Talk:Pi/Archive 9

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Edit request from LynneMD80, 6 June 2011

Add

• Pilish, a style of writing in which the lengths of consecutive words match the digits of the number π

in the section under

"See also"

LynneMD80 (talk) 01:55, 6 June 2011 (UTC)

 Done, although I put it in the "In popular culture" section instead, as I thought it was more appropriate there. –CWenger (^ • @) 04:12, 6 June 2011 (UTC)

Edit request from Yazzcoat, 12 June 2011

Yazzcoat (talk) 11:50, 12 June 2011 (UTC)

ARITHMETIC PII

Surround rooms, living rooms witch is circle, what have bossebility know square meter. 6 meter long diameter 6x 2 × pii = m2 12 x 3,14 = 37,68m2.

8 meter long, diameter = 8 multiplication 2 x pii ( 8x 2 x 3,14) = m2.

 Not done. There is already a section on geometry. Feezo (send a signal | watch the sky) 13:40, 12 June 2011 (UTC)

Edit request from 24.10.49.212, 6 July 2011

10,000 Colors of Pi

Suggest addition of this link:

http://www.donnelly-house.net/funcrec/picolors/ — Preceding unsigned comment added by 24.10.49.212 (talk) 22:34, 6 July 2011 (UTC)

 Not done. Adds little encyclopedic value. — Edokter (talk) — 00:30, 7 July 2011 (UTC)

suggestion, adding that the first 3 digits of pi, when looked at in a mirror, resemble the English word pie. — Preceding unsigned comment added by 75.104.47.201 (talk) 20:13, 22 July 2011 (UTC)

That isn't really encyclopaedic. Cheers, Ben (talk) 00:41, 23 July 2011 (UTC)

Pi in the sciences

I've removed the claim that pi appears in formulas that have no relationship to Euclidean geometry. It was incorrectly cited, but I think more importantly, it's misleading. All the formulas we give as examples _are_ related to Euclidean geometry in the sense that they use pi to calculate density functions (abstracted from geometry), or to enable translations between linear and radial measurements. My concern is that we are suggesting that pi is a _physical_ constant, which arguably it isn't. Perhaps this distinction should be clarified more in the text? But from the list of examples, it is clear that pi gets used in a diverse range of places. Ethan Mitchell (talk) 20:37, 6 August 2011 (UTC)

Perhaps we need some examples of statistics or probability where pi shows up? — Loadmaster (talk) 17:45, 8 August 2011 (UTC)

We have some. But in these instances, I think(?), pi is being used to create a density index based on an asbtract radial measurement. Ethan Mitchell (talk) 00:24, 10 August 2011 (UTC)

Kurt Mendelssohn's pi

In his book The Riddle of the Pyramids, physicist Kurt Mendelssohn notes the relations to pi in the measurements of the Pyramids. He proposes that since we know the Egyptians did not achieve the value of pi until much later than the building of the pyramids, that the relationships most likely originate in pragmatic building techniques. He notes that the Egyptians couldn't have used ropes to measure long distances, because they stretch, and that a good solution is to count the number of revolutions of wooden drum. If you make the diameter of the drum, for example, one cubit, and then make the base the same number of "rolled" cubits as you make the height in "regular" cubits, then the relationship to pi emerges by itself, as a consequence of the tools used. You can find the reference in Chapter Three of Mendelssohn's book, "The Unsolved Problems." In my paperback edition (Cardinal, 1976, from the 1974 Thames & Hudson edition), the discussion is on PP76-79, where the proposal is sourced to electrical engineer T.E. Connolly. — Preceding unsigned comment added by Theonemacduff (talk • contribs) 23:13, 23 August 2011 (UTC)

Pi unrolled

Can we please put the image File:Pi-unrolled-720.gif back in the lead, where it was when the article received GA status? I'm aware, of course that User:Anythingyouwant is, for whatever reason, opposed to this image. But it is the simplest and best picture illustrating the meaning of π, which is traditionally defined as the ratio of the circumference of a circle to its diameter. It does this without any equations, and so is accessible to the most naive reader. By contrast, the new lead images favored by User:Anythingyouwant both require equations of some form to understand, and so are going to be less accessible for a large number of potential readers (which is likely to include grade-school geometry students less comfortable with abstract equations). There has been consensus for this lead image in the past. I would like to put it back in. Let me know what you think. Sławomir Biały (talk) 00:33, 17 September 2011 (UTC)

Of course, I'm not opposed to using the animated image in the article; it's a nice image and it's properly used prominently in the article. But as a top image, I'd recommend the two images there now. As stated in my edit summary, they show the concept of a circle's area, which the animated image does not. I don't think that the current images are any harder to understand. On the contrary, since they are not constantly changing, the current top images are easy for a beginner to understand; a still image is generally easier to absorb than a moving image.Anythingyouwant (talk) 00:53, 17 September 2011 (UTC)

How so? Both still images require an equation to understand at all. The animation only requires the notion of unrolling a wheel. Which of these do you think is likely to be more understandable to an elementary school student? Sławomir Biały (talk) 01:04, 17 September 2011 (UTC)

If a kindergartner is told that Goliath is twice as tall as David, that's perfectly understandable even though it involves an equation. Ask a nursery school student if he'd like three times as much dessert as he had yesterday, and you're likely to get an affirmative response. Just because an equation is involved doesn't mean that kids can't understand, I think. Using an animation at the top kind of makes it seem like the subject is too complicated for a still picture, which is sort of misleading. Also, more concentration is required to follow a moving image than a still image. Pi is primarily a geometric concept rather than a dynamical concept, so animation just seems like a poor fit for the top image.Anythingyouwant (talk) 01:12, 17 September 2011 (UTC)

That's a spurious analogy. Kids know what "two" and "three" mean. You're not trying to define the notion of "two" by David and Goliath, or "three" by how much more dessert I would like. But you are defining π as the solution of an equation. This is a level of abstraction that is beyond most elementary school students.

Also, the issue of area is something of a red herring. As far as I know, the Wikipedia article is the only article that tries to define pi in terms of the area. Most sources on geometry accept that pi is defined as the ratio of the circumference to the diameter (this gives pi as the natural unit of angles on the circle in trigonometry). The area formula is derived as a consequence of this definition. It is certainly important, but not nearly as important as $\pi =C/D$. Sławomir Biały (talk) 01:26, 17 September 2011 (UTC)

Well, I'm certainly willing to go along with the consensus if others feel the animation should go at the top, but I've given my sincere reasons for thinking that an animation shouldn't be used at the top of this article. Even if we were to use an animation, this particular one would not be the best, because it starts out by showing four separate circles simultaneously, whereas the concept of pi is applicable to a single circle without need for three more.Anythingyouwant (talk) 01:33, 17 September 2011 (UTC)

Having read the discussion above, I agree with Sławomir Biały. Anythingyouwant's argument about David and Goliath is silly and misses the point. The pi-unrolling image is excellent. I think it is much better than the images that Anythingyouwant wants to put there. —Mark Dominus (talk) 07:24, 17 September 2011 (UTC)

Just to followup, I have no problem with the recent article edits that have changed the double-still-image to a single-still-image at the top. The present image at the top is perfect for this article, in my view. It's very simple and understandable, and it's how virtually every elementary textbook covers the subject.Anythingyouwant (talk) 12:46, 17 September 2011 (UTC)

I agree, but I think the unrolling image is better than what a textbook can do. —Mark Dominus (talk) 04:34, 18 September 2011 (UTC)

Pi-unrolled-720.gif is a featured image, so keeping it over one that isn't seems like a no-brainer.--RDBury (talk) 12:50, 17 September 2011 (UTC)

There are lots of featured images that are used within articles instead of at the tops of articles. Saying that path A is N times longer than path B is an incredibly simple statement that any first-grader can understand. This is a geometric rather than dynamical concept, so a dynamical top image can be confusing, especially since this dynamical image shows four separate circles simultaneously instead of one circle. The dynamical image is fine where it is near the top, but it would not be a good image at the top, IMHO.Anythingyouwant (talk) 12:55, 17 September 2011 (UTC)

I think the still image showing a circumference and a diameter s better. I'm not keen on things moving around for no good reason. It's like having pupils chatting or moving around in a classroom. I think the moving image can be kept down later but I'd much prefer it was slower as currently it is an annoying movement on the page. Is there no way of stopping things like that moving? With controls one could stop it or slow it down oneself. Then when one wanted to look at it one could give it some attention and when one didn't one could stop it sticking its hand up or chatting. Dmcq (talk) 13:31, 17 September 2011 (UTC)

The images are somewhat better after recent edits, but I would still prefer (for reasons already articulated) to have the animation at the top. Sławomir Biały (talk) 14:44, 17 September 2011 (UTC)

In addition to the factors described above, the animated image is limited to the case where "a circle's diameter is 1 unit" whereas the still image does not restrict the number of units in the circle's diameter. This is a minor factor, but it again illustrates the greater simplicity and generality of the current top image, although the animated image later in the article is useful for proving that pi is a little greater than three.Anythingyouwant (talk) 14:56, 17 September 2011 (UTC)

I agree that the "pi unrolled" animation is a good image, and it deserves to be part of the article. But I feel uneasy about having an animation right at the top of the page. I think the main focus of the lead should be the text, not moving pictures. Jowa fan (talk) 03:42, 18 September 2011 (UTC)

What about it makes you uneasy? —Mark Dominus (talk) 04:34, 18 September 2011 (UTC)

I think the movement takes the focus away from the text. Jowa fan (talk) 04:48, 18 September 2011 (UTC)

Pi in multiple bases

What is the point of the infobox showing pi in multiple bases etc.? The best rational approximations are helpful, and I can sorta see the point of having binary and continued fractions, simply to show that there's no obvious pattern of the digits, but why octal, hexadecimal, and sexagesimal? They don't give any useful insight, and have no practical value. You might think the sexagesimal represention has some antiquarian value because of the Babylonian use of sexagesimal, but apparently the Babylonians didn't calculate with pi as a sexagesimal fraction (and certainly not to so many digits), but as the fraction 25/8 (not even 22/7). --Macrakis (talk) 14:37, 17 September 2011 (UTC)

I went ahead and removed the sexagesimal as trivia. The base 11 expansion is more notable since it appeared in Contact. The octal and hexadecimal are basically extensions of binary and might be used as a way of defining the number in a low level computer language, though I doubt that's come up much in the last 20 years. I have doubts about the generalized continued fraction; it doesn't converge particularly quickly and there are dozens of other series, products, etc. that might go in its place.--RDBury (talk) 18:33, 17 September 2011 (UTC)

Octal and hexadecimal may (very rarely these days) be useful constants for computer applications, but WP doesn't need to be in that business: converting the decimal to binary is trivial. --Macrakis (talk) 18:52, 17 September 2011 (UTC)

Agreed that having multiple bases may be excessive, but either octal (3 binary digits each) or hex (4 binary digits each) should be retained, binary would be unnecessary. As for generalized continued fraction, I reset it in the more standard format; it does converge at 3 decimals per 4 iterations, much faster than the other GCFs in the linked article, and surprisingly the same speed as the GCFs for both the natural logarithm and the nth root of 2 in unfolded notaion. — Glenn L (talk) 01:17, 18 September 2011 (UTC)

Huh???? Sexagesimal is not notable, although it was used in Ptolemy's Almagest, but base-11 is notable because it appeared in some obscure novel?? I don't see any great need for so MANY digits in base-60 as what we saw there, but it's historically significant that base-60 was once standard in some eastern Mediterranean countries and was used in the most famous of all books ever written on astronomy. Michael Hardy (talk) 02:18, 18 September 2011 (UTC)

I've now restored base-60 to the article (without as many digits as what appeared there before) because of its obvious historical importance. Michael Hardy (talk) 02:36, 18 September 2011 (UTC)

I agree about base 11 (which I don't think has been in the article recently anyway), but don't follow your logic about base 60. Should we also say, instead of 22/7, κβ' δια ζ' or whatever Euclid used as notation? Is Ptolemy's base-60 notation for pi in fact attested (I don't think it is -- but if it is, can you cite chapter and verse)? Do secondary sources mention Ptolemy's base-60 value? If so, we should use that value, not a modern value translated into base-60. And is it useful to have any base-60 value in the infobox? The very fact that the textual explanation is too big for the infobox tends to indicate that it doesn't belong there. --Macrakis (talk) 03:12, 18 September 2011 (UTC)

I'll let somebody else tackle base-60. But since nobody seems to object to substituting hex or octal for binary, I'm restoring hex and removing binary. Beginning with the traditional decimal value looks nicer anyway. — Glenn L (talk) 05:27, 18 September 2011 (UTC)

Let's discuss for a minute why it is useful to have binary/octal/hex in there at all. I'd think that the main reason is to demonstrate to the reader that there is no obvious pattern in the binary digits. Of course, you and I know that there is no obvious pattern in the digits of most irrational numbers (in fact, irrational numbers with obvious patterns often seem to be transcendental! ***). But for the general reader, I think that's a useful demonstration. But most general readers -- I'd venture to say in fact even many mathematicians who aren't computer scientists -- won't be familiar with octal or hexadecimal as compact ways of writing binary. So I think binary is better than octal or hex here.

