This is an archive of past discussions about Pi. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.
I've rearranged the images a bit to try and improve the format. Previously, there was a lot of white space in the text, some text was blocked out by images, and the images at the top of the article looked a bit ugly. I also added some info about the Old Testament.Anythingyouwant (talk) 05:00, 20 May 2010 (UTC)
Old testament
I have reverted the bare claim that the Old Testament claims pi equals 3, but I agree that the issue should be dealt with (surprised it isn't already — should look through the history and see if it's been removed at some point). What it actually says is that some king (I think it was) made a "molten sea" ten cubits across, and thirty cubits did compass it round about, something like that. To get from there to "pi equals three" involves several questionable steps of logic. --Trovatore (talk) 05:05, 20 May 2010 (UTC)
I have heard the following mishna, which I think is worth finding a notable quote of if you can:
The usual word for "length" is קו, which has a Gematria number of 106. However, in this passage, the word is קוה, which has a Gematria number of 111. So this suggests a value of 3 × 111 ÷ 106, which gives the value 3.1415 to four decimal places. (Collin237) —Preceding unsigned comment added by 166.217.168.155 (talk) 14:23, 22 July 2010 (UTC)
Let's consider this: "And it was a handbreadth thick; and the brim thereof was wrought like the brim of a cup, like the flower of a lily: it received and held three thousand baths."(2Ch 4:5) Does it mean that also 2*2 wasn't 4, but something else? Was the volumetric calculation also inprecise or just the vessel wasn't full to the maximum?
Please consider thoughtfully the above reasoning and, if you will, edit to the best possible.
Image at top
I see that there is some disagreement about what image should go at top. I like it this way, with a large Greek letter pi at the top. What do others think? The table looks kind of ugly, and if you go to the link I just gave, you'll see that the table is broken up into two pieces, each located lower down in the article (one is in the section on "Estimating pi" and the other is in the "See also" section).Anythingyouwant (talk) 10:07, 20 May 2010 (UTC)
I moved the infobox back to the top of the article. This is consistent with its placement in other mathematical constant articles, such as Euler–Mascheroni constant and Plastic number. The whole point of an infobox is that it provides easy access to summary information - if it is hidden half-way down an article, that defeats its purpose. As for the giant letter pi image, I thought it was ugly, intrusive and uninformative - we all know what the letter π looks like, so what was the point of a giant 350px image ? I much prefererd the (now removed) rolling circle animation. But let's see what other editors think. Gandalf61 (talk) 10:23, 20 May 2010 (UTC)
Pi to 1120 digits was first obtained using a gear-driven calculator in 1948, by John Wrench and Levi Smith. This was the last, best estimate before electronic computers took over.[FN]
FN: Wrench, John. "The evolution of extended decimal approximations to π", The Mathematics Teacher, volume 53, pages 644–650 (1960).
Pi is a much higher-profile concept, and is studied at a much earlier age, than Euler–Mascheroni constant and Plastic number. I doubt a reader will stay for long if the first thing he sees is a table discussing Hexadecimals, binary forms, Apéry's constant, and the like (none of which are important for understanding pi, and none of which are discussed in this article). There's no table like this at the top of e (mathematical constant). Anyway, we'll see what others think. By the way, to the right is another idea for the top image. I'll try this new idea in the article, and see what you think.Anythingyouwant (talk) 10:27, 20 May 2010 (UTC)
Even worse. I have reverted back to the infobox. Please stop charging around making unilateral changes. Either be patient and wait for other editors to join this discussion and establish consensus, or, if you want to be more proactive, raise the issue at Wikipedia talk:WikiProject Mathematics. Gandalf61 (talk) 12:03, 20 May 2010 (UTC)
I'm kind of surprised that you prefer the infobox at top. Anyway, I'm glad to wait around and see what others think. Note that I did suggest it here at the talk page 45 minutes before editing the article. Are you opposed to including the box at right ANYWHERE in the article? I think it's quite an amazing box, and I did not know that a thousand digits had not been calculated until 1948, and then by non-electronic means. Also, please explain how Hexadecimals, binary forms, Apéry's constant, and the like are important for understanding pi, or are discussed in this article. Thanks.Anythingyouwant (talk) 16:36, 20 May 2010 (UTC)
Here’s a new template, analogous to the one for “e”. If there is no objection, what I would like to do is put the image of the mosaic at the top of the article, immediately followed by the new template. The table currently at the top of the article would be put lower in the article as done here. I also think that the box with pi to a thousand places would be okay in the section on "Estimating π".
{{Π (mathematical constant)}}Anythingyouwant (talk) 20:11, 20 May 2010 (UTC)
I broadly support all of Anythingyouwant's ideas for this page (except the humungous π image, default size is fine as is). The new infobox is far better. The whole page needs a spruce up! Get rid of the cheap gif animation, it's reminiscent of an amateurish AOL page. Also need to improve presentation of the list of formulae (maybe a table of some sort?). Let's make this page interesting. Ropata (talk) 01:26, 21 May 2010 (UTC)
Hey, you New Zealanders aren't all bad after all. :-) I'll wait until tomorrow to see if there is more feedback, before editing the article.Anythingyouwant (talk) 03:37, 21 May 2010 (UTC)
The new infobox looks good to me. And the mosaic image is better than the alternatives. But please don't make it too big - this unbalances the appearance of the article. Gandalf61 (talk) 08:29, 21 May 2010 (UTC)
Not sure what to do about that. Wikipedia renders differently for various browsers and screen sizes. Might need a more experienced editor to come up with something Ropata (talk) 01:42, 29 May 2010 (UTC)
Was there a problem with it in the previous format? If you were just trying to get highlighting, maybe that can be done with the old format. On the other hand, I didn't want to draw too much attention to the "999999" because then we might be obliged to say something about it in the caption.Anythingyouwant (talk) 01:45, 29 May 2010 (UTC)
The old format had too much bold text and the numerous digits took up a lot of space. I wanted to try smaller text. I will make a couple of other changes that I think will help. Ropata (talk) 01:48, 29 May 2010 (UTC)
Pi to 1120 digits was first obtained using a gear-driven calculator in 1948, by John Wrench and Levi Smith. This was the last, best estimate before electronic computers took over.[FN]
FN: Wrench, John. "The evolution of extended decimal approximations to π", The Mathematics Teacher, volume 53, pages 644–650 (1960).
Restorations
As far as the recent restorations, I have no problem with them. I had removed the Euler's identity box because the exact same equation is already to the left. I had removed the last term of a series just in case it might collide (in some browsers) with the box containing the 1120 digits. And, I had removed the Archimedes pic because it seemed to be causing some clutter in my browser. Anyway, re-including those three things is fine with me. Thanks for letting me be bold and mess with the article.Anythingyouwant (talk) 17:52, 30 May 2010 (UTC)
No problem, it's good to try out different things. The image I think is most relevant is Archimedes, since π is also known has Archimedes' number. This article still has a ways to go but it's getting there. Cheers, Ropata (talk) 21:47, 30 May 2010 (UTC)
Minor Correction in the Main Page
Under one of the pictures in the main article we read: 'Squaring the circle was not possible for ancient geometers, because π is a transcendental number.' The text is formally correct, but this is not a correct presentation. It implies that squaring was not possible for the ancient geometers, but probably it is possible for present day geometers(which is wrong). Sqaring IS NOT POSSIBLE, this is a fact, and we should not use Past Tense to denote this fact. Correct presentation would be: Squaring the circle is not possible, because π is a transcendental number. —Preceding unsigned comment added by 79.100.15.225 (talk) 22:38, 7 June 2010 (UTC)
You are correct, although to be completely precise we must add that it is not possible if we restrict ourselves to using a compass and straightedge and a finite number of steps. Anyway, I have changed the caption in the article. Gandalf61 (talk) 08:32, 8 June 2010 (UTC)
It's funny, all of this talk and yet no one answers the most common question: why are there infinite digits? It is because a "segment of a curve" is not 'a line curved'. A segment of the circumference of a circle is a series of infinitely-redirected, infinitely small lines. That's why the digits of 'pi' never stop... —Preceding unsigned comment added by 151.151.16.22 (talk) 20:41, 22 June 2010 (UTC)
It's actually a lot more complicated than that, and your argument can be easily proven fallacious: there are many curves that have a rational arc length between two rational points. The simplest, easiest-to-understand proof is probably the one given by Ivan Niven in 1945; take a look at http://www.mathlesstraveled.com/?p=548 for a good explanation of this proof. --LucasBrown15:25, 21 July 2010 (UTC)
...which of course doesn't have much to do with having infinitely many digits. Every real number's decimal expansion has infinitely many digits. --Trovatore (talk) 18:44, 21 July 2010 (UTC)
No it doesn't. 1 is a real number and has only 1 digit. (unless you are really picky and say that it is extended each side by an infinite number of zeros). Si Trew (talk) 20:09, 21 July 2010 (UTC)
The natural number 1 has only one digit. The real number 1, which is a different thing conceptually, has infinitely many zeroes (or nines, if you prefer) in its decimal representation. Each zero is independent of all the other ones and gives you new information.
