plastic number. I doubt a reader will stay for long if the first thing he sees is a table discussing Hexadecimals, binary forms, Apéry's constant, and the like (none of which are important for understanding pi, and none of which are discussed in this article). There's no table like this at the top of e (mathematical constant). Anyway, we'll see what others think. By the way, to the right is another idea for the top image. I'll try this new idea in the article, and see what you think.Anythingyouwant (talk) 10:27, 20 May 2010 (UTC)

Even worse. I have reverted back to the infobox. Please stop charging around making unilateral changes. Either be patient and wait for other editors to join this discussion and establish consensus, or, if you want to be more proactive, raise the issue at Wikipedia talk:WikiProject Mathematics. Gandalf61 (talk) 12:03, 20 May 2010 (UTC)

I'm kind of surprised that you prefer the infobox at top. Anyway, I'm glad to wait around and see what others think. Note that I did suggest it here at the talk page 45 minutes before editing the article. Are you opposed to including the box at right ANYWHERE in the article? I think it's quite an amazing box, and I did not know that a thousand digits had not been calculated until 1948, and then by non-electronic means. Also, please explain how Hexadecimals, binary forms, Apéry's constant, and the like are important for understanding pi, or are discussed in this article. Thanks.Anythingyouwant (talk) 16:36, 20 May 2010 (UTC)

File:Pi monumentum.jpg

Sculpture of pi at Harbor Steps in Seattle, Washington

Mosaic at entrance to mathematician's building, Berlin Institute of Technology

These two are pretty nice looking representations of pi, and either would be a big improvement at the top of the present article, I think (though the Seattle sculpture image doesn't seem to have good info at Commons).Anythingyouwant (talk) 18:32, 20 May 2010 (UTC)

New template

Here’s a new template, analogous to the one for “e”. If there is no objection, what I would like to do is put the image of the mosaic at the top of the article, immediately followed by the new template. The table currently at the top of the article would be put lower in the article as done here. I also think that the box with pi to a thousand places would be okay in the section on "Estimating π". Template:Π (mathematical constant)Anythingyouwant (talk) 20:11, 20 May 2010 (UTC)

I broadly support all of Anythingyouwant's ideas for this page (except the humungous π image, default size is fine as is). The new infobox is far better. The whole page needs a spruce up! Get rid of the cheap gif animation, it's reminiscent of an amateurish AOL page. Also need to improve presentation of the list of formulae (maybe a table of some sort?). Let's make this page interesting. Ropata (talk) 01:26, 21 May 2010 (UTC)

Hey, you New Zealanders aren't all bad after all.  :-) I'll wait until tomorrow to see if there is more feedback, before editing the article.Anythingyouwant (talk) 03:37, 21 May 2010 (UTC)

The new infobox looks good to me. And the mosaic image is better than the alternatives. But please don't make it too big - this unbalances the appearance of the article. Gandalf61 (talk) 08:29, 21 May 2010 (UTC)

Okay, thanks.Anythingyouwant (talk) 11:52, 21 May 2010 (UTC)

Done.Anythingyouwant (talk) 13:00, 21 May 2010 (UTC)

Pi "Unrolled" animation

The subject seems to have changed, so I've made a new section. This animation is still used in the Circumference article. Ropata (talk) 03:27, 28 May 2010 (UTC)

What the...? The Pi animation was the best part of the page! I've never seen a more eloquent representation of a mathematical concept. It was a Picture of the Day, for Chrissake! C1k3 (talk) 07:54, 22 May 2010 (UTC)

It is an interesting image, but placement was a problem. I moved it down in the article because I didn't think it was good at the top, and then Ropata suggested removing it altogether and I tended to agree, so I did. However, it is very relevant to the Circumference article, so I have added it there.Anythingyouwant (talk) 08:09, 22 May 2010 (UTC)

Dude, it's a visual representation of π; it belongs on the page. C1k3 (talk) 08:13, 22 May 2010 (UTC)

I assume that you read Ropata's comment above, with which I tend to agree. All the same, it is a Featured Picture, and it is relevant to this article, so I wouldn't necessarily object to putting it back in, but not at the top. For example, the last section of the article says, "Probably because of the simplicity of its definition, the concept of π, and in particular its decimal representation, have become entrenched in popular culture to a degree far greater than almost any other mathematical construct." So, we could put the animated image there to emphasize the "simplicity of its definition." The image of the plate doesn't do anything for me, so we could get rid of it (although plate fans might come out of the woodwork!).Anythingyouwant (talk) 08:52, 22 May 2010 (UTC)

Restored the animation, to the section "Computation in the computer age" Ropata (talk) 00:48, 29 May 2010 (UTC)

That looks good, thanks.Anythingyouwant (talk) 01:24, 29 May 2010 (UTC)

Pi to 1120 digits

The table of pi to 1120 digits looks messed up on my monitor. There's only ten digits in the second row.Anythingyouwant (talk) 01:29, 29 May 2010 (UTC)

Not sure what to do about that. Wikipedia renders differently for various browsers and screen sizes. Might need a more experienced editor to come up with something Ropata (talk) 01:42, 29 May 2010 (UTC)