Another possible reason for including hex is for programmers who want to include constants in assembly-language programs or some such. But (a) there are vanishingly few such people; (b) very few applications need fixed-point representations (as opposed to floating-point -- and I hope no one is suggesting we include the IEEE 754 representation in hex); (c) it is trivially easy to generate the hex from the decimal representation.

So... what exactly do you think is the reason for including binary/octal/hex? And why do you prefer hex to binary? --Macrakis (talk) 16:31, 18 September 2011 (UTC)

*** I wonder if there is some way to make that precise and prove it.... cf. Liouville number, Champernowne constant --Macrakis (talk) 16:31, 18 September 2011 (UTC)

Some time later this month it will become possible to write two archaic Greek letters in TeX in Wikipedia articles. Those two letters were used in Ptolemy's Almagest in the numeral system he used, with base 60 and subbase 10. So after that I will go check out his book from the library again, and do some further editing of the article about his table of chords. At that time, I will see exactly what he says about π, and probably say something about it in this article. Michael Hardy (talk) 22:15, 18 September 2011 (UTC)

Numerology versus Mathematics for science

I like to say that first off Wikipedia is an encyclopedia, not a course in advanced astrophysics. Even so calculating Pi() to 40 digits would suffice in all possible uses in astrophysics. This page is deeply flawed in its emphasis. Pi critical function is in defining circular parameters and derivation of trigonometric phenomena. Pi, for instance, tells us the number of radians in a circle. E.g. (180/pi() = 1 radian in degrees). The radian is essential for the calculation of sines and cosines based on alpha, because it defines how many radians there are in a circle and because it makes if possible for us to relate angles in radians to angles commonly used in daily life (30, 45, 60, 90, 120, etc.). Several aspects of the mathematical usefulness of pi are virtually glossed over for this numerology which is nothing more than amateur science taken to an extreme. Most pages would place 80% of whats on this page into a paragraph "Pi in popular culture". This page is on the same caliber as the Apollo 16 page.

pi/2 = 90 (an arbitrary base 360' system in which is better based on the pi/radian based system) pi/3 = 60', in a right triangle the adjacent side is 1/2 the hypotenuse. pi/4 = 45', in a right triangle both the opposite and adjacent sides are equal, and the length is 1/(2^0.5) the hypotenuse pi/6 = 30', in a right triangle the opposite side = 1/2 the hypotenuse.

This page is an excellent example of the fact that mathematics is not a pure science, but a representative language-tool for science. Pi() has scientific meaning in that its properties supercede base-systems. But knowing the digital representation in base 10 is therefore meaningless, even less meaningful in the age of computers when its precision is arbitrarily set to 8, 16, 32, or 64 digits and can be implemented without any knowledge using terms like pi(). Memorizing 100,000 digits is even more meaningless. These numerologistic analysis are the equivelant of a page on supercalifragilisticexpialidosious. PB666 ^yap 22:13, 14 October 2011 (UTC)

What's in the article is what books an articles specifically about pi talk about. And that's what qualifies material for inclusion in Wikipedia. And by the way I do not view mathematics as a science, and while it may be used as a representational tool in science that isn't what it is either. It just is mathematics, one of the endeavours people get up to. Dmcq (talk) 08:42, 20 October 2011 (UTC)

10 trillion digits

Just saw that another calculation has it to 10 trillion digits. http://www.numberworld.org/misc_runs/pi-10t/details.html — Preceding unsigned comment added by 67.169.191.53 (talk) 03:46, 20 October 2011 (UTC)

Yeah, by the same guys:

http://www.newscientist.com/blogs/shortsharpscience/2011/10/pi-10-trillion.html

Ricardobeat (talk) 18:39, 22 October 2011 (UTC)

Extra factor,4, in Gregory-Leibnitz series

It should be on the left or on the right, but not both sides, eh?68.2.46.143 (talk) 20:21, 11 November 2011 (UTC)

Top image

I've inserted a slightly modified top image. I made it myself, so the quality isn't so good. But, I've submitted a request to the image gurus to fix it up.Anythingyouwant (talk) 19:27, 18 September 2011 (UTC)

More than slightly modified I would say. You are right about the quality which has a number of problems: it's badly pixelated, badly compressed and is difficult to read at that size. It's also not clear the point it's making: without a lengthy explanation it's not obvious the curved sections are the same length as the diameter. Finally it's not a good idea to use colour to convey important information, for readers with non-colour displays and colour-blind readers. In light of all this I've restored the previous version which does not have these problems.--JohnBlackburne^words_deeds 22:31, 18 September 2011 (UTC)

Here's the image so people can see what's being discussed. Your comments have merit, but all the same I think there are features of this image that could be used to improve the present top image (which isn't bad).

The circumference of a circle is slightly more than three times as long as its diameter. The exact ratio is called π.

Anythingyouwant (talk) 22:36, 18 September 2011 (UTC)

I like this image a lot. — Preceding unsigned comment added by 173.66.156.8 (talk) 15:19, 13 November 2011 (UTC)

π to the 50:th decimal in the lead section

I saw that the 50 decimal representation of π I added to the lead section was removed. I think it should be there, and I reason like this:

Many times when people visit this article, it is only to get an accurate numerical value of π, why it is important that the value is easy to find. Therefore, it should be in the lead section of the article, or at least somewhere close to it so it can be seen immediately when the article is loaded. For example, I usually use Wikipedia to look up both physical and mathematical constants when I need them for either programming or for calculations. In those cases, I don't want to have to look through a large part of the article in order to find the numerical value, and for π, 3.14 is simply not enough. —Kri (talk) 01:09, 16 November 2011 (UTC)

An accurate value for π is to no more than 8 or 10 dp: even if someone wanted more digits they'd be pushed to use them as whatever calculating device they use will ignore the extra precision. And rather than search Wikipedia I imagine someone prepared to do such calculations will know how to get at the value easily, from their calculator or programming language for example.--JohnBlackburne^words_deeds 01:25, 16 November 2011 (UTC)

As a compromise, how about replacing 3.14 with 3.14159 in the second sentence? It's accurate enough for most practical purposes (if you're doing something with a tolerance of less than one part in a million, you shouldn't be using Wikipedia for your data), and doesn't take up too much space. Jowa fan (talk) 03:58, 16 November 2011 (UTC)

Isn't that already in the pi template (big three followed by digits of diminishing size)?Anythingyouwant (talk) 06:47, 16 November 2011 (UTC)

The reason a lot of people come here is not to see a practical value of pi to use in calculations, but precisely to see a huge number of digits after the decimal point. It's a "fun" part of maths. Teaching kids in high school, I grasp at anything like this that might build that sense of wonder about mathematics. Don't take away the fun. Put the "big" number back. (Show a "usable" number too, if that's important to some.) HiLo48 (talk) 09:30, 16 November 2011 (UTC)

There's more digits than anyone in their right mind will ever want further down in a box on the right. On the other hand fifty does seem to be about the number of digits commonly provided for the digiphiles so I would on balance support keeping the fifty decimal places. Dmcq (talk) 10:31, 16 November 2011 (UTC)

Repeats indefinitely

Yes, "its decimal representation never ends or repeats indefinitely" is vague compared to a longer explanation like "... repeats infinitely like 5/6=0.8333333 ... or 3/22=0.13636363636 ...". But "repeats indefinitely" is less vague than just "repeats", which is simply wrong; the decimal representation does repeat finitely. Art LaPella (talk) 06:35, 10 October 2011 (UTC)

How about "repeats forever"? --Trovatore (talk) 06:43, 10 October 2011 (UTC)

OK. Note that the definition of "repeat" says "To do or say again (and again). The scientists repeat the experiment in order to confirm the result." which doesn't necessarily imply that the scientists repeat the experiment forever. Art LaPella (talk) 14:01, 10 October 2011 (UTC)

True. I guess that's why you linked repeat to repeating decimal. I've just changed the page back to "... never ends or repeats", because someone else had changed it to "... has no end", which is slightly misleading (the decimal expansion of 1/3 also has no end). Since we're phrasing it in the negative, I think "repeats forever" doesn't work in this context: "... never ends or repeats forever" strikes me as clumsy. But I don't mind if someone can think of a better solution. I guess what we really want to say is "... never ends and never becomes periodic", but we're trying to keep the lead non-technical, right? Jowa fan (talk) 00:47, 11 October 2011 (UTC)

"has no end" is true as far as it goes. It doesn't say it isn't like 1/3, but readers don't expect us to list everything it isn't; they just want to be able to trust what we say it is, even if they don't click the link. Not mentioning repeating is better than saying it doesn't repeat, because it does repeat. So "has no end" without mentioning repeating, is less misleading than saying it doesn't repeat. I would also prefer "never ends and never becomes periodic" to "never ends or repeats". Art LaPella (talk) 01:38, 11 October 2011 (UTC)

How about "never ends, and never reaches a point after which it repeats forever". It's true that it's a little longer-winded, but maybe it should be, because the "never repeats forever" is on its face of higher logical complexity than "never ends". (At a slightly deeper level, of course, no decimal expansion ever "ends", but only turns into repeating zeroes, but we don't have to go there.)

By the way I agree strongly that the information should not be encoded into a link. --Trovatore (talk) 02:43, 11 October 2011 (UTC)

Possibly we could replace colloquial expressions 'never ends or repeats' with more specific 'is not finite and not periodic'...? --CiaPan (talk) 20:45, 26 October 2011 (UTC)

What about "never repeats completely", or "never repeats any one part indefinitely"? Arguably, it repeats whenever it comes across a 3, but we want to say that the end behaviour, so to speak, is just as irrational as the beginning. 24.114.252.235 (talk) 19:57, 25 November 2011 (UTC)

"Alternative notation" section (tau)

There's recently been an edit war regarding the content of Pi#Alternative_notation. My feeling is that we already have an article for Tau (2π), so there's no need to repeat too much of that content here. I'm concerned that appears in the current version reads like an advertisement for the use of tau: it gives undue weight to this notation. I'd prefer to see this section cut right back: people can go to the main article if they want to learn more. Jowa fan (talk) 03:21, 17 November 2011 (UTC)

Absolutely agree. The tau thing is a minor curiosity at this point. If it ever gets any real traction, there'll be plenty of time to say more about it. --Trovatore (talk) 03:35, 17 November 2011 (UTC)

Agree: there's really no need for so much coverage, and definitely no need for so much propaganda, on something that is essentially a fringe topic and entirely outside mainstream mathematics.--JohnBlackburne^words_deeds 03:39, 17 November 2011 (UTC)

I'm sorry if what I wrote sounded like propaganda. I meant to make the case why someone might want to go read the main Tau_(2π) article. At the end of this long article about Pi, which everyone clearly knows is a useful and important number, an explanation of why tau could be of interest to them would include mainly tau's strengths. What I especially disliked about the original "Alternative notations" section, and is true again now since you've put it back, is that it wastes half of its limited space on trivial facts. You only allow one short paragraph, then waste half of it with the following trivia instead of talking about why a 2π constant would be of interest:

...Hermann Laurent in Traité D'Algebra wrote equations using 2π as a single symbol. Robert Palais proposed to use a "pi with three legs" ($\pi \!\!\!\!\;\pi$) to denote 1 turn, while physicist Michael Hartl proposed to use the Greek letter τ (tau) to refer to the constant 2π.