The thing to remember about real numbers is that they encode infinitely much information, all in one tidy package. Every real number does that, even the ones where the information is kind of repetitive. --Trovatore (talk) 20:47, 21 July 2010 (UTC)
Physics
Someone ought to mention in the section on physics that the appearance of pi in equations like Einstein's Field Equations really has no physical significance, because the constants (like "G") can simply be redefined to absorb pi. The appearance of pi in those equations is thus more an artifact of history, or simply for convenience, rather than being of any fundamental importance.166.137.137.122 (talk) 16:45, 27 June 2010 (UTC)
Yes it certainly is for convenience and simplicity. Those constants, while scalar, are still defined in relation to the units of measurement (meters,kg,sec or whatever) and absorbing pi would add unnecessary complexity. Showing pi in the equations is a good indicator of rotation or spherical coordinates. Ropata (talk) 10:23, 7 July 2010 (UTC)
May be not. Look at these modifications and revert after...it is not a provocation : this day, on the french-wikpedia, this physics-Pi has been wrenched. I agree with rationalized system S.I. and "spherical-problem" but in same time : and ? I doubt--Guerinsylvie (talk) 20:36, 16 August 2010 (UTC)
In this sentence:
..."the decimal representation of π truncated to 11 decimal places is good enough to estimate the circumference of any circle that fits inside the earth with an error of less than one millimetre"...
"earth" refers to the planet, so it should start with upper case Earth. —Preceding unsigned comment added by Carlos Antonio Gil (talk • contribs) 11:07, 19 July 2010 (UTC)
You're correct. I've made the change - thanks for pointing it out! (I also moved this comment to the bottom of the page, since you'd accidentally put it in the middle of another section.) Olaf Davis (talk) 13:32, 19 July 2010 (UTC)
This article states: "the Greek letter is not capitalized (Π) even at the beginning of a sentence, and instead the lower case (π) is used at the beginning of a sentence." Uh, this is basically saying the same this twice - once should be sufficient. —Preceding unsigned comment added by 192.158.61.141 (talk) 14:33, 23 July 2010 (UTC)
Not necessarily, it could have been that although a capital Pi was not used at the beginning of a sentence, some symbol other than a lower case Pi was used. Martin Hogbin (talk) 12:29, 12 August 2010 (UTC)
New Record
Gizmodo as well as many other sources are reporting that a new record of 5 trillion digits has been calculated. I'm waiting on a change until I read more about the proof but here's a link to a story on Gizmodo. Other sources are cited at the bottom of the article. OlYellerTalktome13:56, 6 August 2010 (UTC)
There is an incorrect "citation needed" next to text stating Pi to 39 digits being accurate enough to calculate a circle in the observable universe to an error of 1 hydrogen atom. The particular text is in question is already cited further up the page.62.49.92.201 (talk) 22:12, 25 September 2010 (UTC)
It would be nice to see the following body of text elaborated on. Pi being irrational is a huge thing. Proofs demonstrating it would be nice links or journal articles. Meta or elaborative would be great reads. And it would also be nice to give the German credit where credit is due.
"π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. It is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics. Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture."70.50.128.228 (talk) 05:01, 8 October 2010 (UTC)
Numerical value in the lead
It would probably be best to remove this sentence from the lead: "It is approximately equal to 3.14159265 in the usual decimal notation." The reason for removing it is because the template to the right already gives an approximate value, and that' s sufficient. The more precise values can properly be found later in the article.
Per WP:ICONDECORATION, icons such as the one in the template should be informative, and indeed that icon is informative in all the listed articles that do not otherwise give an approximate value. In this article, the icon is only useful if we remove the sentence in the lead.166.137.138.215 (talk) 21:10, 9 October 2010 (UTC)
The proper cure for that (if we want it cured at all; it doesn't bother me) would be to do away with the graphics. A decimal approximation is important enough to belong in the lede in any article about a mathematical constant, and we should not hide it from readers who (for whatever reason) cannot see images. –Henning Makholm (talk) 05:48, 10 October 2010 (UTC)
I'm not for removing the graphic, because it's informative in many of the articles where it appears. It's slightly redundant in this article, but still it usefully reiterates the most important aspect of pi. So, doing nothing is okay with me (I only brought up this subject because someone mentioned ICONDECORATION in the template's edit history).166.137.137.17 (talk) 23:10, 11 October 2010 (UTC)
Additional References
Isaac Asimov wrote an essay in "The Magazine of Fantasy & Science Fiction" titled "Piece of Pi" (December 1960 and then republished in a Book titled "Adding a Dimension" {1964}) where he uses the value of pi to 35 places (as calculated by Ludolf van Ceulen in 1615) to state:
"For example, suppose you drew a circle ten billion miles across, with the sun at the center, for the purpose of enclosing the entire solar system, and suppose you wanted to calculate the length of the circumference of this circle (which would come to over thirty-one billion miles) by using 355/113 as the approximate value of π. You would be off by less than three thousand miles.
But suppose you were so precise an individual that you found an error of three thousand miles in 31,000,000,000 to be insupportable. You might then use Ludolf's value of π to thirty-five places. You would then be off by a distance that would be equivalent to a millionth of the diameter of a proton.
Or let's take a big circle, say the circumference of the known universe. Suppose large radio telescopes under construction can receive signals from a distance as great as 40,000,000,000 light-years. A circle about a universe with such a radius would have a length of, roughly, 150,000,000,000,000,000,000,000 (150 sextillion) miles. If the length of this circumference were calculated by Ludolf's value of π to thirty-five places, it would be off by less than a millionth of an inch."
Heh. Very surprised to see this remark about Plouffe's recent (2006) identities:
...for some rational number p where the denominator is a highly factorable number, though no rigorous proof has yet been given.
Bull-hockey. Plouffe asked me to prove this, I did, I thought I'd clean it up, get it ready for publication, and in doing so, found out that the result is "well-known", having been independently rediscovered, and published some 6 or 8 times since the 1920's (including generalizations), and, if you know where to look, even Ramanujan gives the identity in his notebooks. Plouffe is well aware of this, we've corresponded. Here's an online version of the paper: http://arxiv.org/abs/math/0609775 This arxiv paper even reviews some of the times its been re-discovered, and then points at an article that does an in-depth review of these rediscoveries! So there! Hah! Anyway, I'm removing this sentence; I can insert a reference to the above, or any other paper of your choice ... linas (talk) 05:47, 23 November 2010 (UTC)
The concept should definitely be mentioned as well as the article, "Pi is Wrong!" and related discussion that led to the idea of using tau. To that end I have added such examples to the "See Also" section. -- PiPhD (talk) 07:16, 25 December 2010 (UTC)
Shoudln't the first image be of the actual symbol, not a mosaic of it? It would be weird in any other article on a mathematical term. Yaksar (talk) 01:30, 11 December 2010 (UTC)
I like the mosaic at the top. You'll find that a lot of science books have artistic book covers, so being artistic need not be deprecated here.Anythingyouwant (talk) 01:41, 11 December 2010 (UTC)
In my opinion the natural abode of the circle is the plane. Talking about circles in space seems like a superfluous kind of pedantry. Why not talk about a circle in infinite-dimensional Hilbert space for the same price? Tkuvho (talk) 17:45, 27 December 2010 (UTC)
"Euclidean space" could be the Euclidean plane — the dimension is not specified. (For that matter, it could also be the Euclidean line, in which case the phrase under discussion doesn't make sense.)
I don't agree that "Euclidean space" could also be the Euclidean line. Perhaps "a Euclidean space" could also be that. But anyway, since "Euclidean space" refers more to physics than to mathematics, I agree. I will self-undo and remove the bad pipe. DVdm (talk) 22:57, 27 December 2010 (UTC)
"Euclidean space" does not refer more to physics than to mathematics. Euclid did not do physics. And the way the term is generally used today is that Rn is called "n-dimensional Euclidean space". Michael Hardy (talk) 21:14, 30 December 2010 (UTC)
Pi in octal
Recently an octal approximation to π was added to the Number System box that already compares its equivalent in binary, decimal and hex notation. However, 3.111 111 111 111...8 is nothing more than the octal equivalent of 11.001 001 001 001...2 = 3.142 857 142 857...10 = 3.249 249 249 249...16, = 22/7 10. So I have corrected the octal approximation, which is not that difficult once the first sixteen hex digits (3.243 F6A 888 5A3 08D16) are converted to binary (2+60 bits, grouped in fours) and then regrouped in threes (to 1+20 octal digits). — Glenn L (talk) 18:03, 27 December 2010 (UTC)
precise calculations of pi = stunts?
"Reports on the latest, most-precise calculation of π (and related stunts) are common news items"- in whose opinion are these attempts "stunts"?Ninahexan (talk) 06:19, 21 January 2011 (UTC)
I didn't find any mention of the concept "stunt" in the refs. An analysis of possible patterns on the numbers of pi is a dimension of interest for researchers (enough to warrant a wiki page about the Feynman Point), so I don't think stunt would be the correct term. Perhaps a memorisation and recitation of Pi might qualify, but that is not what is discussed.Ninahexan (talk) 02:08, 24 January 2011 (UTC)
The whole parenthetical is vague and ought to be removed. What's a feat related to calculating a lot of pi digits? Calculating which country eats the most pies? Or calculating the average number of calories in a slice of pi pie?Anythingyouwant (talk) 02:55, 24 January 2011 (UTC)
Base-10...