Was there a problem with it in the previous format? If you were just trying to get highlighting, maybe that can be done with the old format. On the other hand, I didn't want to draw too much attention to the "999999" because then we might be obliged to say something about it in the caption.Anythingyouwant (talk) 01:45, 29 May 2010 (UTC)

The old format had too much bold text and the numerous digits took up a lot of space. I wanted to try smaller text. I will make a couple of other changes that I think will help. Ropata (talk) 01:48, 29 May 2010 (UTC)

OK, no problem. If your fixes don't work, then I'm sure someone else will know what to do.Anythingyouwant (talk) 01:52, 29 May 2010 (UTC)

I gave it a try. Is that okay?Anythingyouwant (talk) 02:01, 29 May 2010 (UTC)

Sure, I tweaked it again but this time I think it should render better. Ropata (talk) 04:31, 29 May 2010 (UTC)

Looks good, thanks.Anythingyouwant (talk) 09:23, 29 May 2010 (UTC)

3. 1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 3809525720 1065485863 2788659361 5338182796 8230301952 0353018529 6899577362 2599413891 2497217752 8347913151 5574857242 4541506959 Pi to 1120 digits was first obtained using a gear-driven calculator in 1948, by John Wrench and Levi Smith. This was the last, best estimate before electronic computers took over.[FN] FN: Wrench, John. "The evolution of extended decimal approximations to π", The Mathematics Teacher, volume 53, pages 644–650 (1960).

Restorations

As far as the recent restorations, I have no problem with them. I had removed the Euler's identity box because the exact same equation is already to the left. I had removed the last term of a series just in case it might collide (in some browsers) with the box containing the 1120 digits. And, I had removed the Archimedes pic because it seemed to be causing some clutter in my browser. Anyway, re-including those three things is fine with me. Thanks for letting me be bold and mess with the article.Anythingyouwant (talk) 17:52, 30 May 2010 (UTC)

No problem, it's good to try out different things. The image I think is most relevant is Archimedes, since π is also known has Archimedes' number. This article still has a ways to go but it's getting there. Cheers, Ropata (talk) 21:47, 30 May 2010 (UTC)

Minor Correction in the Main Page

Under one of the pictures in the main article we read: 'Squaring the circle was not possible for ancient geometers, because π is a transcendental number.' The text is formally correct, but this is not a correct presentation. It implies that squaring was not possible for the ancient geometers, but probably it is possible for present day geometers(which is wrong). Sqaring IS NOT POSSIBLE, this is a fact, and we should not use Past Tense to denote this fact. Correct presentation would be: Squaring the circle is not possible, because π is a transcendental number. —Preceding unsigned comment added by 79.100.15.225 (talk) 22:38, 7 June 2010 (UTC)

You are correct, although to be completely precise we must add that it is not possible if we restrict ourselves to using a compass and straightedge and a finite number of steps. Anyway, I have changed the caption in the article. Gandalf61 (talk) 08:32, 8 June 2010 (UTC)

 Done Per him. :| TelCoNaSpVe :| 04:54, 9 June 2010 (UTC)

Why are there infinite digits?

It's funny, all of this talk and yet no one answers the most common question: why are there infinite digits? It is because a "segment of a curve" is not 'a line curved'. A segment of the circumference of a circle is a series of infinitely-redirected, infinitely small lines. That's why the digits of 'pi' never stop... —Preceding unsigned comment added by 151.151.16.22 (talk) 20:41, 22 June 2010 (UTC)

It's actually a lot more complicated than that, and your argument can be easily proven fallacious: there are many curves that have a rational arc length between two rational points. The simplest, easiest-to-understand proof is probably the one given by Ivan Niven in 1945; take a look at http://www.mathlesstraveled.com/?p=548 for a good explanation of this proof. --Lucas Brown 15:25, 21 July 2010 (UTC)

...which of course doesn't have much to do with having infinitely many digits. Every real number's decimal expansion has infinitely many digits. --Trovatore (talk) 18:44, 21 July 2010 (UTC)

No it doesn't. 1 is a real number and has only 1 digit. (unless you are really picky and say that it is extended each side by an infinite number of zeros). Si Trew (talk) 20:09, 21 July 2010 (UTC)

The natural number 1 has only one digit. The real number 1, which is a different thing conceptually, has infinitely many zeroes (or nines, if you prefer) in its decimal representation. Each zero is independent of all the other ones and gives you new information.