Since I have three mathematicians here, could you help me understand better your objections about tau? Do you think people who say tau is a better "circle constant" than pi are wrong? Do you think they're right about the "circle constant" part, but that there's so much more to mathematics than 2-dimensional Euclidean circles? None of you actually said that people advocating for tau were wrong/mistaken, and that there are reasons why pi is the more fundamental constant, and that's why tau will fizzle. Trovatore especially (in the comment above) seems to leave the door open that tau could take off, which wouldn't be true if tau advocates were just simply wrong/mistaken. But he wrote "the tau silliness has no real traction; nothing will ever come of it" in his edit summary. Silly, not wrong. Could you explain? Thanks, Joseph Lindenberg (talk) 17:02, 17 November 2011 (UTC)

I think, if we were starting from scratch, sure, tau is arguably a better choice. Slightly better. But the difference is completely trivial. There's simply no good reason to mess with it, and no one is going to. --Trovatore (talk) 19:39, 17 November 2011 (UTC)

I'm not even sure it's slightly better, but whether it's a marginal improvement or not the previous text was clearly non-neutral in this respect. If it were much better then people would use it. A good example is quaternions: discovered then forgotten for a century but on rediscovery they quickly took off as a tool for e.g. 3D transformations superior to the matrices and Euler angles that everyone was using, even though it meant re-learning much theory and practice. The barrier to adoption of Tau is much less: it's more like whether h or ħ is used for Plank's constant. If it really offered any significant advantage it would be widely used.--JohnBlackburne^words_deeds 20:18, 17 November 2011 (UTC)

I replaced the summary with new text which explains the rationale under the introduction of the new constant. (The question "why" pops up immediately and naturally.) Max Longint (talk) 02:18, 18 November 2011 (UTC)

This looks OK to me. Jowa fan (talk) 02:31, 18 November 2011 (UTC)

I'm OK with that if everyone else is. But can I propose just one more change? That the section title have the word "tau" in it. All the main people involved in this have endorsed the use of the symbol τ. Michael Hartl wrote the "Tau Manifesto". Peter Harremoës' website uses it. Bob Palais' website has a message endorsing it. And heck, I endorsed using tau for this over 20 years ago. (See the "Background" section on my website sites.google.com/site/taubeforeitwascool if you want to read about that weird coincidence.) Although there's criticism that it conflicts with other uses of the symbol, nobody visible is using anything else any more. (By the way, thanks Max Longint.) Joseph Lindenberg (talk) 03:32, 18 November 2011 (UTC)

How about "Tau as alternative notation for twice pi"? Joseph Lindenberg (talk) 04:46, 18 November 2011 (UTC)

Or "Tau as proposed notation for two times pi". Joseph Lindenberg (talk) 05:02, 18 November 2011 (UTC)

When animated, the strips on the circle will unfurl one by one to form the triangle.

"Tau as an alternative circle constant". This section title would make a lot of sense. Before Max Longint brought us back to editing the article, I had asked a question trying to separate the idea of whether tau or pi was better generally from whether tau or pi was a better "circle constant". In grade school, most kids are taught that somehow the ultimate significance of pi comes from a (2-dimensional Euclidean) circle. And even if you do later learn that's not true, it's still hard to stop thinking of pi as the circle constant. I don't know if you looked at my website, but the very first thing there is a 3-panel graphic on circles. I don't understand how a mathematician can look at that, and at this drawing to the right here, and say that it's not overwhelmingly clear that tau is the right choice for "circle constant", not pi. Do you all agree with that much? Because beyond that, I agree that we're really just counting up where pi works better, and where tau works better. (By the way, while writing this, I discovered something you may want to fix. And recognize this as a sign of good faith, because the tau page doesn't get much traffic to begin with. Someone apparently set the term circle constant to redirect to Tau_(2π). I consider this correct, but for now it's not the generally accepted meaning of the term.) Joseph Lindenberg (talk) 10:05, 18 November 2011 (UTC)

Nobody posted any objections, so I have changed the section title to "Tau as an alternative circle constant". I will monitor this Talk page for the next few days, so please post any new objections here instead of just reverting my edit. I'll be sure to respond promptly. And I'm still eager to hear any thoughts you have on whether tau is the best circle constant, versus whether pi or tau is better everywhere else. Thanks. Joseph Lindenberg (talk) 22:40, 18 November 2011 (UTC)

My only real concern about that is that I'm not sure the term circle constant is really standard. I don't believe I've ever actually heard the term outside this (general) discussion. --Trovatore (talk) 23:27, 18 November 2011 (UTC)

On the other matter, frankly this is getting away from what talk pages are for. But I'll indulge myself in just a few words. The whole enterprise of trying to decide which is the "more fundamental", of two things easily definable in terms of each other, is frankly distasteful; it has a Scholastic feel to it, and I just think we shouldn't go there at all.

But if I did want to go down that path, I think I could make a pretty good argument that, for example, the cosine function is "more fundamental" than the sine function. So by the reasoning you seem to be using, it's the sine function that should have "co" in the name — maybe rename cosine as "trig" and sine as "cotrig" or something. Would anyone go along with that, even if they accepted my view that the cosine is "more fundamental"? Certainly not; it would just be silly. And that's the way I feel about "tau". --Trovatore (talk) 23:32, 18 November 2011 (UTC)

This is really weird, but you may be right. I just googled the term "circle constant", and almost all the links (where "circle constant" is actually used as a term) have to do with tau. I thought I'd heard pi described that way quite often over the years. Well, I'll be happy to change the section title to "Tau as the circle constant", since my google search just seemed to confirm that's the commonly accepted use of the term. If nobody objects. Joseph Lindenberg (talk) 23:56, 18 November 2011 (UTC)

I can't believe you just said that about cosine! I remember thinking the same thing many times. Unfortunately, I've been away from mathematics for so long, up until this past June, that I can't remember why anymore. But I remember thinking that often, and being frustrated when I'd write something like "we know it's a sine wave," or "it's sinusoidal", then writing a cosine function. Nobody says "it's cosinusoidal". Count me in if you ever mount a campaign to change that. Now, I just have to remember why I preferred cosine. One thing I recall is describing the motion of something like a pendulum or a spring, which you begin from a displaced postion, so cosine works better there. Joseph Lindenberg (talk) 23:56, 18 November 2011 (UTC) One other reason I just remembered is that the cosine function is the real part in Euler's Formula. Joseph Lindenberg (talk) 00:15, 19 November 2011 (UTC)

"Tau's advantages as a constant for circles"? You may reject this as being biased, but it does describe the topic of the section. Joseph Lindenberg (talk) 00:51, 19 November 2011 (UTC)

We could use the line from my website, "Tau is the circle constant. Pi is the semicircle constant." Joseph Lindenberg (talk) 01:00, 19 November 2011 (UTC)

On searching I wouldn't be surprised if you get more hits with Tau than π for 'circle constant', as it's only with Tau it needs explaining or disambiguating what it is: everyone learns π from an early age. So π is very much the circle constant it's just rarely necessarily to say so.--JohnBlackburne^words_deeds 01:08, 19 November 2011 (UTC)

Maybe I'm used to hearing it spoken, to clarify that they were talking about "pi, the circle constant" instead of "pie, the dessert". Also, when describing multiple constants, like the ones in Euler's Identity, they might say, "0, the additive identity", "1, the multiplicative identity", "pi, the circle constant". (And I'm gonna have to draw a fourth panel in that graphic on my website, for a semicircle, with pi in the formulas. Pi really is the semicircle constant. But yes, I realize most people would think of pi when they read the words "the circle constant".) Joseph Lindenberg (talk) 01:50, 19 November 2011 (UTC)

"Tau as a constant sized for circles"? Any objections to that? Joseph Lindenberg (talk) 02:19, 19 November 2011 (UTC)

That implies π isn't for circles. But it is. C = πD and all that. Anything that emphasises Tau as being better or preferred is POV and given the relative popularity of the two simply wrong.--JohnBlackburne^words_deeds 02:26, 19 November 2011 (UTC)

"Tau as a constant sized for radians"?

"Tau as a constant sized by circle radius"? Joseph Lindenberg (talk) 02:33, 19 November 2011 (UTC)

No, there's no need for that and it would confuse things: that it's an alternative notation is the main thing.--JohnBlackburne^words_deeds 02:38, 19 November 2011 (UTC)

"The proposal to replace pi with tau"? Joseph Lindenberg (talk) 02:50, 19 November 2011 (UTC)

Again, the main thing is it's an alternative notation. It's very unlikely readers will be helped by adding or replacing it with a statement about Tau which is almost unknown, even among mathematicians. So I've restored the previous heading to make it clearer that's what's covered.--JohnBlackburne^words_deeds 03:09, 19 November 2011 (UTC)

The word "proposal" makes it very clear that it isn't mainstream. And if somebody doesn't even know what tau is, then you certainly don't have to worry that they'll just read the title and start using it without reading the section body. I would like to see the word "tau" in the title. That's the name people have been hearing about it by, not "alternative notation". Joseph Lindenberg (talk) 03:31, 19 November 2011 (UTC)

I'd also like to object to your going ahead and changing the title without warning like that when we're in the middle of discussing this. I've offered many suggestions, none of which seem to be to your satisfaction. I am getting the impression that you want to suppress the word "tau". While I understand that you are strongly opposed to the proposal of switching to tau, trying to hide its existence is inappropriate. There aren't multiple "alternative notations" in that section. It's only about tau. "The proposal to replace pi with tau" makes it very clear that the section is about a suggestion to replace pi with some other number. If they don't know what tau is, you don't have to worry that they'll start using it without reading further anyway. The first words they read in the section are "A proposed alternative", so they known it isn't mainstream. Please offer just one suggestion for a title that includes the word "tau" and isn't derogatory. Joseph Lindenberg (talk) 04:00, 19 November 2011 (UTC)

Because there aren't any other "alternative notations" listed in that section, I presume you will have no objection to me changing the title to "Tau as alternative notation". But I will actually post this message first, then wait a short while before making the change, in case you wish to object. Somehow that just seems like the proper order to do them in. Joseph Lindenberg (talk) 04:35, 19 November 2011 (UTC)

After waiting two hours, I changed the title first to "Tau as alternative notation", then to "Tau as alternative notation for two pi", in order to offer two options. Either one's fine with me. The first one's a bit shorter, but I anticipated a possible objection that it might lead some people who only read the title to think they could just write the symbol τ in place of the symbol π.

Although I'll continue to monitor this talk page for a few days, if we are actually all done with this, then this post will be my last activity at the pi page for the foreseeable future, so I'll say goodbye now. Please let us be actually all done with this. Joseph Lindenberg (talk) 07:41, 19 November 2011 (UTC)

Pi=3 from the bible? no

The history section of this article claims a source, which makes an inaccurate assumption from the Bronze Sea description in 1Kings 7:23-26. The description in 1Kings includes that "the walls were sloped like a lily" showing taper.

If the bronze sea was vertically walled, pi=3 would stand, but it's approximately a frustum of a cone. A simple description is shown at the following link: http://www.yihyeh.com/the-bronze-sea.html

Since the value of a bath is known, and the number of baths that the bronze sea held is known, determining the volume provides a great estimate of the value of a biblical cubit. The key is that the simplest number of measurements is given, as expected when manufacturing screws or any crude form that was tapered. No938 (talk) 04:16, 27 November 2011 (UTC)

In the Bible both the diameter and the circumference is given as integers. These are clearly approximate values. There is no indication that the circumference was calculated by multiplying the diameter by a universal constant. The authors just wanted to indicate that the bronze sea was huge. Obviously, Christian fundamentalist do not like this place in the Bible and have all kinds of ways to explain it away, but, please, do not let such discussions invade Wikipedia. Entropeter (talk) 04:31, 28 November 2011 (UTC)

The inclusion of the Biblical implied value of pi is reasonable, but needs to be written better. It's been discussed since ancient times (see Rabbi Nehemiah, AD 150), so having a mention of it here seems appropriate. — Loadmaster (talk) 18:36, 28 November 2011 (UTC)

Capital question

In the article it says:

When used as a symbol for the mathematical constant, the Greek letter (π) is not capitalized at the beginning of a sentence. The capital letter Π (Pi) has a completely different mathematical meaning; it is used for expressing the product of a sequence.