This article discusses pi solely in terms of the base-10 numbering system. Can the end of pi finally be solved by rendering it into base-12, base-8, or any of them? A mathematician (which excludes myself) should attempt this and show results. —ᚹᚩᛞᛖᚾᚻᛖᛚᛗ (ᚷᛖᛋᛈᚱᛖᚳ) 04:59, 24 January 2011 (UTC)
By "the end of pi" do you mean that it might have a terminating expansion in some other integer base? No, that is not possible. This follows just from the fact that pi is an irrational number.
It's not true that the article "discusses pi solely in terms of [decimal]". It is true that the article doesn't spend much if any screen ink on the expansion in other bases, but that's because these are not really particularly more interesting than the expansion in base 10. --Trovatore (talk) 05:12, 24 January 2011 (UTC)
That's not quite right. Base 16 (and other power of 2 bases) have the remarkable property that one can compute a digit position in pi without calculating all the previous digits. As far as I am aware there is no similar formula known for other bases. That is mentioned in the article but could be expanded upon.--agr (talk) 15:49, 24 January 2011 (UTC)
I was aware of that result but don't really consider it a result about the radix expansion per se. I suppose you can if you want. --Trovatore (talk) 18:30, 24 January 2011 (UTC)
While such digit position formulas do exist for power of 2 bases, it does not change the fact that, since pi has been proven to be irrational (and transcendental) in base 10, it is likewise in all other bases. Were that not the case, a continued fraction expansion could be found that terminates. The pattern for simple CF's is known to be both random and non-terminating, and furthermore, the listed generalized CF's, while not definitely not random, are likewise non-terminating. The CF's can be converted to other bases by simply converting the partial numerators and denominators into the target base.
The full sentence was questionable: The limit (better sequence) converges because it converges to pi. (?) Changed it a little bit, but it is still using a wrong or at least oversimplified argument.--LutzL (talk) 10:39, 28 January 2011 (UTC)
"The letter π"
"The name of the Greek letter π" is not "pi", but πι. "Pi" is its Latin name, used in English, where it is traditionally pronounced as /ˈpaɪ/. Could anyone correct the article? (I'm not a native speaker.) — Mikhail Ryazanov (talk) 23:38, 1 February 2011 (UTC)
I've attempted a fix and also edited the section to be a bit more concise. Thank's for pointing out the problem.--agr (talk) 01:03, 2 February 2011 (UTC)
I think that this section should be at the bottom of the article, where already is "in popular culture". That's because right now its before "use in mathematic and science" what makes no sense given that Pi is a mathematical constant —Preceding unsigned comment added by 200.117.26.41 (talk) 01:21, 4 February 2011 (UTC)
Pi in a different universe
I've often seen the assertion that "in a different universe, pi would have a different value". It's nonsense, of course, and this fact is briefly alluded to in the article (in the "Physics" section):
Although not a physical constant, π appears routinely in equations describing fundamental principles of the Universe ...
I would say that pi is not an inherent property of reality, unless you're willing to include abstract mathematic concepts as part of reality. Pi is an abstract idea based (initially) on geometric concepts (independent of any physical reality), and (later) on analytic geometry, complex algebra, etc. That being said, the value of pi does occur in certain physics equations that describe fundamental properties of (our particular) universe. — Loadmaster (talk) 23:28, 17 May 2010 (UTC)
Pi with a different value is not so abstract as to need another universe. The value of pi derives only from the metric used to measure distance. The value of pi referred to in this article is using the only metric most people know, the l² norm (also called Euclidean distance). For example, if you used the l^p norm for a different value of p, you would get a different value of pi. Pi in the l¹ norm is 2*sqrt(2), and pi in the l^infinity norm is 4*sqrt(2). ~~ —Preceding unsigned comment added by 128.2.118.172 (talk) 23:44, 16 March 2011 (UTC)
π in the Greek language (fun facts)
The phrase "ΜΗΚΟΣ ΠΕΡΙΦΕΡΕΙΑΣ ΚΥΚΛΟΥ" means "length of the circle's circuit" has a lexarithm of 2294. The word ΔΙΑΜΕΤΡΟΣ means diameter and has a lexarithm of 730.
For those who do not know what a lexaritm is, it is the pythagorean notion that Greek letters are numbers so that:
Α=1 Β=2 Γ=3 Δ=4 Ε=5 F=6 Ζ=7 Η=8 Θ=9 Ι=10 Κ=20 Λ=30 Μ=40 Ν=50 Ξ=60 Ο=70 Π=80 Q=90 Ρ=100 Σ=200 Τ=300 Υ=400 Φ=500 Χ=600 Ψ=700 Ω=800 S=900
it is the correct way to use in both written and oral Greek (ancient and modern) in other words it sounds natural (instead of artificially designed) 92.236.81.144 (talk) 19:02, 20 March 2011 (UTC)AΚΕΡΣΕΚΩΜΗΣ
Another use in physics
In the Physics section of "Use in mathematics and science", could we add the fact that pi is implicated in the calculation of the period of simple harmonic motion? —Preceding unsigned comment added by 86.183.0.214 (talk) 13:51, 20 March 2011 (UTC)
What the...? The Pi animation was the best part of the page! I've never seen a more eloquent representation of a mathematical concept. It was a Picture of the Day, for Chrissake! C1k3 (talk) 07:54, 22 May 2010 (UTC)
It is an interesting image, but placement was a problem. I moved it down in the article because I didn't think it was good at the top, and then Ropata suggested removing it altogether and I tended to agree, so I did. However, it is very relevant to the Circumference article, so I have added it there.Anythingyouwant (talk) 08:09, 22 May 2010 (UTC)
I assume that you read Ropata's comment above, with which I tend to agree. All the same, it is a Featured Picture, and it is relevant to this article, so I wouldn't necessarily object to putting it back in, but not at the top. For example, the last section of the article says, "Probably because of the simplicity of its definition, the concept of π, and in particular its decimal representation, have become entrenched in popular culture to a degree far greater than almost any other mathematical construct." So, we could put the animated image there to emphasize the "simplicity of its definition." The image of the plate doesn't do anything for me, so we could get rid of it (although plate fans might come out of the woodwork!).Anythingyouwant (talk) 08:52, 22 May 2010 (UTC)
I put it back in at the lead. The image is far more informative and relevant to the subject of this article (which is the mathematical constant) than an image depicting the Greek letter. Sławomir Biały (talk) 18:45, 3 April 2011 (UTC)
I moved it back down, pending consensus to get rid of the mosaic. If this article could only have one image, then maybe the mosaic would not be the best one. But, as a lead image that precedes many other images, I think the mosaic is very good. It's pretty, it shows the simple symbol that first comes to mind, and it eases the reader into the subject without overloading the reader right off the bat. I agree the mosaic is not extremely utilitarian or informative, but those aren't the only criteria for a lead image, or even for an article title (otherwise we might re-name this article "Cad" which is the 3d letter followed by the 1st followed by the 4th).Anythingyouwant (talk) 19:03, 3 April 2011 (UTC)
The image is now buried down in a section where it is much less relevant. There it is used only to illustrate a computer animation. Presented where it was, it illustrates the definition of pi in a way that is immediately understandable to most readers. This is a very important aspect to conveying the relevant information of the article, which is about the mathematical constant, not the Greek letter. Sławomir Biały (talk) 19:40, 3 April 2011 (UTC)
I agree that we should not lead with a picture of a Greek letter in an article that is about mathematics and not about Greek letters. The animation is a much better choice. —David Eppstein (talk) 19:53, 3 April 2011 (UTC)
The first section, on fundamentals, has a subsection about the main ways to define pi; one definition is the area of a circle divided by the square of the radius (that's not illustrated by the animated image). There are three images at the end of that subsection which I think adequately illustrate the definition of pi. However, if other editors would like to move the animated image to the top of that subsection, then I think doing so would be preferable to moving it to the top of the article. Incidentally, the image of the letter pi in the fundamentals section seems redundant.Anythingyouwant (talk) 19:59, 3 April 2011 (UTC)
I love the animation, and it made a great Picture of the Day. I certainly think it should be in this article, but I don't think it should be in the lede -- too visually distracting. I have no strong opinion on what should go there, whether the mosaic or something else. CRGreathouse (t | c) 21:14, 3 April 2011 (UTC)
I'm opposed to the mosaic because it doesn't convey any useful information: it's pure decoration. Besides conveying useful information, the animation is also very easy to understand, and making the information in the lead both pertinent and easy to understand is an important consideration both for WP:MTAA and WP:LEAD guidelines. The image File:Pi_eq_C_over_d.svg currently featured in the "Fundamentals" section could be used to convey similar information as the animation, but it requires giving an equation in the caption, and so it is less likely to be understood by many prospective readers (who may include elementary school children). I am somewhat sympathetic to the criticism that animations are visually distracting. However, that's a matter of taste that I think is trumped in this case by other reasons for keeping this image in the lead. Personally, I don't find it to be one of the more distracting animations that we have. Sławomir Biały (talk) 21:50, 3 April 2011 (UTC)
Do you think the image of the letter pi in the "Fundamentals" section is purely decorative? It seems clear to me that an image of the universal symbol for pi is more than decorative.Anythingyouwant (talk) 21:59, 3 April 2011 (UTC)
In a subsection about the Greek letter, it is obviously more relevant, but there is a main article for that already, unless you are proposing a merger? Sławomir Biały (talk) 22:02, 3 April 2011 (UTC)
No, I'm not proposing any merger. I think it's extremely important for readers to understand that when they see the Greek letter, that is the symbol for the mathematical constant. That was the main rationale for having the mosaic at the top of this article. I agree with CRGreathouse that the animated gif is distracting, but I have tried to offer a compromise whereby the animated gif could go MUCH HIGHER in this article, in the section on "Fundamentals". And as I said, the gif only shows one of a plurality of ways to define pi.Anythingyouwant (talk) 22:13, 3 April 2011 (UTC)
The article is (mostly) about the mathematical constant, not the Greek letter. So the lead should emphasize the mathematical constant, rather than its symbol, if possible. (Proportionality of coverage is at least one consideration of WP:LEAD.) There are several images in the article that do this. But as far as I can see this is the only image that does a very good job of saying what pi is without any words or equations. It defines the subject of the article visually in a way that no amount of text can possibly do. As for the statement that there are many different ways of defining pi, I don't find this argument for removing the animation persuasive for two reasons. First, if there are other images that are equally good for the other definitions, then we can discuss those as well. But I've already said why I don't think the images in the "Fundamentals" section don't have the same expository value. Secondly, by and large the most common definition of pi (at least in elementary geometry) is the ratio of the circumference to the diameter (which is illustrated by the animation). I don't see any problem picking the most common elementary definition of pi and illustrating that one, to the exclusion of the others. Sławomir Biały (talk) 22:27, 3 April 2011 (UTC)
Pi-unrolled does have clear presentational value that overcomes my dislike for animations in general. However, in order to do any good, it has to come very early in the article. It's a better lede image than anything else I've seen proposed. On the other hand, down in a subsection we'd just get the distraction of something-that-moves without reaping any presentation benefit (any reader who makes it to a section deep into the article will already know the information conveyed by the animation). –Henning Makholm (talk) 22:09, 3 April 2011 (UTC)
The animation is a little bit distracting, but I agree with Sławomir Biały that it's a much better choice for the lead than the mosaic. Ben (talk) 01:02, 4 April 2011 (UTC).