The thing to remember about real numbers is that they encode infinitely much information, all in one tidy package. Every real number does that, even the ones where the information is kind of repetitive. --Trovatore (talk) 20:47, 21 July 2010 (UTC)

Physics

Someone ought to mention in the section on physics that the appearance of pi in equations like Einstein's Field Equations really has no physical significance, because the constants (like "G") can simply be redefined to absorb pi. The appearance of pi in those equations is thus more an artifact of history, or simply for convenience, rather than being of any fundamental importance.166.137.137.122 (talk) 16:45, 27 June 2010 (UTC)

Yes it certainly is for convenience and simplicity. Those constants, while scalar, are still defined in relation to the units of measurement (meters,kg,sec or whatever) and absorbing pi would add unnecessary complexity. Showing pi in the equations is a good indicator of rotation or spherical coordinates. Ropata (talk) 10:23, 7 July 2010 (UTC)

6/(Pi^2) in Probability

I think this article should mention that the odds of two integers being coprime is 6/(Pi^2) Grifguy123 (talk) 23:41, 17 July 2010 (UTC)

Why? — Arthur Rubin (talk) 05:15, 18 July 2010 (UTC)

Because it is a somewhat unexpected occurrence of Pi. I agree it should be in the article. Martin Hogbin (talk)

In what context:

• $\zeta (2)={\frac {\pi ^{2}}{6}}$
• That the probability that two numbers or coprime is ${\frac {1}{\zeta (2)}}={\frac {6}{\pi ^{2}}}$?

— Arthur Rubin (talk) 19:56, 21 July 2010 (UTC)

Earth

In this sentence: ..."the decimal representation of π truncated to 11 decimal places is good enough to estimate the circumference of any circle that fits inside the earth with an error of less than one millimetre"... "earth" refers to the planet, so it should start with upper case Earth. —Preceding unsigned comment added by Carlos Antonio Gil (talk • contribs) 11:07, 19 July 2010 (UTC)

You're correct. I've made the change - thanks for pointing it out! (I also moved this comment to the bottom of the page, since you'd accidentally put it in the middle of another section.) Olaf Davis (talk) 13:32, 19 July 2010 (UTC)

Historical Names

The history section is missing a very important item: What was this number called before 1710?! (Collin237) —Preceding unsigned comment added by 166.217.168.155 (talk) 14:30, 22 July 2010 (UTC)

Redundant

This article states: "the Greek letter is not capitalized (Π) even at the beginning of a sentence, and instead the lower case (π) is used at the beginning of a sentence." Uh, this is basically saying the same this twice - once should be sufficient. —Preceding unsigned comment added by 192.158.61.141 (talk) 14:33, 23 July 2010 (UTC)

Not necessarily, it could have been that although a capital Pi was not used at the beginning of a sentence, some symbol other than a lower case Pi was used. Martin Hogbin (talk) 12:29, 12 August 2010 (UTC)

New Record

Gizmodo as well as many other sources are reporting that a new record of 5 trillion digits has been calculated. I'm waiting on a change until I read more about the proof but here's a link to a story on Gizmodo. Other sources are cited at the bottom of the article. OlYeller^Talktome 13:56, 6 August 2010 (UTC)

Pi and god

I've recently discovered pi in a geometric form, send to me through kabbalahmeditation. It covers the 4 elements which is earth, water, air and fire. earth = kabbalah, water = tarot, air = astrology, fire = numerology.

In numerology there is the 4 masternumbers: 11, 22, 33, 44. If one add them and put the result at the end of itself, like this:

1+1 = 2 == 112 2+2 = 4 == 224 3+3 = 6 == 336 4+4 = 8 == 448 Add them all togethere: 112 + 224 + 336 + 448 = 1120 i personly find that beautiful

In astrologi 12 is the zodiac, the 12 houses. Aries, libra ect. ect. 0 is Quantum mechanics, the abyss, or the nothingness that combine our solarsystem with the universe. In tarot 21 is the universe. In kabbalah there is 10 spheres.

Well here it goes:

112 * 224 * 336 * 448 = 3776446464 3776446464 / 1202100000 = 3,14154102309384

              OR

1,12 * 2,24 * 3,36 * 4,48 = 37,76446464 37,76446464 / 12,021 = 3,14154102309384

Hope you find it interesting, and feel free to play along.

But π is not 3.14154102309384, it is 3.14159265358979... Gandalf61 (talk) 12:46, 12 August 2010 (UTC)

Close enough for most people like 22/7. There's another, more accurate version, but i have to upload the geo-form to explain it. Just thought this was a fun way to calculate pi. Most of us don't care about the 5 trillion digits. —Preceding unsigned comment added by 192.38.226.229 (talk) 13:02, 12 August 2010 (UTC)

But you used six two-digit numbers (and a lot of mumbo jumbo) to produce an approximation that is only accurate to five significant figures. Gandalf61 (talk) 13:11, 12 August 2010 (UTC)

Yup, like i said .....a fun way to calculate pi by including the 4 elements. I don't see the mumbo jumbo, i think it's cuite simple and i like the syncrocity. Feel free to be positive ;-) —Preceding unsigned comment added by 192.38.226.229 (talk) 13:22, 12 August 2010 (UTC)

But i sense you'll like the other version better, cause it just appers out of the blue. No calculating. Hang on a couple of days. —Preceding unsigned comment added by 192.38.226.229 (talk) 14:00, 12 August 2010 (UTC)

Do the trick for the sake of experimenting and draw your own conclusions if you wish

ERASED

—Preceding unsigned comment added by Mdiavaro99 (talk • contribs) 16:10, 13 August 2010 (UTC)