Yet in the article, the capital 'Π' instead of 'π' is used consistently at the start of sentences. Do we not contradict ourselves? Is there a problem with {{pi}}? Kleuske (talk) 09:16, 10 December 2011 (UTC)

There is a problem with {{pi}}, which is that it's used at all. The font-mixing thing, inline, is just bad and should be dropped. --Trovatore (talk) 10:20, 10 December 2011 (UTC)

Opinion noted. Note that {{pi}} is used to diplay the mathematical symbol, not the Greek letter. If it shows too big, have a look at this note. — Edokter (talk) — 13:52, 10 December 2011 (UTC)

It's not that it looks too big. It just looks bad, mixing serif and sans-serif typefaces inline like that.

Mathematical typesetting has never "distinguished between the mathematical symbol and the Greek letter", certainly not by changing typeface. --Trovatore (talk) 20:38, 10 December 2011 (UTC)

This is an old discussion. Math has traditionally been typeset in serif, simply because a lot of characters and symbols in serif lose distinguishable features necessary to tell them apart (remember I vs. l, or rather I vs. l). Math is just pretty useless in sans-serif. — Edokter (talk) — 21:13, 10 December 2011 (UTC)

I wouldn't object to using css to put whole math articles into serif, but note that the Beamer class, which is the most used way of doing mathematical slides, uses sans-serif. The idea of using typeface to distinguish between the letter pi and the symbol pi seems to be an innovation here, and it's an unwelcome one. The letter is the symbol; it's always been used like that. Using typeface to distinguish them reminds me of overly neat-minded schemes like the upright d for differential. --Trovatore (talk) 21:35, 10 December 2011 (UTC)

Where is the capital incorrectly used? I've had a quick look at the article and can't see any instances of it, and {{pi}} works fine at the start of a sentence. The only place Wikipedia enforces capitalisation is in article names which always begin with a capital. If this is a problem {{DISPLAYTITLE}} should be used.--JohnBlackburne^words_deeds 13:48, 10 December 2011 (UTC)

First sentence, first letter. Second sentence, first letter. Third sentence halfway through. In fact every pi shows up as a capital pi. Same thing in Tau (2π), btw, where π is capitalized in the title, too, though 'τ' is unaffected. Kleuske (talk) 17:16, 10 December 2011 (UTC)

How this this π look? Are you sure it is a capital, and not just an enlarged small pi? What are the font setting in your browser? — Edokter (talk) — 17:25, 10 December 2011 (UTC)

{{frac}}

As far as I can tell, this hasn't been discussed recently, but I thought use of {{frac}}, such as in the section Pi#Estimating the value, is discouraged in mathematical articles, per WP:MOSMATH. — Arthur Rubin (talk) 16:07, 10 December 2011 (UTC)

Discouraged, yes. Not forbidden. The same format was already in use (as if it were substed), along with some instances of frac, so no change there. I'm building a new version of frac anyway to display real fractions. — Edokter (talk) — 16:32, 10 December 2011 (UTC)

I don't have a bot to search for substituted usage, but your additions are the only place in the article where the template is used, and it probably would be OK in the infobox to use any format; I'd probably replace it by ${\frac {3}{1}},{\frac {22}{7}},{\frac {333}{106}},{\frac {355}{113}},\cdots$, to save horizontal real estate. — Arthur Rubin (talk) 16:44, 10 December 2011 (UTC)

It's not otherwise in use in the article, unless additional spaces are in the < sub> tag, such as < sub > — Arthur Rubin (talk) 16:46, 10 December 2011 (UTC)

Go to this revision and count again; you will find five ohter instances of frac. Prior to my edit, the ones I placed were done using sup and sub, with the exact same result. — Edokter (talk) — 16:56, 10 December 2011 (UTC)

(Fixed oldid...) No, the only uses of < sub> (referring to a fraction) or {{frac}} are the ones you changed. I still don't think they should be there, it's marginally acceptable in the infobox, but not in the text. Still, I won't revert again, until some discussion ensues. — Arthur Rubin (talk) 17:07, 10 December 2011 (UTC)

On the other hand, there's no reason the {{frac}} template should be in this article, at all. If no reason for the usage is given, I will assume it was originally added by mistake or contrary to guidelines, and remove it. — Arthur Rubin (talk) 01:43, 14 December 2011 (UTC)

Since when does one need a reason? That's backward thinking here. Anyway, see Template:Frac/testcases. — Edokter (talk) — 10:25, 14 December 2011 (UTC)

Well I certainly think the frac template used in the text looks bad, I'd prefer just 22/7 etc. As to the box can't it use <math> formatting and that would look better. So overall I see no use for it and it is discouraged so it's okay for people to remove them. Dmcq (talk) 10:42, 14 December 2011 (UTC)

Yes it does look better I think with ⁠22/7⁠ etc. Dmcq (talk) 14:17, 14 December 2011 (UTC)

Edit request on 21 December 2011

hi i want to edit this wiki page as i have the first 100,000 didgets of pi in a txt document which i can put a link to on my current website http://skweekz.sexyi.am/upload/PI.txt

thanks for reading

p.s i would be happier if you would to deny this and edit the page yourself if thats no problem.

best regards richard aka skweekz

Skweekz (talk) 14:10, 21 December 2011 (UTC)

I don't think the article needs a link to the series; I believe that there are plenty in the article already. Thanks for wanting to contribute, though. :) Disavian (talk) 15:18, 21 December 2011 (UTC)

Hatnotes

I've added a hatnote to deal with capital Pi. Frankly, the lack of a hatnote to this effect was disgraceful... many readers of Wikipedia have not completed high school mathematics, and might be looking for this meaning; Most probably have, and would laugh at the current redirect even now we explain it.

See also Template talk:Hatnote templates documentation#Is there a suitable template for this. Andrewa (talk) 19:41, 5 December 2011 (UTC)

The hatnote is redundant, as that topic is linked to in Pi (disambiguation), which in turn is already linked from here. — Edokter (talk) — 22:28, 5 December 2011 (UTC)

Disagree. The point of the encyclopedia is to make information available. As it is, someone who runs across Π for the first time and searches for it will get to this page, with an unhelpful message saying Redirected from Π. They must then guess that it's the wrong page before they will go to the other uses link, which they are most ill-equipped to guess if they haven't seen or at least haven't understood this notation before. The current redirect is only there due to an unfortunate technical limitation; An explicit hatnote will mostly contain the damage. Andrewa (talk) 01:38, 6 December 2011 (UTC)

I think a whole line for one use of Π (and there are many uses for Π) is overkill, but I do see the issue raised, so I've expanded the hatnote slightly to point out that readers should visit the dabpage if they got here via π or Π and weren't looking for 3.14.... This would not normally work except for the shortness of "pi, π and Π", so seems like a good compromise.--JohnBlackburne^words_deeds 02:18, 6 December 2011 (UTC)

I like JohnBlackburne's solution - comprehensive without being cumbersome.--A bit iffy (talk) 02:39, 6 December 2011 (UTC)

It is certainly an improvement on what there was before. My main problem with it is that it doesn't explicitly deal with the totally incorrect redirect from Π to this article. Pi the title is OK as the redirect target for Π, but this article is not. Its topic is unrelated to the redirected term.

I wonder whether in view of this technical problem, perhaps this might be a case where making the article title recognizable to readers, unambiguous (my emphasis) might trump other considerations, and the DAB be moved to Pi undisambiguated. The logic goes like this: The primary meaning of Pi may well be the constant, but in Wikipedia using that article name leads to an ambiguity best dealt with by a DAB.

To sum up, a definite improvement but still not IMO ideal. Andrewa (talk) 19:47, 6 December 2011 (UTC)

Agree that the other uses of Π deserve consideration. Andrewa (talk) 19:47, 6 December 2011 (UTC)

Unfortunately that π and Π link to the same page is unavoidable as WP ignores the capitalisation of the initial letter. The question of which page belongs at π is a different one, and depends on which if anything is the primary topic for pi and π. One thing we can look at for this is pageview statistics:

Pi has been viewed 273502 times in the last 30 days

Pi (disambiguation) has been viewed 4450 times in the last 30 days

Π (the redirect) has been viewed 1689 times in the last 30 days

The current page is overwhelmingly the article sought by users reaching here: few visit the disambiguation page after, and under 1% use the redirect Π to get here. So the current page is the primary topic and there is very little evidence readers are looking for another topic instead of the one here.--JohnBlackburne^words_deeds 20:24, 6 December 2011 (UTC)

I think we already knew most of that. I am still uncomfortable that Π currently redirects to a page on an unrelated topic, and which gives so little help to those who follow this redirect in good faith, and amazed that nobody else seems to care. But we seem to have a rough consensus that it doesn't matter. So be it; Let's move on. Andrewa (talk) 11:11, 9 December 2011 (UTC)

The pi value was given by the Indian mathematician ARYABHATA. — Preceding unsigned comment added by S.R.Aniruddha (talk • contribs) 17:00, 1 January 2012 (UTC)

Edit request on 21 December 2011

Typo for the caption under the digits of pi: "An calculation" should be "A calculation".

Deadwisdom (talk) 22:07, 21 December 2011 (UTC)

Done. You could have edited it yourself; the article is only semi-protected. — Edokter (talk) — 23:16, 21 December 2011 (UTC)

Individual digits

On article there is equation for calculation of individual digits. I'm not sure about this because none of terms in sum has finite decimal representation, and I think hexadecimal representations are also infinite. So I think that to find digit N we must find Nth digit in first term, Nth digit in second term,...,Nth digit in (N-1)th term, and remainders from further digits. Because of this I think this method isn't to effective, but one simpler ones. This is rather question about mistake in my thinking, not any proof Wojowu (talk) 17:32, 3 January 2012 (UTC)

I haven't investigated, but have you looked at the source of the formula? A very cursory skim through it suggests that whatever infinite series result, you can cut them off eventually when the terms get too small. Leonxlin (talk) 04:34, 7 January 2012 (UTC)

Edit request on 7 January 2012

I was going to type that computers are still trying to get a non repeating number

Jcarcerano (talk) 03:22, 7 January 2012 (UTC)

Do you have a source to cite for that? Ian.thomson (talk) 03:27, 7 January 2012 (UTC)

And what do you mean? pi was proven to be non-repeating centuries ago. PrimeHunter (talk) 03:37, 7 January 2012 (UTC)

Not done: per above. --Bryce (talk | contribs) 07:42, 7 January 2012 (UTC)

Edit request on 20 January 2012

Please add a link for "Ramanujan" (a mathematician who is mentioned in this article): there is a wikipedia page for him. http://en.wikipedia.org/wiki/Srinivasa_Ramanujan Eternal fizzer (talk) 12:24, 20 January 2012 (UTC)

Done, thanks. He's now linked in two distant sections in this article. Adrian J. Hunter^{(talk•contribs)} 12:57, 20 January 2012 (UTC)

In 1706 John Machin was the first ...

In the paragraph that starts, "In 1706 John Machin was the first ...", I find it perplexing that Machin attempts to compute π based on 4atan(1/5)-atan(1/239) when π/4 = atan(1). Surely, if he were sophisticated to do what is said, he should have known of the simpler formula. Ksn (talk) 16:07, 15 February 2012 (UTC)

The article says:

In 1706 John Machin was the first to compute 100 decimals of π, using the arctan series in the formula

${\frac {\pi }{4}}=4\,\arctan {\frac {1}{5}}-\arctan {\frac {1}{239}}\!$

with

$\arctan \,x=\sum _{k=0}^{\infty }{\frac {(-1)^{k}x^{2k+1}}{2k+1}}=x-{\frac {x^{3}}{3}}+{\frac {x^{5}}{5}}-{\frac {x^{7}}{7}}+\cdots .\!$

The above arctan formula converges very slowly for x = 1 so using the formula for atan(1) is useless to compute many decimals of π. Compare x⁷/7 for x = 1/5 and for x=1. Then consider how many terms are needed before x^2k+1/(2k+1) becomes smaller than 1/10¹⁰⁰, corresponding to getting around 100 correct decimals of pi. Computers would never be able to get anywhere near it. PrimeHunter (talk) 21:10, 16 February 2012 (UTC)

Thank you! Ksn (talk) 15:36, 20 February 2012 (UTC)

Featured article?