Formula for pi computation
In case anyone would want to know, I added information about the new record for computing pi. However, I did not add the formula used, transcribed here, as I am still getting used to Wikitext format. Anyone who has greater experience in Wikitext formatting please consider adding the formula. Thanks, Bulldogedit my talk pageda contribs03:32, 26 March 2011 (UTC)
hi. This is great! Thanks for updating the article. However, I am not sure about the relevant formula. Reading the article on [[1]] it seems they used a variant of the BBP formula. However I am unsure what the one on the BBC news article really mean. Anyhow, you can get help on writing math formulae here: Help:Displaying_a_formula. It's basically Latex.- Subh83 (talk | contribs) 06:54, 26 March 2011 (UTC)
Requested move
The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.
The result of the move request was: insufficient consensus to move. Consistency has never been one of Wikipedia's strong suits. NW(Talk)23:38, 12 April 2011 (UTC)
Pi → π — I thought I would open up a discussion about moving this article from Pi to π. At the moment I'm in favour, for the following reasons:
Considering browser support, the character is now widely available.
The wiki-software now allows us to display the lower-case π as the article title (it used to be an issue that the wiki software would force the upper case version until Template:lowercase title became available).
There doesn't seem to be an issue using non-Latin characters elsewhere on the 'pedia, for example: Göttingen.
Our other π related articles use the symbol without any problems or complaints from readers, see for example:
Oppose "π" is ambiguous, it is a Greek Letter first and foremost. The mathematical concept/number/relation is frequently spelt out as "pi". π and Π are exactly the same according to the way Wikipedia handles first letters in titles, and these are two different mathematical symbols. It also has a numerical value of "80" which is not 3.14... 65.93.12.101 (talk) 01:24, 4 April 2011 (UTC)
Comment As noted in the rationale above, your "first letter in titles" point is false. See Template:lowercase title for details about this. Your ambiguity point is relevant to addressing disambiguation, but π already redirects to Pi and the disambiguation hatnote present addresses the ambiguity. Ben (talk) 03:52, 4 April 2011 (UTC)
Support. π currently redirects to here, so this will cause no new surprises for people expecting the Greek letter. And if there's some evidence that the spelling-out as "pi" is actually frequently used in contexts where mathematics is professionally typeset (school textbooks, etc), I'd like to see a citation for it. —David Eppstein (talk) 01:32, 4 April 2011 (UTC)
Support. Pretty much all the browsers can handle "π" nowadays. It's not like a Chinese character that might turn up as a square if there is no character support. If it needs to be disambiguated, then it should be π (mathematical constant) -- certainly not "Pi". Kauffner (talk) 02:38, 4 April 2011 (UTC)
If it is not possible to put π in the article title, but only π, then there is no particular advantage to the move. If Greek letters do not show up on the most widely used screen reader, that is a disadvantage. Kauffner (talk) 11:24, 6 April 2011 (UTC)
Comment. I agree that it is first and foremost a letter of the Greek alphabet, but I think there are other considerations. I'm pretty undecided on this proposal so far. Michael Hardy (talk) 01:44, 4 April 2011 (UTC)
Oppose. So which word is someone more likely to enter in the Search box, "pi" or "π"? Does your average reader know how to type "π"? Does your average reader know how to pronounce "π"? — Loadmaster (talk) 02:47, 4 April 2011 (UTC)
Comment, that cuts both ways. As long as π redirects to pi, the question of what someone puts in the search box is a non-issue. Flamarande (talk) 20:05, 4 April 2011 (UTC)
Well, yes. What's your point? My goal was to refute a specific argument in favor of pi, not per se to argue for π. --Trovatore (talk) 18:04, 5 April 2011 (UTC)
Comment: the reasons given above explain why going from pi to π is feasible, but doesn't explain why this change is desirable in my opinion. Perhaps the reason is obvious, but I am not seeing it. An explanation of the benefits would be greatly appreciated. Thanks.TStein (talk) 03:32, 4 April 2011 (UTC)
"Pi" is certainly more common overall. But a piece of writing that focuses on math, as this article does, normally uses the Greek letter. The Greek letter is used everywhere in this article and the title should correspond to usage in the text. It would be easy enough to change usage inside the article, but that would be dumbing it down. Kauffner (talk) 05:36, 4 April 2011 (UTC)
Equivocation: Where does "π" come in an (English) alphabetised list? My first reservation is that I don't have π on my English keyboard, though I can (demonstrably) find a cut/paste version with the help of WP. My second reservation is that if I go to en.wikipedia.org/wiki/π, it is currently transmuted to en.wikipedia.org/wiki/Π, which is quite different, mathematically speaking. But that automatic capitalisation could change. On the other hand, the use of π would certainly seem to be in line with expanding internet naming conventions (no longer insisting on the Roman alphabet), and it hardly matters so long as π, pi,"pie", paɪ, & "3.1415926535" (whatever) all redirect to the same place. Memethuzla (talk) 06:30, 4 April 2011 (UTC)
{{lowercase title}} should work to make the title appear correctly. And my keyboard does have π on it (option-p on the Mac keyboards), but that's largely irrelevant: I think the only real effect of this proposal would be to change what is displayed as the title of the article (and to change its default url, but the other url will still work). —David Eppstein (talk) 07:06, 4 April 2011 (UTC)
It is not irrelevant: "titles are expected to use names and terms that readers are most likely to look for in order to find the article"(WP:AT). Are most people without access to a "π" on their keyboard going to put that into their search engine? Also the name effects the ordering in Google searches. At the moment the article under "Pi" is returned first for both searches on "Pi" and "π". Looking at the return for "π" Wiktionary is listed on the first page ("http://en.wiktionary.org/wiki/%CF%80"--also notice the HTML string does not contain a human readable rendition of "π"), but is not listed in the first page for "pi". Redirects do not seem to count when Google searches are compiled, instead it looks at the name of the article and whether the name appears in the text of the article. -- PBS (talk) 09:36, 4 April 2011 (UTC)
Weak oppose. I can't see anything blatantly wrong with either title, so I'd just leave it alone per WP:TITLECHANGES, second paragraph, second sentence. FWIW, I've opened four articles at random from Special:WhatLinksHere/Pi, and the link caption was “pi” in two of them and “π” in the other two. --― A. di M.plédréachtaí10:06, 4 April 2011 (UTC)
Also, having the symbol appear in title case would address the concern expressed by User:Anythingyouwant in an earlier thread that the lead insufficiently emphasizes the symbol π. (In the past there was even talk of replacing the lead image by an image of the character, a change that I see as counterproductive.) 11:45, 4 April 2011 (UTC)— Preceding unsigned comment added by Slawekb (talk • contribs)
Oppose. In my view, pi is the name of the concept; π is the symbol conventionally used to denote it in formulae. The distinction is blurred by the fact that π is the Greek letter pi, and that this is in fact the etymology of the name. Nonetheless I do not consider π a name. It is merely a conventional symbol. We might just as well move Celcius to °C, since the latter usage is far more common. Hesperian10:42, 4 April 2011 (UTC)
The difference is that, even in discussions about the concept, pi is almost never written out, whereas Celcius in often written out in discussions of the temperature scale. Sławomir Biały (talk) 11:47, 4 April 2011 (UTC)
What is the different between name and symbol? They are both just a denotation for a concept. And in fact pi is just a way to spell out the pronunciation of π.--Netheril96 (talk) 12:26, 4 April 2011 (UTC)
Support as the strongest statement of disagreement to Hesperian's reasoning. The name is neither "pi" nor "Pi" but "π", and as such it's reasonable to have an article about it at that location. It's worth mentioning that when talking about the Greek letter (rather than simply using it) it is also typically written out as "pi". CRGreathouse (t | c) 15:20, 4 April 2011 (UTC)
I think within mathematics you are correct that π is the only name of the constant; but see Pi day, and try search for news articles about Pi day.. it appears that "Pi" or "pi" is becoming a common English name of the constant. Mlm42 (talk) 17:40, 8 April 2011 (UTC)
Accessible? Given the importance of this article, are there any accessibility issues here? How well do common screen readers work with a Greek letter? Remember people with disabilities may not have the most up-to-date equipment. --agr (talk) 15:36, 4 April 2011 (UTC)
Pi will still redirect to π. And if accessibility is that important, π's in the whole article should be replaced by pi. --Netheril96 (talk) 15:50, 4 April 2011 (UTC)
Good question. Symbols like "π" can create acessibility issues, especially with screen readers. However, we cannot know the result in a screen reader without testing each character. Thus, it is best to ask user:Graham87 for input on this issue. Either the symbol "π" will have a textual transcription like "Pi" given by the screen reader JAWS, and then it's OK. Either it will be read as a question mark, and then it would be better to keep the title "Pi".