I'm planning on working on the article, with the ultimate goal of reaching WP:FA status. I've gotten a few books from the library, including π: A biography of the world's most mysterious number (by Posametier & Lehmann); and Pi Unleashed (by Arndt and Haenel). The article is already in decent shape (and is already GA status), with some great illustrations. The biggest jobs appear to be (1) ensuring that all material has a good source, per WP:V; and (2) ensuring that the article is comprehensive. Plus, making sure the prose is professional quality (not my strong suit). Any help, suggestions, sources, etc. would be appreciated. --Noleander (talk) 21:08, 8 March 2012 (UTC)

I see there has been considerable discussion in the past about "π" vs "pi" for the article title. Apparently the current consensus is "pi" for the title, but "π" within the prose. I'm fine with that. But if anyone has any comments in that regard, or if they think it could impact FA, please speak up. --Noleander (talk) 22:08, 8 March 2012 (UTC)

the in popular culture section would probably need some tightening up. AIRcorn (talk) 00:37, 9 March 2012 (UTC)

Yeah, the reviewers at WP:FAC probably don't look too highly on that. I'm loath to delete cited material ... but maybe I can spin-off a subarticle per WP:SPINOFF; or move some material into footnotes. In any case, the section should be rather tight. --Noleander (talk) 01:12, 9 March 2012 (UTC)

You don't need to delete it all, it is probably one of the few articles where a popular culture section is justified. Personally I would just keep it to instances where the mention or use of Pi is a significant part of the media. In most of the films/TV shows it is used simply as a, sometimes minor, plot device. If there is no secondary source mentioning its use then it is probably not notable enough to include. You can always create the Pi in popular culture article as a last resort. AIRcorn (talk) 01:38, 9 March 2012 (UTC)

"Pi" is for text and titles, "π" is for formulas. See Britannica, Columbia, Wolfram's MathWorld, Mathematics, MacMillan Dictionary, Collins English Dictionary, Oxford Dictionaries, Merriam Webster, and American Heritage. It's the usual practice to spell out Greek letters: Chi-squared distribution, Dirac delta function, gamma function, Omega constant and so on. Kauffner (talk) 01:22, 9 March 2012 (UTC)

Thanks for the input. I notice the article uses π everywhere in the prose (not just formulas). Since that is the status quo, my inclination is to leave it alone (since it has already been brought up in the Talk pages in the past, and the status quo should be maintained absent a compelling reason). Personally, I have no strong preference one way or another. If anyone wants to propose a new convention (e.g. "pi" when not in a formula) the best path is to do an RfC. --Noleander (talk) 01:32, 9 March 2012 (UTC)

I've finished reading three books on pi, and I'm ready to start making some edits. As I observed above, the article is already in great shape, and to get to FA status, it will mostly be (1) improving prose; (2) ensuring comprehensiveness; and (3) adding cites. If anyone has any suggestions, please speak up. --Noleander (talk) 00:59, 15 March 2012 (UTC)

Why Pi day is on March 14

Well,it's because of the first 3 digits of π,3.14,it tell us that it's on 3/14 which is March 14. — Preceding unsigned comment added by 207.237.10.60 (talk) 23:38, 14 March 2012 (UTC)

First 1120 of Pi

The first 1120 of Pi are:3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193 8521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715 3643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430 8602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925 8923542019956112129021960864034418159813629774771309960518707211349999998372978049951059737328160963859502445945534690830264252230825334468503526193118817101000313783875288658 7533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301 9520353018529689957736225994138912497217752834791315155748572424541506959 — Preceding unsigned comment added by 207.237.10.60 (talk) 23:48, 14 March 2012 (UTC)

Looks to me like you suffer piarrhea. That does not contribute to improving the article. Dmcq (talk) 23:52, 14 March 2012 (UTC)

Pi Unrolled Not Working

THis image was working before http://en.wikipedia.org/wiki/File:Pi-unrolled-720.gif Now it isn't. Is this a local problem? Picklebobdogflog (talk) 00:18, 16 March 2012 (UTC)

It's working fine for me, both full size (following the above link) and where it is in the article. If it was working for you but now isn't you might try clearing your browser cache or forcing a reload of the page.--JohnBlackburne^words_deeds 00:24, 16 March 2012 (UTC)

Yeah thanks, probably just on my end. New safari update came out so that might fix it. — Preceding unsigned comment added by Picklebobdogflog (talk • contribs) 00:33, 16 March 2012 (UTC)

It was not working for me either, for about a day. It seems to be working now. --Noleander (talk) 19:33, 17 March 2012 (UTC)

Tau

For a mathematical constant as thoroughly studied as π, the section on renaming it to τ should not be here. It is a gross violation of WP:WEIGHT. Moreover, none of the sources referenced meet even the most minimal standards of scholarship needed for inclusion in an encyclopedia article. The symbol τ is not used in any mainstream mathematical sources. Sławomir Biały (talk) 11:00, 19 March 2012 (UTC)

I agree that an entire top-level section on tau is too much: tau is a bit WP:FRINGE, and has a hint of WP:RECENTISM. On the other hand, it is documented by sources, and is closely related to pi. I'm in the middle of working on the article, trying to get it up to FA status ... could take a couple of months or more. I propose to de-emphasize the tau material by reducing it to a paragraph or subsection within a new "Miscellaneous" top-level section ... treating it comparably to "pi in popular culture". You are welcome to reduce the tau material now if you want (unless other editors object); or I'll get to it soon. --Noleander (talk) 13:51, 19 March 2012 (UTC)

Given the vast amount of literature on π I agree that an entire section on this τ proposal is unnecessary, however a sentence under the history section (which itself seems a bit of a mess) or a see also link might be appropriate. On a related note, does the In popular culture section need some trimming too? Perhaps limiting the entertainment stuff to a single paragraph (with more discussion and less list)? Cheers, Ben (talk) 13:57, 19 March 2012 (UTC)

A link in the "see also" section may be sufficient. Tkuvho (talk) 13:58, 19 March 2012 (UTC)

I was thinking that maybe the Palais reference could be used to add a sentence somewhere like "Bob Palais in the Mathematical Intelligencer has argued that 2π is more fundamental than π", perhaps in the pop culture section. It's clear to me though that the "tau" business is so marginal to have no place in an encyclopedia article about the mathematical constant. Sławomir Biały (talk) 13:59, 19 March 2012 (UTC)

I agree, 'tau' is fringe. Martin Hogbin (talk) 14:24, 19 March 2012 (UTC)

Animation of Circle Area Derivation

Noleander, consider using this animation when you do. I haven't gotten around to turning it into a smaller gif file yet. Also, I can revise the wording if you want. But the single most common question people ask about tau – by far – is doesn't it make $\pi r^{2}$ more complicated as ${\tfrac {1}{2}}\tau r^{2}$ ? This animation explains why the ${\tfrac {1}{2}}$ was originally there, without needing Calculus. Joseph Lindenberg (talk) 03:14, 20 March 2012 (UTC)

Oh, I forgot to mention, obviously I would take my name and website URL off the bottom of it before it was ready to go up on an actual Wikipedia page. I had simply uploaded this converted copy of the file that was already on my personal website so that everyone could more easily discuss it over on the Talk page for Tau_(2π). Joseph Lindenberg (talk) 04:45, 20 March 2012 (UTC)

Cont Frac: not under History

The two subsections " Representation as a continued fraction" and "Memorizing digits" are currently under the "History" top level section, which is not appropriate. I'll move them out to be top level sections for now, but that is not ideal, since that would lead to a lot of top level sections. This article may need a "Miscellaneous" top level section, to hold "Tau", "In Popular Culture", "Representation as a continued fraction" and "Memorizing digits" ... but "Misc" is not ideal either. Any thoughts? --Noleander (talk) 19:32, 17 March 2012 (UTC)

This has been done. --Noleander (talk) 10:16, 22 March 2012 (UTC)

History section prelude

The History section has an Antiquity subsection; but before that is an intro paragraph about Egypt. Clearly, that Egypt material belongs in the Antiq section, so I'll move it.

There seem to be several "obvious" changes to make, similar to that, so I'll forge ahead without notifications here on the Talk page. If anyone sees a mistake, or does not agree with a particular change, feel free to revert. Or, better yet, just drop a quick note here on the Talk page and I'll remedy any issues. --Noleander (talk) 19:42, 17 March 2012 (UTC)

This has been done. --Noleander (talk) 10:16, 22 March 2012 (UTC)

Pyramids

The pyramids section seems a bit verbose; and also a bit polemic, emphasizing the "they were based on pi" viewpoint. I suggest tightening that section a bit, and also relying more on secondary sources. I think the tone should be something like "Some egyptologists have speculated ..., but others view the proposal with skepticism ...". Thoughts? --Noleander (talk) 19:59, 17 March 2012 (UTC)

This has been done. --Noleander (talk) 10:16, 22 March 2012 (UTC)

Large table of AGM style equations in "Computer era" section excessive?

The Pi#Computer_era section has a large table of about 20 infinite sum equations for pi. This seems excessive. This article is a main article, with several subarticles. The kind of detail in that table should be moved down into a subarticle such as Approximations_of_π or List of formulae involving π. Of course, a few key formulae (from that table) could be left in this article if secondary sources specifically mention them prominently. Thoughts? --Noleander (talk) 14:51, 19 March 2012 (UTC)

The table does seem to be excessive for this article. It could be moved somewhere more appropriate, like List of formulas involving π. Sławomir Biały (talk) 15:03, 19 March 2012 (UTC)

Fully agree that list seems a better place and just stick in a link. And besides I would have though we shouldn't have big tables where the individual entries have not been shown to be of any interest - that's what references are there for. I mean what are the criteria for ever stopping a table like that otherwise? Dmcq (talk) 15:19, 19 March 2012 (UTC)

There is quite a large body of literature on these type of series. Ideally these should be mentioned in this article and link to a sub-article titled Ramanujan-type series involving π or similar, where the history, applications and the less well-known π^2, π^3 and π^4 examples are discussed. Unfortunately, I simply don't have the motivation to get this started at the moment. Cheers, Ben (talk) 15:41, 19 March 2012 (UTC)

I think the article mentioned above, List of formulae involving π, should meet that need. The key point of this inquiry (in the Talk page) is to get concurrence on removing the material from this article, since it is an obstacle to FA status. If I remove it, I won't delete the table from WP: I'd just transfer it into List of formulae involving π. --Noleander (talk) 17:58, 19 March 2012 (UTC)

This has been done. --Noleander (talk) 10:17, 22 March 2012 (UTC)

Should incidental formulae be placed in boxes on the side?

When displaying incidental formulae, the article has the choice of placing them in between paragraphs (inline), or in a sidebar box. I have no preference one way or another, but as an experiment, I've placed a few on the side in the Pi#Infinite_series section. The convention in WP math articles seems to favor centering the formulae in-line. For instance the Logarithm article, a FA article within the Math project puts all its formulae inline. If anyone objects to this temporary formatting experiment, I can move them back in-line, no problem. At some point, before this is nominated for FA status, we'll have to decide on way or another. As I say, I have no preference on way or another, but it is worth considering. Thoughts? --Noleander (talk) 21:01, 20 March 2012 (UTC)

Is it possible to centre the formulas in the box? Cheers, Ben (talk) 03:48, 22 March 2012 (UTC)

Those boxes are using the {{Quote box}} template. The documentation says there is a parameter "qalign" that has values left/right/center, and which applies to the text in the box. I don't have time to try it right now, but qalign=center should do the trick. --Noleander (talk) 03:52, 22 March 2012 (UTC)

Worked like a charm. Cheers, Ben (talk) 04:13, 22 March 2012 (UTC)

web site reliable source?