Aside from the question about accessibility, this decision to rename the title will have a huge (huge) impact on search engines. Users type "Pi" into Google, not "π". Google will ussume the page is about "π" and not "Pi". Thus, the ranking of the page in Google will significantly decrease. Dodoïste (talk) 22:24, 4 April 2011 (UTC)
The first google books hit with π in title is "Metal π-complexes: Complexes with mono-olefinic ligands". There's not a single hit about the number on the 1st page when I search for that, but I do get Euclid's Elements, but only because it contains a fair bunch of Greek script (in the preview snippet). If I type "number π" in google books I get more meaningful results. So, I'm not sure this move is a wise idea without making context clear as in π (number), which I would support. Besides we have an over-representation of WT:WPM in the votes above; there was a recent post there about this. Tijfo098 (talk) 18:30, 4 April 2011 (UTC)
That would work as well; plenty of valid gbooks hits for "mathematical constant π", although "number π" wins by an order magnitude, probably due to brevity. Tijfo098 (talk) 20:33, 4 April 2011 (UTC)
It was also on the physics page and what is important is not who says what or even how many say what but the arguments they make. TStein (talk) 20:43, 4 April 2011 (UTC)
Oppose. Sorry, but the average reader doesn't know how to type "π". I don't know how to type it. IMHO it's a matter of common keyboards, which AFAIK simply don't a π-key. Flamarande (talk) 20:05, 4 April 2011 (UTC)
comment I checked other similar titles. All the Greek letters are spelled out unlike the Latin letters. A few of the Greek letters such as delta (letter) are qualified with (letter). The pi (disambiguation) page doesn't seem to contain any show stoppers for changing it. Somewhat surprisingly to me the primary page for numbers such as 2 (number) wasn't spelled out. It surprises me since numbers are spelled out if they start a sentence. I expected something similar for symbols like Greek letters. (On a completely unrelated note why does 2 represent 2 CE or 2 AD and not 2 (number)?) TStein (talk) 20:43, 4 April 2011 (UTC)
Hysterical raisins; namely, consistency with 2004 being about the year, 2003 being about the year, ..., 3 being about the year, etc.: in the olden days it was common to link to as many years as possible, so it would have been impractical to call them year 2, year 3, ..., year 2008, and so on. ― A. di M.plédréachtaí22:07, 4 April 2011 (UTC)
Oppose - so this a requested move to move an article to become a redirect back to that article? Obviously no-one's going to type the Greek letter. What a curious discussion. Most of my education and professional life has referred to this as "pi" because 99.9% of the known universe doesn't know Greek but does know about circles. The Rambling Man (talk) 21:17, 4 April 2011 (UTC)
Oppose - This article should teach readers about the Greek symbol, not presume that they already know about it. Moreover, suppose we re-name this article and then someone comes to this article via a WikiLinked Greek letter; later that person may want to come back to this article, but cannot type the Greek letter, and does not realize that they could type "pi" instead to get here by redirect. In sum, let's keep the present title, and discuss something more useful.Anythingyouwant (talk) 22:16, 4 April 2011 (UTC)
Weak oppose - I don't really care whether the article title is Pi or π... but since it is already here, just leave it be. Blueboar (talk) 22:54, 4 April 2011 (UTC)
Comment What's your point? The symbol π is used overwhelmingly in mathematical writing in English. There is no English-vs-Greek question here; everything is English. --Trovatore (talk) 22:59, 4 April 2011 (UTC)
Oppose - the symbol "π" is read out as "p" with JAWS by default. This is not a major problem in the article text, where a screen reader user could quickly figure out what the article is saying by using contextual clues. However it is a big deal in the title, since screen reader users often rely on the page title for navigation purposes (especially when navigating by tabs in a browser or between different applications). Also, I don't believe that popular pages should be moved without a very good reason, and I don't find the arguments above to be compelling. Graham8700:32, 5 April 2011 (UTC)
Weak oppose I just don't like π for the mathematical constant and that's what it would look like in the title, never mind the problems with it showing up as Π sometimes with the way Wikipedia's software works. I'd like it to show as π and we wouldn't get that. Pi is a common name and a reasonable title. Dmcq (talk) 09:46, 5 April 2011 (UTC)
Strongest possible oppose - Changing from a title that is easily recognisable by any screen reader to one that is not accurately spoken by one of the commonest (JAWS) does a severe disservice to the visually-impaired. Any possible gain from such a move would be insignificant in comparison to this major disadvantage. --RexxS (talk) 13:07, 5 April 2011 (UTC)
Oppose The arguments for a move are at the "it might be a little nicer" level, and the accessibility problems, confirmed by an experienced editor who relies on a screen reader, should trump all but the most compelling reasons to make a change.--agr (talk) 22:54, 5 April 2011 (UTC)
Oppose There is no real gain, either for users seeking the topic or reading it (as long as 'π' redirects to 'pi'). There's no gain also in using this specific letter, as Wikipedia does not distingush Π from π – both links point at the same page. Also the 'consistency' argument about the article title and contents seems not significant to me – the reader easily identifies 'pi' with 'π'. And the strongest reason against move: it will cause lots of unnecessary work either with correcting links in about half thousand articles linking to Pi or with traversing redirects (and I suppose the Pi article is one of the most often read in Wikipedia...) --CiaPan (talk) 06:18, 6 April 2011 (UTC)
Reluctant oppose. In an ideal world (in which, of course, no one would be blind, and in addition everyone could fly) I would like to see the article at π, because it is essentially never called "pi" in mathematics. Also I think the arguments about what people are going to put in the search box are terribly weak (there might be a tiny bit of merit in the one about how people are going to get back to the page, but we don't worry much about that for other articles). But yeah, if it doesn't work with the most used screen reader, that's a problem. --Trovatore (talk) 07:18, 6 April 2011 (UTC)
Oppose the redirect issue is a red herring, because local consensus at any redirect page can retarget that page and π should probably be about the Greek character, not the math symbol. SchmuckyTheCat (talk)
Comment Retargeting is a red herring — there is no way pi (or π) would ever be targeted anywhere other than the article about the real number. The real number is more notable than the Greek letter. --Trovatore (talk) 17:22, 6 April 2011 (UTC)
Oppose. The name of the constant is "pi" -- "π" is its symbol. There's a difference. We should name articles for the name of the thing in question, not for its symbol. Nobody would propose moving square root over the redirect at √, would they? –Henning Makholm (talk) 18:07, 6 April 2011 (UTC)
Well, that assumes that there's a word pi that refers to the number. The way I see it, π is the name of the number; pi is the name of the name. As the White Knight explained, the name of the song is called "Haddocks' Eyes". --Trovatore (talk) 21:27, 6 April 2011 (UTC)
Comment: π is a Greek letter which technically doesn't exist in the Latin alphabet. Pi is its English translation. Flamarande (talk) 21:41, 6 April 2011 (UTC)
Well, I think it turns out to be also a name of the number that the letter denotes: “pi is irrational” seems way less weird than “cee is the maximum speed at which causal effects can be propagated” to me. (It might be that it's just because there are systems where you can write “pi” but not “π” but there obviously can be no system where you can write “cee” but not “c”, though.) Not that I think such subtleties matter that much... ― A. di M.plédréachtaí23:41, 6 April 2011 (UTC)
On further thought, I think that another reason for my different perceptions of weirdness is that c does have a name other than the symbol in widespread usage in English (namely “speed of light”), whereas π doesn't. (Things like “area of the unit circle” or “Archimedes' constants” are attested but are orders of magnitude rarer than “π” or “pi”.) ― A. di M.plédréachtaí23:49, 6 April 2011 (UTC)
Strong oppose "Pi" is the name of the constant, whereas "π" is the symbol we use to represent that constant in mathematical formulas. For example, this is the reason we have the article about Planck's constant at Planck constant, and not "h". Bcperson89 (talk) 00:03, 7 April 2011 (UTC)
Not parallel. h means all sorts of other things. The default meaning of π is the real number, overwhelmingly so. Sure, it can be used for other things (e.g. it's the usual letter chosen for a projection map), but if you see the letter without other contextual clues (even whether or not you expect the writing to be about math), the smart money is overwhelmingly that it means the number. --Trovatore (talk) 00:06, 7 April 2011 (UTC)
On the other hand € doesn't redirect to euro even though it never means anything else. (Not sure of whether that's the best thing, but anyway my point is that such matters should be decided pragmatically on a case-by-case basis, not because WP:OTHERSTUFFEXISTS. ― A. di M.plédréachtaí00:39, 7 April 2011 (UTC)
oppose There should be an article about the letter at π and the name should redirect to that. Then there should be a disambiguation sentence at the top saying. "This article is about the letter. For the constant see π (circle constant)" or some such. Of course, we lack the article about the letter for the time being. -- ke4roh (talk) 01:08, 7 April 2011 (UTC)