There is a web site [1] "About Pi. Ask Dr. Math FAQ" - it is used as a ref four times. It does not strike me as a reliable source. My intention, when I see refs like this, is to replace them with reliable secondary sources listed in the new References section. I don't see any material yet that should be outright deleted, but the sourcing is relying too much on primary sources. So, I don't foresee too many changes: just replacing a few cites; consolidating some material; improving the prose a little bit. --Noleander (talk) 20:04, 17 March 2012 (UTC)

This is not a reliable source. I say kill it. Also, it is attached to the word "Euclidean" in the lead. In my opinion, this word should be eliminated entirely. Links to Euclidean geometry should be worked in less artificially elsewhere in the lead. (But IMO the lead will need to be rewritten completely after the rest of the article is updated, so this is not an urgent matter.) Sławomir Biały (talk) 00:45, 27 March 2012 (UTC)

See also section & Indiana pi bill

The FA criteria suggest that an ideal article should not have a "see also" section, on the theory that a truly comprehensive article's body would mention (& have a link to) any related article. This article has about 5 articles in the See also section, including the Indiana pi bill (and it is also mentioned in the Approximations of π subarticle). I suggest adding a very brief mention of that article somewhere in the article .. perhaps in some "crackpot" paragraph about continued attempts to square the circle after 1882. Personally, I have no objection to See Also sections in FA articles, but moving such articles into the body is a desirable goal. --Noleander (talk) 20:35, 17 March 2012 (UTC)

I don't thinks that's the case. Lot's of featured articles have See also sections. In the case of this article, it's clear that a see also section is needed to accommodate certain topics that would not meet the requirements of WP:WEIGHT if they were included in the main text. Examples are the Indiana Pi Bill, and Tau (2π). In my opinion, such topics should not be discussed in the main article, as they are totally peripheral to the subject. They can, however, be farmed out to sub-articles if there is scope for expansion in that direction (e.g., Pi in politics or some such.) Sławomir Biały (talk) 00:50, 27 March 2012 (UTC)

Sounds good. I have no objections to See Also sections. --Noleander (talk) 01:29, 27 March 2012 (UTC)

Another web site source

I just stumbled on this citation: [2] which is used three times in the article. I propose to replace it with a more reliable source. --Noleander (talk) 16:31, 20 March 2012 (UTC)

I thought MacTutor History was okay? Dmcq (talk) 18:46, 20 March 2012 (UTC)

The web site is http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Pi_through_the_ages.html. It does not appear to be reliable. I'm not familiar with what web sites the Math project has adopted as acceptable, but in my opinion, anything other than http://mathworld.wolfram.com/ is not satisfactory. --Noleander (talk) 19:31, 20 March 2012 (UTC)

Well we have a small article about it MacTutor History of Mathematics archive and there are links to reviews. I'd have thought it would be okay as it is written by recognized authorities. If you can find better sources though no problem about replacing. Dmcq (talk) 19:26, 20 March 2012 (UTC)

Yes, there are many reliable sources (books published by university presses, etc) so there is really no need to be using web sites at all. --Noleander (talk) 19:30, 20 March 2012 (UTC)

Consensus in the past has been that MacTutor is an acceptable reference, but where possible it should be supplemented with a better source. I should add that Wolfram's MathWorld is not particularly reliable either. It's not peer reviewed, and is largely the work of a single non-mathematician. What few topics in my specialty areas MathWorld has articles on, they are often full of errors, invented notations, and other inconsistencies with the published literature. MacTutor has a much better reputation for historical accuracy than Wolfram (this is based on reviews of both), and MacTutor is something of a de facto standard for history of mathematics in the same way as MathWorld is for certain other topics. Sławomir Biały (talk) 13:55, 25 March 2012 (UTC)

Contradiction on most accurate calculation before computers.

Under Estimating the value it says (under the greyed "image" to the right) "A calculation of π accurate to 1120 decimal digits was obtained using a gear-driven calculator in 1948, by John Wrench and Levi Smith. This was the most accurate calculation of π before electronic computers came into use." while under Infinite series it says (last paragraph) "Infinite series based on the arctan function generally converge much faster than other infinite series, and were used to set records for the next 300 years, culminating in a 620 digit approximation in 1946 by Daniel Ferguson – the best approximation calculated without the aid of an electronic computer."
At least one of those two statements must be false - or?
Also Chronology of computation of π says that in 1949 D. F. Ferguson and John Wrench (not John Wrench and Levi Smith in 1948) calculated π with 1120 decimals and the page on John Wrench says that he and Levi Smith used a desk calculator to calculate π with 1160 decimals during 1945 to 1956. I.e. yet some more contradictions...
--Episcophagus (talk) 17:33, 26 March 2012 (UTC)

Thanks for pointing out that error. According to Arndt, p 205, the records were:

620 digits in 1946 by Ferguson - manual (no calculator)

808 digits in 1948 by Ferguson & Wrench - used a desk calculator

1,120 digits in 1949 by Smith & Wrench - used a desk calculator

2,037 digits in 1949 by Reitwiesner - on ENIAC electr computer

I'll straighten the article out to be correct. --Noleander (talk) 18:10, 26 March 2012 (UTC)

John Wrench himself writes (in this link, page 322):

"With the collaboration of Levi B. Smith (...) the writer computed π to 818 places by February, using a desk calculator. The result was published to 808 places in April 1947 (...) Collation of this 808-place approximation with results obrtained by Ferguson later that year revealed several erroneous figures behind the 723rd place (...) Correction of these errors and extensions of Ferguson's results appeared in a joint paper by Ferguson and the writer in January 1948, which concluded with an 808-place approximation to π of guaranteed accruacy. Subsequently, Smith and the writer resumed their calculations and by June 1949 had obtained an approximation to about 1120 places. (...) In November 1954, Smith and the writer extended their calculation to 1150 places, and in 1956 reverted to this work once more to attain their final result, which was terminated at 1160 places, of which the first 1157 agree with those obtained on the ENIAC."

--Episcophagus (talk) 18:15, 26 March 2012 (UTC)

Thanks for that info. I think it is consistent with material from the Arndt secondary source. I find it interesting that they continued working until 1956 to get up to 1,160 digits, when ENIAC had already gotten up to 2,000 digits in 1949. I've updated the article to be accurate now, speak up if you see any other errors. --Noleander (talk) 18:27, 26 March 2012 (UTC)

In the same book as I linked to above (on page 280) the 1950 article by Reitwiesner is also (in part) published. There π is given by 2035 places, not 2037.

--Episcophagus (talk) 18:52, 26 March 2012 (UTC)

Charters of sections need to be clarified

The article has a few sections whose charters are a bit fuzzy:

1. Pi#Irrationality and transcendence - Does not include a discussion of normal or random
2. Pi#Decimal representation - Includes the "39 digits are sufficient" issue; & irrationality & randomness
3. Pi#Estimating the value - Includes some history & formulae
4. Pi#History - history & formulae

I think the material is good, but the sections could be cleaner if they were reorganized as follows:

1. Properties - (irrationality, transcendental, etc)
2. Randomness - (incl why interesting to mathematicians; Is it normal? statistical tests of randomness, Feynman point, etc)
3. Approximations - (include decimal/hex representations; and some well known coincidental equations)
4. History (leave as-is)
5. Motivation for high accuracy - ("39 digits is sufficient"; bragging rights; exercise supercomputers; test high-precision arithmetic algorithms, provide data for analyzing randomness of digits, etc)

I'm not proposing to remove any material, simply to clarify the charters of the sections and move things around a bit to better track the secondary sources. Thoughts? --Noleander (talk) 10:33, 22 March 2012 (UTC)

I think normality (I think the word randomness should be avoided) can just be included as part of the discussion on properties. That fact that it's an open question is cool. Also, the note about π's irrationality measure can be included here. I prefer Estimating the value or Estimations over Approximations, but that is just a personal preference. The rest looks good. Cheers, Ben (talk) 22:55, 22 March 2012 (UTC)

It might also be worth renaming the Geometric definition section to Definition so we can include a more proper discussion of how we can define π. Cheers, Ben (talk) 23:01, 22 March 2012 (UTC)

The above proposal has been implemented, including Ben's suggestions. --Noleander (talk) 20:36, 30 March 2012 (UTC)

Buffon's needle in Probability section?

The Pi#Probability and statistics section contains a couple of paragraphs on pi and Buffon's needle. The context of that section is showing how pi appears (usually unexpectedly) in various scientific disciplines .... the example (in that section) of pi in gauss normal distribution is a great example. But Buffon's needle problem is circular/trigonometric in nature, and pi is expected there. So, I think Buffon's needle is better treated (in this article) as a monte carlo approach to estimating pi. So perhaps the Buffon's needle material should be split out into a new section "Monte Carlo estimations". That new section could also include the dart board approach to calculating pi (which is described in Approximations_of_π#Summing_a_circle.27s_area, but is not yet in the pi article). Thoughts? --Noleander (talk) 11:40, 22 March 2012 (UTC)

This has been done: A new section on Monte Carlo methods was created, and the Buffon needle material was moved into it. --Noleander (talk) 20:37, 30 March 2012 (UTC)

Illustration vs. NavBox at top of article?

The picture of a rolling wheel at the top of the article is really, really good. Probably worth more than a thousand words. But, there is also the convention that sidebar navboxes, if present in an article, are placed in the upper right corner of the article. So, we should have a discussion about whether the rolling wheel should be above or below the sidebar navbox. When this article achieved GA status in 2007, the rolling wheel was at the top, but that was before the sidebar navbox was introduced in May 2010. There is an archived Talk page discussion on which should be on top, from May 2011, but it was inconclusive. Personally, either way seems okay; I can see arguments both ways. But I am planning on nominating this for FA status soon, so we should probably have the discussion and get consensus one way or another. --Noleander (talk) 14:55, 4 April 2012 (UTC)

Or merge them. Easier to show this than describe it so I've gone ahead and done it, but only on this page using a parser function in Template:Pi box. Seems to work and have not broken anything. It could instead be changed to always use that image or even use it based on a parameter in the infobox (that might be a more standard way to do it).--JohnBlackburne^words_deeds 15:07, 4 April 2012 (UTC)

Great solution! --Noleander (talk) 15:14, 4 April 2012 (UTC)

Examples of trig definitions

The Definitions section currently has 5 sample definitions based on trig:

• π is the smallest positive x for which sine(x) equals zero
• π is the smallest positive x for which cosine(x) equals –1 (π = arccos(–1))
• π is twice the smallest positive x for which sine(x) equals 1 (π = 2 arcsin(1))
• π is twice the smallest positive x for which cosine(x) equals zero (π = 2 arccos(0))
• π is four times the smallest positive x for which tangent(x) equals 1 (π = 4 arctan(1))

Most sources that mention this kind of definition only cite 1, 2 or 3 examples. I'm wondering if having 5 would give readers the wrong impression that these are critical, and all five are significant somehow? Maybe trim down to 2 or 3? --Noleander (talk) 03:38, 7 April 2012 (UTC)

I just trimmed it down to three - one for each trig function. — Glenn L (talk) 01:20, 9 April 2012 (UTC)

"Geomorphology and chaos theory" section

The section titled "Geomorphology and chaos theory" seems a bit fishy to me. First, it says " Albert 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 I find hard to believe. Second, the word "chaos" does not appear in the text of the section, so why is it in the title? I'll do some research and make sure the material reflects the sources, but if anyone has some thoughts, please speak up. --Noleander (talk) 03:25, 4 April 2012 (UTC)

Done: i removed Einstein and "chaos", and re-worded to simply reflect what the source says. --Noleander (talk) 15:22, 10 April 2012 (UTC)

Remove conjecture?