Hmm? No we don't. It's at pi (letter). I just made a redirect to it from π (letter). This is the appropriate priority; clearly the real number is the primary topic. (I think it's the only case, among the Greek letters, where the letter is not the appropriate primary topic — a slightly regrettable inconsistency, maybe, but any other result would just be totally unreasonable.) --Trovatore (talk) 01:40, 7 April 2011 (UTC)
Obviously I am having trouble reading today. I'll go back to sitting quietly on the sidelines for now. -- ke4roh (talk)
Oppose. As a mathematician, my first impression was that the title of this article was wrong, because I would have guessed that the primary topic for the title "Pi" is the Greek letter, not the mathematical constant. But after doing a few google searches (for example all the news articles relating to Pi day), it surprised me to learn that "Pi" may also be a common English name for the constant. Granted the reason for this could be because so many people in the media don't know how to render the letter π in their articles; but the underlying reasons aside, the conclusion is that "Pi" may be a common name of the constant. Although I think within mathematics, π is actually the name of the constant (and not "just a symbol", as some editors suggest), perhaps in common English usage it isn't so clear cut. So unless it can be shown that "π" is the unique common English name of the constant, then there's no reason to move the page (per WP:TITLECHANGES). Mlm42 (talk) 17:30, 8 April 2011 (UTC)
Oppose: Where a usable equivalent in the English 26-letter alphabet exists, I think Wikipedia should use it. How it should look in a nice printed encyclopaedia (and how it should be alphabetized, — sorry, αβized — there), is a different question because looking and finding articles in printed works is different from seeking them on line. For that reason, I'm against using umlauted German letters and the es-zett in article titles, when they can almost always be equally well represented by ae, oe, ue and ss or sz (Goering, Strauss, Grosz, etc.) And while I've learned and memorized many of the 256 ASCII characters that my Window keyboard can call up by depressing the Alt key while typing in four digits (e.g. Alt+0233 for é), I have no easy way of typing in the character for Π or π. I also agree with the intuitive arguments here: "pi" is what people will look for, not "π". In addition, the sanserif versions Π and π that appear on my computer by default don't instantly identify themselves as the Greek letter; at first glance the lower case pi looked like TT in small capitals. (This may be one reason that the math template π uses Times Roman instead, as discussed in the discussion topic below; the example templates use Georgia as in Π and π.) —— Shakescene (talk) 05:18, 11 April 2011 (UTC) — ¶ P.S. See also how Wikipedia treats Aleph-nought, Gamma globulin, Phi Beta Kappa and Sigma Chi. If we phoneticize Greek letters (following common North American practice; cf. "The Sweetheart of Sigma Chi") in one context, readers might expect that to be our customary practice, and not expect to switch gears or alphabets. And if en.Wikipedia starts using non-Latin characters for "Pi" when a commonly-used and -understood phoneticization is available, then why not also for the Hebrew or Arabic alphabets, which are far harder for most English-speaking people to recognize and retrieve on ordinary keyboards? Besides, one can treat Pi at this point (especially the irrational mathematical constant which can't be expressed with our ten numerals) as a word which has anglicised, together with an English phoneticisation, just as so many others have, e.g. as in the Mississippi Delta. —— Shakescene (talk) 06:21, 11 April 2011 (UTC)
The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.
SC*
WHAT does SC mean?
It says pi may be an SC number ... but what is that there is no link or anything saying what an SC number is please I wondered.
It is usual to try and make what you write understandable rather than place an unnecessary burden on people reading. How are we to know what 'SC' refers to or what 'it' refers to or what the 'TY' on a line on its own is for. Also it is usual to set up a new section when starting on another topic. Please see WP:TALK. Dmcq (talk) 12:20, 15 April 2011 (UTC)
Thanks I've found that in the computation section now. I was going to stick in a link and I just noticed it has a '*' after as in SC* in the text. Is this something slightly different do you know thanks. I failed to find it before because I looked with a spaces round first and then on my second search without them just missed it as it was far down. Dmcq (talk) 19:24, 15 April 2011 (UTC)
The two symbols
Can someone please explain to me why there is this insistence on using π instead of just π? I see that they look (slightly) different; I don't see that either looks particularly better. Putting templates in section headings is an especially bad idea, because section edits then produce broken links in the edit summary. --Trovatore (talk) 18:56, 7 April 2011 (UTC)
I wasn't saying it was changed recently necessarily. I probably just recently noticed it. But I think it's kind of suboptimal. Do we really need this complication, that as far as I can tell produces a symbol just as strange-looking as if we left it out? --Trovatore (talk) 04:48, 8 April 2011 (UTC)
The title of the main article shouldn't be the section headings anyway; I rewrote them. "π" corresponds to the way the symbol is represented in the formulas. Isn't it obviously better to have a consistent representation throughout the article? Kauffner (talk) 06:57, 8 April 2011 (UTC)
The only effect that {{math|π}} has in this case is to display the same symbol (π) in a font called "Times New Roman" at 120% of the default size. Whether or not that corresponds to the way the symbol is represented in the formulas depends on what the viewer is using as a user agent (browser), the fonts installed locally, and how the user agent interacts with those fonts. It looks slightly different on my phone from on my PC, for example. I could only guess at how it looks using Safari on a Mac. Consistency is often a moving target when trying to cater for all our viewers. --RexxS (talk) 16:27, 8 April 2011 (UTC)
That's not an entirely correct description. What {{math}} does is put the content inside a HTML <span> with the same CSS class as is used for <math> formulas. What the default CSS skin does in response to this is to choose Times New Roman. However, users can (and some do) change their CSS to react in different ways. Someone might choose explicitly to edit their style sheet such that "texhtml" uses a different font, such as one where the Greek letters are designed to work better as mathematical symbols, and/or change the non-texhtml font to one where the Greek letters are designed to work together to form words in Greek, which would not work as well in mathematics. Using {{math}} allows such users to get the font variant they want for math, rather than the one they want for Greek text. This is the official, supported, way to achieve consistency here. Its purpose is precisely to track the "moving target" automatically. –Henning Makholm (talk) 15:15, 9 April 2011 (UTC)
Thanks for correcting my over-simplification. However, I ought to point out that it's actually what the user agent does in response to the "texhtml" class that decides how it is rendered. No amount of changing a CSS will persuade Lynx, for example, to display anything other than the the letter 'p' in response to {{math|π}}, or JAWS to speak anything other than 'p'. It's easy to fall for the illusion that what we see is how an article is rendered for the rest of the world. --RexxS (talk) 18:42, 9 April 2011 (UTC)
Are you sure? I'm using Lynx v 1.180 ("out-of-the-box") and this is how the article looks. You'll see that 'π' is rendered as 'p', but the kludged list separators actually display as 'π'. --RexxS (talk) 13:06, 13 April 2011 (UTC)
That pi looking character in Lynx isn't pi but a top right corner character with a single bar at the top and two bars at the side used for line drawing. Dmcq (talk) 14:32, 13 April 2011 (UTC)
Errm, it's not as old as I am. It's on an old box running Win2K that I use for testing old stuff, so maybe it dates back to sometime around 2002. I'm pleased that a new, improved version is available, so I'll concede that I was too harsh on Henning, although I stand by my point about it being the user agent that determines how stuff is rendered. --RexxS (talk) 18:57, 19 April 2011 (UTC)
π is how it is normally represented in mathematics. Just bring up Google images and look for 'pi'. I would say that is the maths symbol for the constant, it isn't a Greek letter any more that the set of reals is denoted by the letter R. Dmcq (talk) 19:30, 8 April 2011 (UTC)
Well, the analogy isn't that good. π is just the glyph for π in the serif font used for mathematical symbols, but ℝ is a different character altogether than R. ― A. di M.plédréachtaí13:08, 11 April 2011 (UTC)
What does Unicode have to do with this? “Blackboard bold” ℝ has been used to denote the set of real numbers since before Unicode even exists, and it's also used in handwriting (guess where the name blackboard bold comes from). ― A. di M.plédréachtaí17:01, 11 April 2011 (UTC)
You talked about 'the glyph in serif', what has that got to do with mathematics? Why do you think 'blackboard bold' is important in one case but do not think 'serif' is important in another? The only reason I can see is that Unicode has assigned a different code in one case but not the other.Dmcq (talk) 17:10, 11 April 2011 (UTC)