The "Properties" section contains the following sentence:

"Bailey and Crandall showed in 2000 that the existence of the Bailey–Borwein–Plouffe formula and similar formulas imply that the normality of π in base 2 can be reduced to a plausible conjecture of chaos theory.[29]"

I read the source, but it doesn't seem to warrant inclusion in this article. The way I read it is the authors have some ideas, but they have not proven anything yet. There must be hundreds of "plausible conjectures" about pi, but we cannot include them all in this article. Unless some strong secondary sources mention this conjecture, I suggest removing it. Thoughts? --Noleander (talk) 17:54, 4 April 2012 (UTC)

It is quite an old ref so, unless anyone can show signs of progress in this theory or continued interest in it in a good source, I would say delete. If someone can give a half-decent reason to keep I would not argue. Martin Hogbin (talk) 20:09, 4 April 2012 (UTC)

Done: I removed it. --Noleander (talk) 15:23, 10 April 2012 (UTC)

Bulleted lists in the "In mathematics and science" section?

The subsections of "In mathematics and science" use a variety of approaches to text formatting: the Number Theory, Geometry and trigonometry, and River sections use a simple prose paragraph. The Physics and Probability sections use a bulleted technique. The Complex numbers and calculus sections are non-bulleted, but list-like. I think the big question is: Should the sections use bullets? or avoid bullets? The MOS says "Do not use lists if a passage is read easily as plain paragraphs." I believe that the Featured Article reviewers, in general, view bullets unfavorably. Looking at the text in question, I see no harm in removing the bullets. One upside is that it will induce editors to add textual background & explanation of the formulae, and thus make it more informative to lay readers. Thoughts? --Noleander (talk) 14:12, 5 April 2012 (UTC)

I removed the bullets, and converted to plain text. --Noleander (talk) 15:21, 10 April 2012 (UTC)

Pronunciation in Greek

The following sentence in the Name section either says the same thing twice (that in English, we pronounce π as "pie") or erroneously says that Greeks also pronounce it this way: In English, π is pronounced as "pie" (/ˈpaɪ/), which is the same pronunciation used for the Greek letter. Joseph Lindenberg (talk) 21:31, 9 April 2012 (UTC)

Thanks for pointing that out ... I'll fix it. --Noleander (talk) 21:38, 9 April 2012 (UTC)

Use of pi before William Jones

What I had read was that William Oughtred used ⁠π/δ⁠ to represent ⁠perimeter/diameter⁠ since π and δ are the Greek equivalents of p and d. I read this in the last paragraph of this article. He cites page 292 of Pi: A Source Book as his source. I also see it mentioned in the book The Joy of Pi. See the 5th page here. Joseph Lindenberg (talk) 22:29, 9 April 2012 (UTC)

Yes, I have (for another 2 days :-) Pi: A Source Book ... and indeed that fact does appear. It appears that π was used by Oughtred not in the modern sense (a ratio = circum/diam) but rather simply to mean circumference (or periphery). So, that fact does not directly bear on the number π, although it does provide some historical background. Maybe I'll put it in a footnote for now ... putting it in the prose may cause more confusion than enlightenment. --Noleander (talk) 23:51, 9 April 2012 (UTC)

Okay, I put that in as footnote #6: " See Schepler, p 220: William Oughtred used the letter π circa 1630 to represent the periphery (i.e. circumference) of a circle." --Noleander (talk) 23:55, 9 April 2012 (UTC)

Magnetic permeability not a good example

I'd like to hear other people's opinions on this, but I don't think magnetic permeability $\mu _{0}=4\pi \cdot 10^{-7}\,\mathrm {N/A^{2}} \,$ is a good example to use. The presence of π in it is entirely man-made and arbitrary. Scientists set the size of SI units to produce that result. (It was done so that the 4π would cancel out the 4π in formulas like the Biot-Savart Law.) They could just as easily have set the size of their units to make $\mu _{0}$ equal their favorite lottery number. You'll notice that none of the other physics formulas listed have units attached. Using the Biot-Savart Law instead would just seem more intellectually honest. (Ultimately though, the 4π in it and in Coulomb's law come from the 4π in the surface area of a sphere.) Joseph Lindenberg (talk) 02:09, 10 April 2012 (UTC)

Tend to agree. --Trovatore (talk) 02:16, 10 April 2012 (UTC)

I replaced the magnetic permeability formula with the Biot-Savart Law. If another formula would be superior, speak up. --Noleander (talk) 04:16, 10 April 2012 (UTC)

As Joseph Lindenberg says, many laws of physics that contain pi essentially just reflect the formula for the surface area of a sphere and the system of units used. This does not necessarily mean that we should not mention them here but I would suggest that we have at most just one such formula, as an example of pi being used in physics. Martin Hogbin (talk) 08:28, 10 April 2012 (UTC)

I see no problem with removing 1 or 2 of the physics formulae, if they are not adding anything to the article. That section does begin with the disclaimer: "Although not a physical constant, π appears routinely in equations describing fundamental principles of the Universe, often because of π's relationship to the circle and to spherical coordinate systems." Two that are a bit duplicative are Einsteins field equation & the cosmological constant immediately following it. --Noleander (talk) 13:37, 10 April 2012 (UTC)

Peer review soon

I'm still planning on nominating the article for FA status. There are a few tasks remaining, such as ensuring that all citations are uniformly formatted; validating all citations to make sure they support the material in the article; and reviewing the lead to make sure it is a good summary of the entire article. After that, I'll open up a peer review request and then, if the PR outcome is good, nominate for FA. If any editor has suggestions or ideas for improvement, please speak up! --Noleander (talk) 16:59, 10 April 2012 (UTC)

Firstly, well done so far. Just a few thoughts:

Is the lead a good summary of the article as a whole?

Why now "piems", in quotes, rather than pilish which has its own article.? Martin Hogbin (talk) 17:14, 10 April 2012 (UTC)

I have not looked at the lead yet: I figure it is better to wait for the body of the article to settle down, and only then do the lead. At first glance, the lead looks okay, but it doesn't seem to mirror the body very closely (not that it has to slavishly follow the body). As for piem vs. pilish: Yes, it looks like that could be clarified & improved. There seem to be several overlapping concepts: Piphilology (any mnemonic technique to memorize pi's digits); pilish (any story/poem with word-lengths that represent pi's digits); and piems (rhyming pilish). I'll see if I can improve the article to clarify all that. --Noleander (talk) 17:25, 10 April 2012 (UTC)

I agree with you about the lead; it is not at all bad and it is best to wait until the body is complete but I guess we are nearly there now. Martin Hogbin (talk) 17:44, 10 April 2012 (UTC)

I improved the section on memorizing digits. I looked in the secondary sources, and none of the three terms (piphilology, piem, or pilish) appear much ... the authors just speak of "memorizing" or "mnemonics". I removed "pilish" from this article, because the sources just dont use it. I left in piphilology and piem, but even those I'm not sure about. A good case could be made for renaming the article piphilology to Memorizing pi, but I won't go down that path. If anyone think the Memorizing section could be improved in any way, please speak up. --Noleander (talk) 20:15, 10 April 2012 (UTC)

Rivers & pyramids

An editor removed material on pyramids & the meandering river. I restored the pyramid material, because it is discussed in many reliable secondary sources on pi. Perhaps that text could be improved to make it clearer that most modern scientists/egyptologists don't think that pi was involved in the pyramid shapes, but total removal is a bit much. The meandering river material is not as widely discussed by 2ndary sources, although it is in the Posamentier source. So that is less clear case for inclusion ... although it is a great example of unusual places in the sciences where pi pops up, which is the point of that section. Thoughts? --Noleander (talk) 19:52, 10 April 2012 (UTC)

Unless someone objects, I propose to restore the "meandering river" example to the article because it serves to illustrate the ubiquitous nature of π. --Noleander (talk) 03:18, 11 April 2012 (UTC)

Include rope around equator?

There is a rather famous paradox involving pi: if a rope is wrapped tightly around the equator; then lengthened by 10 meters; then made into a perfect circular shape and lifted above the earth's surface (but still centered on the earth's center): How high is the rope above the earth's surface. Most people expect a small value, like a few millimeters, but the answer is nearly 2 meters. I realize this is rather trivial puzzle, and the article should not be a collection of brain teasers, but I've seen this particular paradox in many, many sources, and it seems like something that would be informative to a lay reader. Thoughts? --Noleander (talk) 16:37, 11 April 2012 (UTC)

I've not heard this particular brain teaser before. If you find it commonly used in discussions of pi, then it might be appropriate to include just for that reason. But what it describes would also be true if the Earth were a giant cube. The rope would rise 10/8 of a meter. So this is not really a pi-related phenomenon. Joseph Lindenberg (talk) 00:25, 12 April 2012 (UTC)

Yeah, I guess you're right. I'll leave it out. I wonder if there is a WP article that holds brain teasers? --Noleander (talk) 00:47, 12 April 2012 (UTC)

String_girdling_Earth Joseph Lindenberg (talk) 01:05, 12 April 2012 (UTC)

Wow, a whole article on it! Thanks for pointing that out. --Noleander (talk) 01:25, 12 April 2012 (UTC)

Glad I could help. Joseph Lindenberg (talk) 01:34, 12 April 2012 (UTC)

Images of mathematicians

The article feels overcrowded with images, especially images of mathematicians. I think that ultimately the images should be thinned, starting with those of mathematicians. The images of mathematicians really don't provide any additional detail that is useful in understanding the article. Although sometimes such images can provide visual cues for some readers, they are probably counterproductive in an article already rich with (mathematical) imagery. Sławomir Biały (talk) 12:15, 18 April 2012 (UTC)

Well, for one I think the huge pi symbol should go again. It has no additional value at that place, IMO. Nageh (talk) 12:21, 18 April 2012 (UTC)

It seems a little more relevant that an image of Euler, but that's just my humble opinion. Also, the mosaic image seems particularly out of place in the continued fraction section (and it might interfere with the display of the equations in that section on some browsers). Sławomir Biały (talk) 12:30, 18 April 2012 (UTC)

Indeed, while the mosaic images is a nice one it just doesn't fit there. But maybe we should first think about how to organize the History and the Approximations sections before we think about images. Nageh (talk) 12:57, 18 April 2012 (UTC)

Regarding the photo of a mosiac of pi: I have no objection to removing that one. It is a nice image, and could probably go in the Popular culture section, but that section already has an image. --Noleander (talk) 13:05, 18 April 2012 (UTC)

Sorry, I just removed an image, without realizing that a discussion was on-going about the images. Regarding the pics of mathematicians: I think they are great. They are colorful, and make the article more inviting to lay readers. This is not just any math article: it is of great popular interest, and has a lot of history intertwined. This article is #433 in WP visitation rank. The German article on pi reached featured art status, and has lots of excellent portraits of persons involved with pi. The FA criteria explicitly asks for illustrations. What I'd recommend is: if the images within a particular section are too numerous (larger than the section text) then the image of a person should be removed in favor non-person image. --Noleander (talk) 12:59, 18 April 2012 (UTC)

That would remove quite a lot of images. Indeed, (colorful) images of important figures can make an article more inviting to the layman, and that is certainly important. Nageh (talk) 13:02, 18 April 2012 (UTC)

Maybe I was not clear: I was not proposing to remove any images, or any images of persons. I was just saying that if there were a small section that could hold only 1 picture, and there was a really informative diagram, and a portrait of a mathematician, then the diagram would probably be better, if we had to pick 1 of the 2. But, now, in the article, I don't see a need to make such a choice. --Noleander (talk) 13:05, 18 April 2012 (UTC)

pi font: curve vs straight

An editor recently added the sentence " In some fonts though, a lower-case π lacks curves and looks very similar to a capital Π. " in to the name section. I'm not sure if it belongs there: it seems rather obscure ... I've removed it temporarily, so we can discuss here and figure out the best way to proceed. I think the editor was motivated (as indicated in edit history comment) by the fact that some of the diagrams in the article use a font for pi that looks straight-line-ish, almost like a capital PI. The editor, correctly, was concerned that readers may get confused by seeing the curvy pi in the text; yet the straight-line pi in some diagrams. One solution would be to fix the diagrams to use a curvier pi font. Another would be to insert a sentence like " In some fonts though, a lower-case π lacks curves and looks very similar to a capital Π. " Another would be to do nothing. Thoughts? --Noleander (talk) 13:12, 18 April 2012 (UTC)