I agree that that π looks much better than π, and I think π should be used throughout the article, if possible. The default version looks odd, to the point where I have to keep reminding myself that this is the same as π. Blackboard bold is a non-default font, and it is preferred in some cases; in the same way π uses a non-default font and should be preferred in this case. Mlm42 (talk) 17:52, 11 April 2011 (UTC)
Usually, mathematical formulas in print are entirely in serif fonts, so they don't use a ‘special’ glyph for π for the constant. They use the same glyph they'd use if they needed the same Greek letter for any other purpose (e.g. to denote pions or the prime-counting function). By comparison, ℝ is normally used only for the set of reals, and not to denote e.g. resistivity. ― A. di M.plédréachtaí18:15, 11 April 2011 (UTC)
I'm not sure I understand this comment. For example, throughout the article Pion, they use the character π, except for a few formulas. On the other hand, in this article we should always be using π (even in the text).. fortunately that seems to be the case at the moment. Mlm42 (talk) 01:24, 13 April 2011 (UTC)
It's a pity no one knew about this during the vote, but I have figured how to put a serif π in an article title, as you can see here. Kauffner (talk) 11:05, 16 April 2011 (UTC)
I'm not sure knowing that would have made much difference to the outcome. I think the principle reason the move was opposed was because a screen reader pronounced the symbol π as 'p' instead of 'pi'. Ben (talk) 13:44, 16 April 2011 (UTC)
They must be a bit confused, I wonder how many think it is actually called p now :) The reader should be fixed. Dmcq (talk) 14:56, 16 April 2011 (UTC)
Perhaps if {{pi}} were replaced with <math alt="pi">\pi</math>... (Not entirely sure it would work. Someone with a screen reader should try that.) ― A. di M.plédréachtaí18:29, 16 April 2011 (UTC)
The code <math alt="pi">\pi</math> produces which turns into <span class="texhtml">π</span>. As you can see, alt is an acceptable attribute for the img tag, but is ignored elsewhere. However <math title="pi">\pi</math> which produces does insert a title attribute into the span, but sadly screen readers don't substitute the title for the text, so that's no help either. Using the abbr tag (with a title attribute) would work for a screen reader, but folks object to how their browsers display that. We've been round this discussion numerous times when trying to find universally accessible versions of symbols like †, and in the end settled for an image plus alt text every time. --RexxS (talk) 18:50, 19 April 2011 (UTC)
If the article title was π (mathematical constant), it would be consistent with e (mathematical constant) and the people with screen readers and old browsers would be able to figure out what it meant from context. Math formula won't display in the article title, but if <math alt="pi">\pi</math> is the first character of the main text, that could be another context clue. Kauffner (talk) 01:55, 17 April 2011 (UTC)
I have to say that I think messing around with the font is a really bad hack. A lot of people seem to think that one way looks better than the other, but on my screen they look equally bad, just different. Fonts are supposed to be disjoint from content; you don't change them based on the meaning of what you're representing. --Trovatore (talk) 22:06, 17 April 2011 (UTC)
No I don't. A hack is an inelegant and non-robust programming technique; that's the standard meaning, I believe. {{math}} fits that definition. --Trovatore (talk) 23:27, 17 April 2011 (UTC)
On my system, in isolation both π and π look decent, though the latter looks better; but the former harmonises better with the surrounding sans-serif text. The clash is particularly bad between "straight" quotation marks ("π", "π", the latter reminds me of the anonymous letters you'd see in old films made as a collage of characters each cut off from a different newspaper). But I don't actually give a damn as to which is used, so long that all the ones used in-line in a paragraph use the same format, and all the one used indented in their own line use the same format. (OK, they can look quite different, but they are definitely not as different as a and a are on most systems.) ― A. di M.plédréachtaí00:41, 18 April 2011 (UTC)
Has someone been changing LaTeX to wiki HTML templates, or vice versa, for no good reason? Both methods produce a serif font pi and are therefore "hacks" by the definition given above. I was confused for a while too, but now I think it is unlikely that the real problem with my edits has to do with fonts or LaTeX. Kauffner (talk) 11:37, 18 April 2011 (UTC)
"π" vs. "pi" in running text
I suggest we use "pi" for running text and "π" only for equations and explanations of equations. This is the standard treatment for math symbols in general. Even universally understood symbols like "1" and "2" are spelled out in published text oriented toward the general reader. "π" certainly looks cool, but "pi" remains common usage and by an overwhelming margin. On Google books, pi irrational gets vastly more hits than π irrational. "Pi" is the usage of CNN, BBC, the New York Times, Merriam-Webster, and Oxford. The "pi" entry in Britannica is a good model. They clearly have no policy or technical issue that prevents them from publishing a "π", yet they use it only for equations. Van Nostrand's Scientific Encyclopedia does the same (p. 4105 -- sorry no link). If the symbol "π" represented established specialist use, one would certainly expect Van Nostrand's to use it that way. Math journals can go either way. Check here and here for journal articles with "pi" in their titles. One of the few places I found the π symbol used the way it is here, as if it was an established English-language word, is Petr Beckmann's book. Beckmann was a wonderful crank and even set up his own publishing company because no existing publisher would put the π symbol in the title of a book. Kauffner (talk) 13:37, 20 April 2011 (UTC)
Usage in 'text oriented towards the general reader' is very different to mathematical usage, and print and online sources are not necessarily a good guide as if only a few years old they might pre-date our ability to easily add and display π. At MOS:#Numbers as figures or words it says
Show precise mathematical quantities, measurements, stock prices, etc., as figures
and at WP:ORDINAL it gives a more explicit example.
Numbers in mathematical formulae are never spelled out (3 < π < 22/7, notthree < π < 22 sevenths).
Another minor point to make is that π does not capitalize well (or at all) when used as the first word in sentences. This is a (small) reason to prefer "pi" (and "Pi") in the normal non-mathematical text of the article. — Loadmaster (talk) 16:58, 20 April 2011 (UTC)
Neither one of those journal articles uses "pi" in running text, and we shouldn't either. That suggestion is just awful. I don't think the "Encyclopedia Britannica Online" is the same thing as the real Encyclopedia Britannica (the one we are trying to beat) and it would surprise me if the real one spelled out "pi" like that. If they do, then that's just yet another way in which they are inferior to us. This article is about a mathematical topic and it should follow the conventions of reliable sources on mathematical topics, i.e. math books. If CNN and Merriam-Webster do something different, it's because they're not math sources. 69.111.194.167 (talk) 10:36, 21 April 2011 (UTC)
What "math sources" are you talking about? The Borweins are pacesetters in this field and they put "pi" in the running text.[2]Kauffner (talk) 13:01, 21 April 2011 (UTC)
But then later on that very page you link to they use the symbol in the running text (I'll let you search for it). They don't seem very consistent, these pacesetters of "this field"...btw, is "this field" referring to mathematics? Because that's probably what people are talking about when they say "math sources", i.e. sources in mathematics. If you are saying that "this field" is the very very very small sub-sub-sub-area of mathematics involving approximating π quickly, then I presume whatever conventions or standards exist (if any do in such a tiny sample) should not dictate what happens in all the math articles on Wikipedia that use π....that would be ludicrous, wouldn't it? It'd be like if most gossip column writers decided it was standard to refer to Donald Trump as "The Donald" and now you demand that all mentions of "Donald Trump" in print be replaced by "The Donald" because that's what the majority of the people that spend the most time writing about Donald Trump insist on. --68.199.79.35 (talk) 03:41, 22 April 2011 (UTC) (another anon)
My rationale for favoring the use of "pi" in running text is given in the first post in this section, which you might consider reading. No, it is not because I am star-struck with the Boweins. Kauffner (talk) 15:01, 22 April 2011 (UTC)
I have no problem with math symbols in running text, but it's generally frowned upon to use them to start a sentence, which we currently have done several times in the lead. Can we at least rearrange those to start the sentences with regular capitalized words? Dicklyon (talk) 00:06, 25 April 2011 (UTC)
General questions
Just a question, I'm not an experienced mathematician or a specialist, but my calculator claims that 1686629713/536870912 is pie. I used a TI84 Silver Edition calculator and 30 decimals of pie. Is the calculator rounding or will this work? — Preceding unsigned comment added by Seiji34 (talk • contribs) 00:04, 26 April 2011 (UTC)
It's rounding. π is an irrational number. This means it is not equal to any fraction with integers. Your fraction only gives 9 right decimals. 1686629713/536870912 = 3.1415926534682512... π = 3.1415926535897932... It's a relatively poor approximation for such large numbers. Your denominator is 536870912 = 229. 1068966896/340262731 is the best approximation with smaller numbers. It gives 17 right decimals. See others at [3]. Maybe 312689/99532 will also round to π on your calculator. PrimeHunter (talk) 00:40, 26 April 2011 (UTC)
Criticism of pi?
Why do we have a section on "Criticism of pi"? The section seems to criticize the notation, not the constant itself, whose "criticism" I find fairly meaningless.
158.130.13.28 (talk) —Preceding undated comment added 00:20, 18 May 2011 (UTC).
Lead sentence and lead pics
The lead sentence says: "π (sometimes written pi) is a mathematical constant whose value is the ratio of any Euclidean plane circle's circumference to its diameter...."
This strikes me as wordy and redundant. According to our article for circle, "A circle is a simple shape of Euclidean geometry consisting of the set of points in a plane...." So, it's already inherent in the definition of a circle that it's in a Euclidean plane. Saying a "Euclidean plane circle" in the lead sentence of the present article is redundant, and we should instead just say "circle".
I've also moved the animated gif down a little bit in the article, and put two still pics at the top. The still pics illustrate area, which the animated gif does not (the aesthetics seem better as well).Anythingyouwant (talk) 09:37, 11 May 2011 (UTC)
I wasn't aware of that definition of circle and suspect that many readers aren't either, so I can see no harm in specifying that we're talking about the Euclidean plane anyway. ― A. di M.plédréachtaí10:57, 11 May 2011 (UTC)
Can we specify that later on in the article, instead of putting it in the lead sentence? The lead sentence should be as simple and straightforward as possible. The section on "Geometric definition" specifies Euclidean geometry.Anythingyouwant (talk) 11:00, 11 May 2011 (UTC)
Agree with Anythingyouwant, the lead does not need to contain a precise definition, it does however need to be approachable and sticking in Euclidean is harmful that way. Dmcq (talk) 13:51, 11 May 2011 (UTC)
I've seen quite a few people saying stuff like “π ≠ 3.14159... near a black hole”, so the idea that the definition of π in terms of circles doesn't only apply to the Euclidean plane is a relatively common misconception and we'd better dispel it as soon as possible. But what about replacing Euclidean with flat? ― A. di M.plédréachtaí14:05, 11 May 2011 (UTC)
I agree with Anythingyouwant; just saying "circle" with no qualifiers is less confusing and hence better, especially for the opening sentence. Mlm42 (talk) 15:57, 11 May 2011 (UTC)
It's true that if you take a sphere, and draw a circle on it, then the surface area bounded by the circle will not be given by pi-r-squared. But, such stuff is best alluded to later than in the first sentence of the article.Anythingyouwant (talk) 17:19, 11 May 2011 (UTC)
The formula below resembles the Ramanujan pi formulas although its derivation is entirely different:
Wikipedia is an encyclopaedia, not a publisher of new thought. This sort of thing would have to appear in something like a journal first where it can be properly checked. See WP:Reliable source. Dmcq (talk) 15:22, 20 May 2011 (UTC)
Edit request from 165.215.94.17, 25 May 2011
This edit request has been answered. Set the |answered= or |ans= parameter to no to reactivate your request.
It should be
Statistical estimation of π using random vectors
S. C. Bloch and R. Dressler
American Journal of Physics -- April 1999 -- Volume 67, Issue 4, pp. 298
Is the value for Pi given in the text box with the caption that follows correct?
"An estimate 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 estimate of π before electronic computers came into use." — Preceding unsigned comment added by 86.176.214.150 (talk) 19:04, 24 June 2011 (UTC)
Move request
The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.
Approximations of π → Approximations of pi – Hello everyone, I believe that the following pages should be moved for several reasons. First, there are inconsistencies between this page and some related pages which either use the symbol (π) or its spelled out version (pi). We should go with one of those for consistency. Now we might say, let's use the symbol as it clearly has the majority already, so less moving is required. However, I'm against this, as it makes navigation less user-friendly. The pi symbol isn't on people's keyboard (I wouldn't even know how to type it other than copy-pasting it), making a search for the titles unnecessarily complicated. However, I can also see the point in using the symbol, as it's more correct. And I'm indeed aware how mathematicians love to use that notation instead of its text version. If we decided to use the symbol as article title, we'd have to move this article and Leibniz formula for pi, the other articles appear to be proper names, which wouldn't fall into this category. I'm not sure what to do about 2π theorem (2*pi theorem, 2pi theorem?), as I wouln't know a good title for that one, but I'm sure a solution for this article can be found, too. Looking forward for a good discussion, The Evil IP address (talk) 13:05, 2 June 2011 (UTC)
The articles are mathematical, (or related to the mathematical concept of "π"), and that's the way it's used in mathematics.
Consensus was that this article shouldn't be moved, but that discussion also included the problem of article titles starting with a non-roman letter, sort keys, and other related problems. Those problems don't apply to any of the other articles discussed, leaving onlyLeibniz formula for π as an outlier.
Oppose all for all the same reasons I've given at the previous half-dozen-or-so identical and unsuccessful move requests. —David Eppstein (talk) 15:41, 2 June 2011 (UTC)
There has certainly been a lot of voting on this subject lately. I count two votes in favor of "pi", and two in favor of "π".Kauffner (talk) 17:33, 2 June 2011 (UTC)
Oppose - π is used as a mathematical symbol, not as the greek letter, therefor the π notation is correct. The Wolfram example given above is ambiguous, as it uses both notations in the same article. — Edokter (talk) — 15:55, 2 June 2011 (UTC)
Oppose all: In mathematics the symbol π rather than the word "pi" is used. Outside of mathematics "pi" is usually more appropriate, but these are mathematical articles. CRGreathouse (t | c) 16:15, 2 June 2011 (UTC)
oppose First consistency is not a reason: you yourself note that π is more common, but anyway it's rarely a reason to change a page name on its own. Second it's irrelevant you can't type π: that's what all the redirects are for. You might have noticed as you wrote down the titles you want there are no red links: the redirects exist already so it's easy to find the articles through them. Those seem to be your only reasons so I really don't see you have an argument. π is how it appears in mathematics, and from context in all those titles it is clear that it's the number π not the Greek letter or some other meaning.--JohnBlackburnewordsdeeds18:34, 2 June 2011 (UTC)
Oppose: I see no problem with having titles with characters that are not easy to type. We have redirects so typical users won't have to worry about that anyway. So it really comes down to what we want to show up at the top of the page, and to me the mathematical symbol is superior as it is widely used in the field. –CWenger (^ • @) 00:15, 3 June 2011 (UTC)
Oppose - "pi" is just a transliteration of the letter's name. Shouldn't be used if the symbol is available, and the symbol is available. Xanthoxyl<06:18, 3 June 2011 (UTC)
Reading all of that policy the first bullet point is most relevant: "Sometimes the most appropriate title will contain diacritics (accent marks), dashes, or other letters and characters not found on most English-language keyboards. This can make it difficult to navigate to the article directly. In such cases, provide redirects from versions of the title that use only standard keyboard characters." (my emphasis) and we have the redirects already. The prescription on symbols in the third point seems to be aimed at symbols of the sort loved by advertisers and brand makers: the ♥ in I♥NY for example, not characters. The last point says not to use truly obscure characters like ℘, which hardly applies to π.--JohnBlackburnewordsdeeds22:44, 3 June 2011 (UTC)
The proper spelling of a word is one given in the dictionaries. As a practical matter, the ASCII spelling is nearly always the preferred spelling. "Use the Latin alphabet" works so well as a rule of thumb that it is hardly even necessary to look a word up. Kauffner (talk) 01:44, 4 June 2011 (UTC)
What are the beneficial effects of following this guideline though? Is it just about avoiding redirects? To me the only thing we are really debating here is what shows up at the top of the article page. –CWenger (^ • @) 01:59, 4 June 2011 (UTC)
Support:(edit conflict) Unlike simple accented or variant Roman letters (e.g. É, ä, ç, è, ñ, ô, even Þ, æ. ß or ø), pi isn't part of the basic ASCII set, and so isn't easily callable on Microsoft keyboards. Almost all of the articles listed above are of general as well as specialist interest, so no extra barriers should be erected. And redirects don't solve all problems, e.g. (insofar as I remember) wikilinks to #subsections of those articles. See my comments on the earlier proposed move of this article to π (had to use a template for that) or π (had to pull down "Special characters", then select "Greek" — since "Symbols" wouldn't do — and then the letter). —— Shakescene (talk) 02:10, 4 June 2011 (UTC)
None of those characters you listed are part of ASCII, and ASCII is not very relevant in modern computing systems. And no pi character is needed on the keyboard to access or edit the article (you can copy/paste if you really need to edit in a new copy of the π character like I did here). And section links do now work through redirects (try it). Can you clarify your post? Dicklyon (talk) 02:29, 4 June 2011 (UTC)
The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.
Done Per him. :| TelCoNaSpVe :| 04:54, 9 June 2010 (UTC)
![{\displaystyle \pi =[3;7,17,1,444,1,1,1,2,1,3,1,16,2,1,1,2,2,2,2,1,124,\cdots ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7b1226261dbf056dd27daf1cf4c96b01802ef2f5)
![{\displaystyle \pi =[3;7,13,1,204,1,1,1,2,1,3,1,12,2,1,1,2,2,2,2,1,70,\cdots ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a6819a1b6eb4e8142261677a474e4b03edb6280)
Done There were eight references that changed sub-domains. I have corrected all of them to prevent link rot. Alpha Quadrant talk 22:11, 25 May 2011 (UTC)