I did realize that we could just fix the 5 places in the article with uncurvy π's and search thoroughly for any others. But it seemed like useful information to provide the reader. They'll encounter this issue in other places even if we do successfully eliminate all instances of it from this one page on this one site on the internet. On the other hand, the only reason it seemed truly necessary to mention it was that the article said capital pi was never used to represent 3.14 and meant something different mathematically. If you remove that and just don't say anything about capital pi, at least the potential for confusion would be eliminated. --Joseph Lindenberg (talk) 02:01, 19 April 2012 (UTC)

I don't think there's much potential for confusion. In most fonts, lower case 'v' looks very similar to capital 'V', but people cope, because it's generally the case that capital and lower case letters are different sizes. Also, the meaning is usually clear enough from the context; I don't think people could interpret π in the diagrams for this article as a product. Jowa fan (talk) 03:27, 19 April 2012 (UTC)

The squaring-the-circle picture is the worst occurence, because there's no surrounding text to compare the height of the π to. I'm really not saying that people will think the π is meant to signify a product there. I'm saying they'll be confused (and therefore unimpressed) that the article seems to not even follow its own statement that you should never use capital Π to represent 3.14. Regarding your example of the letter v, the difference here is that everyone is used to seeing a lower-case v with straight lines. But (at least outside the country of Greece) most non-technical people aren't used to seeing a lower-case π with straight lines. So they're more likely to interpret what they see there as being an upper-case Π. --Joseph Lindenberg (talk) 05:23, 19 April 2012 (UTC)

I gave it a try. Have a look, feel free to revert if you disagree. Nageh (talk) 10:59, 19 April 2012 (UTC)

Looks good to me. --Joseph Lindenberg (talk) 21:09, 19 April 2012 (UTC)

This does seem to be a problem that keeps coming up with people saying that the Greek letter shouldn't have an italic form for instance. In LaTeX \pi is counted as a maths symbol, not a Greek letter. In Unicode they have the same encoding but that doesn't make them the same thing. If somebody has a good reference about this it might be worth putting in to point to when people say we should have the straight leg form because that's what the Greeks used. Dmcq (talk) 11:26, 19 April 2012 (UTC)

Featured article update

A peer review was done by user User:RJH at Wikipedia:Peer review/Pi/archive2. User User:Jakob.scholbach has volunteered to do an additional review, which is great. After that second review is done, the article should be ready to go to FAC. Thanks to all editors that have helped by making improvement to the article, often correcting my infelicitous wording. --Noleander (talk) 14:20, 15 April 2012 (UTC)

I am in the process of doing a quick review, correcting minor wording issues in the process. Feel free to revert any changes if you disagree. Nageh (talk) 14:26, 15 April 2012 (UTC)

I didn't think I should start a new section below this one, so I'm posting this here. Also, sorry for bringing this up a bit late in the process.—After someone reads in the Name section that a capital pi means something different mathematically (a product), they might be confused to see what look like capital pi's in a few places on the page. (Contents list, circle squaring drawing, first line of History section, first line of Usage section) It might help if the Name section also explained that in some fonts, a lower-case pi isn't curvy and thus looks like an upper-case pi. I suspect a lot of less-technical readers aren't aware of that whole issue and wouldn't immediately figure it out. --Joseph Lindenberg (talk) 08:20, 17 April 2012 (UTC)

I took a stab at writing it in. Feel free to revert or modify. --Joseph Lindenberg (talk) 10:43, 17 April 2012 (UTC)

We've had two great editors provide input at the peer review so far. A third editor, User:Jakob.scholbach, has said they will provide more input some time this week. My plan is to resolve the issues raised by the 3rd reviewer; then make one final pass thru the article for prose quality; then take it to FAC; probably in May. --Noleander (talk) 13:15, 18 April 2012 (UTC)

I closed the PR on this article, because I'm starting a new PR on another, unrelated article (an editor can have only one open PR at a time). If anyone wants to submit more comments or reviews, please do so here on the Talk page, or start a new PR. I've notified User:Jakob.scholbach, and I hope they can find some time for a review. --Noleander (talk) 22:57, 20 April 2012 (UTC)

In regards to my comment on the Approximations section in the PR, maybe it would help to rename it to Other approximations or Other approximation methods. That could make it more clear why some of the approximation methods are actually being discussed in the History section. Nageh (talk) 15:18, 21 April 2012 (UTC)

Done: renamed to Other approximations. --Noleander (talk) 18:33, 21 April 2012 (UTC)

Beginning sentences with mathematical symbols

Generally, I think it is better to avoid starting sentences with symbols whenever possible, chiefly since it becomes impossible to capitalize the first letter of a sentence, and interferes with reading in other ways (paragraph breaks, etc.) Many of the sentences in the article, especially those of the lead, do start with the symbol π. It might be worth thinking about how to rephrase these to avoid doing that. Sławomir Biały (talk) 20:12, 23 April 2012 (UTC)

Personally, I don't see it as an issue. Nageh (talk) 20:39, 23 April 2012 (UTC)

I've made some corrections subsequent to my original post to ensure that none of the sentences of the lead (except the first one) start with the symbol. Although our own WP:MOSMATH seems to be silent on this issue, most manuals of style in mathematics and the sciences discourage starting sentences with mathematical symbols. We should probably do the same. Sławomir Biały (talk) 20:55, 23 April 2012 (UTC)

This is indeed a common piece of advice about mathematical writing. One reason is that the first letter of a sentence should be capitalized, but the constant π should be lowercase, which leaves a tension. There are also other issues with math expressions that seem less relevant here, but the capitalization one seems the most important here. Of course using "it" every time makes the prose boring, but there are lots of other ways to start a sentence: "The constant", "This number", etc. — Carl (CBM · talk) 21:07, 23 April 2012 (UTC)

Broken rendering?

Wow, that's weird. This diff shows that a comma was changed to a period. Yet, in the source text there is a still a comma. Anyone else seeing this? Nageh (talk) 18:57, 24 April 2012 (UTC)

Now it works. Strange. Nageh (talk) 19:02, 24 April 2012 (UTC)

Restore tau article discussion

I've initiated a discussion at the Tau Talk page suggesting that the tau article be restored. I also believe that a brief mention of tau in this article is okay. If anyone wants to discuss restoring the tau article, please contribute at the tau Talk page (rather than here) to keep the discussion co-located. --Noleander (talk) 14:01, 28 April 2012 (UTC)

Is an infinite product also an infinite series?

The article says that infinite series are "sums or products of an infinite number of terms". It also, for example, calls the Wallis product an infinite series. I'm not used to that definition of series (infinite or not). I thought a series always meant a sum. --Joseph Lindenberg (talk) 02:10, 28 April 2012 (UTC)

"Infinite series" is a bit fuzzy compared to "infinite sum", but you are right: the wording is probably not the best. Maybe "infinite sequence" would be a good umbrella term for both infinite sums and infinite products. I'll re-word it. --Noleander (talk) 02:24, 28 April 2012 (UTC)

Those words have very specific definitions in mathematics. Someone correct me if I'm wrong, but a sequence is defined as a list of numbers. And a series is defined as the sum of the numbers in a sequence. I never liked that second definition, because in regular life, a series means pretty much the same thing as a sequence. But that's how mathematics defines it. I'd really appreciate someone else chiming in on this though, because my math is pretty rusty in areas not related to tau. --Joseph Lindenberg (talk) 02:38, 28 April 2012 (UTC)

A series is also a sequence; it is the sequence of partial sums. Nageh (talk) 10:43, 28 April 2012 (UTC)

That idea does sound familiar to me, but I don't see it reflected in the definitions at either Wikipedia or Wolfram MathWorld. In fact, at Wolfram, it says, "If the sequence of partial sums converges to a definite value, the series is said to converge. On the other hand, if the sequence of partial sums does not converge to a limit (e.g., it oscillates or approaches +/-infty), the series is said to diverge." That seems to imply that the sequence of partial sums is considered a separate entity from the series. --Joseph Lindenberg (talk) 11:57, 28 April 2012 (UTC)

Same thing at Wikipedia:

Definition

For any sequence $\{a_{n}\}$ of rational numbers, real numbers, complex numbers, functions thereof, etc., the associated series is defined as the ordered formal sum

$\sum _{n=0}^{\infty }a_{n}=a_{0}+a_{1}+a_{2}+\cdots$.

The series of partial sum $\{S_{k}\}$ associated to a sequence $\{a_{n}\}$ is defined for each $k$ as the sum of the sequence $\{a_{n}\}$ from $a_{0}$ to $a_{k}$

$S_{k}=\sum _{n=0}^{k}a_{n}=a_{0}+a_{1}+\cdots +a_{k}$.

--Joseph Lindenberg (talk) 12:05, 28 April 2012 (UTC)

It is still a sequence. Nothing in the text contradicts that. Nageh (talk) 13:42, 28 April 2012 (UTC)

A series is formally a distinct object form its sequence of partial sums. The phrase "series of partial sums" is not standard terminology, the partial sums are a sequence rather than a series. — Carl (CBM · talk) 14:09, 28 April 2012 (UTC)

The issue at series (mathematics) was caused by an IP editor whose edits were not reviewed well enough. I fixed it. — Carl (CBM · talk) 15:32, 28 April 2012 (UTC)

Huh. I hadn't even noticed the fact that it said "series of partial sum" instead of "sequence of partial sum". (This is the kind of problem I was talking about with what the word series means in regular life—a sequence—versus what it means in mathematics.) Good catch, Carl. What I did notice, though, is that "partial sum" is singular both there and the next place it's used in the article. When I see something like that done twice, I suspect it's not just a typo. Is there some reason that it shouldn't say "partial sums"? --Joseph Lindenberg (talk) 21:24, 28 April 2012 (UTC)

Thanks, it was the same IP editor who changed that to singular. — Carl (CBM · talk) 22:04, 28 April 2012 (UTC)

I've re-worded the "Infinite Series" section so this potential confusion is no longer an issue. Of course, editors are free to continue discussing terminology! --Noleander (talk) 14:13, 28 April 2012 (UTC)

I'm really sorry Noleander, but I still don't think these two are correct.

"The first infinite sequence discovered in Europe was an infinite product (rather than an infinite sum"

"The second infinite series found in Europe, by John Wallis in 1655, also was an infinite product."

What do you guys think? Am I being overly picky? It is a mathematics article, though. --Joseph Lindenberg (talk) 21:13, 28 April 2012 (UTC)

A "sequence" is a mapping from the set of natural numbers to an arbitrary codomain (but in the context of conventional analysis, usually the set of real numbers). The codomain in question needs to sustain the "addition" operation, or an operation that can be defined as addition.

Take a sequence. For each element in that sequence, add up all the terms for all the elements in that sequence up to that element. What you get is a "partial sum".

A series is a sequence of partial sums.

If you use the words "sequence" and "series" to mean anything else but the above, you won't be understood and will confuse both yourself and the person you are communicating with.

An infinite product, of course, is like an infinite series, except that instead of adding the terms in the sequence, you multiply them together.

So an infinite product is not the same as an infinite series, and anyone confusing them is most likely confused. --Matt Westwood 21:55, 28 April 2012 (UTC)

I see that you and Nageh agree that a series is a sequence of partial sums, while Carl disagrees. (I also disagree but I don't put any stock in what I remember about the topic.) So could you comment on the correctness or incorrectness of those two sentences I quoted above? --Joseph Lindenberg (talk) 22:13, 28 April 2012 (UTC)

I can't comment on the historical priority claims, but: "The first infinite sequence discovered in Europe was an infinite product" is arguable that it sense because an infinite product can be considered as a sequence of partial products, same as a series can be considered as a sequence of partial sums. "The second infinite series found in Europe, by John Wallis in 1655, also was an infinite product" is illiterate nonsense as a infinite series is not an infinite product. --Matt Westwood 22:38, 28 April 2012 (UTC)

Noleander, it looks like you could use the term infinite expression to mean something that could be either an infinite series (which by definition involves summation, not multiplication) or an infinite product. Take a look at the Wikipedia article on it. --Joseph Lindenberg (talk) 22:46, 28 April 2012 (UTC)

Let's not. That's a formally meaningless term that is not used in mathematics. Sławomir Biały (talk) 01:02, 29 April 2012 (UTC)