Talk:Pi/Archive 16

Purgy Purgatorio, it is true that the statement as changed is correct, but the semantics change subtly:

• τ = 6.283185... is typical to indicate that we are dealing with an exact, known value that decimal notation cannot capture precisely.
• τ ≈ 6.283185 merely says what the approximate value is, and does not suggest that the value can be known exactly.

Just an opinion :) —Quondum 14:21, 7 December 2018 (UTC)

Yes, I agree. At first I only noticed the removed dots (with the edit summary "avoiding dots"), so my edit summary "dots are necessary" was not strictly accurate. But as Quondum says, what this is saying is not that two values are approximately equal, but that the value of tau is irrational. I do not understand any problem with the dots, which I think are therefore the best notation, and I am slightly uneasy about the "wavy equals" sign (it's not what I grew up with, which was equals with dots above and below, but it might be standard American; I just don't know. But I would agree with the change in order from tau to pi to numerical approximation. Imaginatorium (talk) 15:15, 7 December 2018 (UTC)

I agree that dots are better here. Moreover, ≈ does not implies that the last digits are correct (in physics, there are rarely all corrects), while the dots suggest that this is a truncated sequence of digits. Thus π ≈ 3.1416 and π ≈ 3.1415 are both corrects, while π = 3.1416... is wrong. D.Lazard (talk) 15:33, 7 December 2018 (UTC)

@Quondum, I strongly adhere to the conviction that τ is given –as mentioned!– by the defining equality

${\displaystyle \tau =2\pi .}$

I believe that Hartl et al. prefer the above to the next, and for myself I am very much inclined to object to a notation like

${\displaystyle \tau =6.2\cdots ,}$ ⟨the previous was rubbish, caused by an uncorrected copy-paste⟩

as it requires presupposed knowledge about the \cdots, whereas I am perfectly fine with

${\displaystyle 2\pi \approx 6.28,\quad }$ or even ${\displaystyle \quad 2\pi \approx 6,}$^[1]

even when this notation is not explicit about any error bounds, but I assume that π is not in need to refer to publications of the Particle Data Group, but its billions of calculated digits are available elsewhere, and its transcendence is well sourced and described in WP. Personally, I take these approximation as truths in my life.

@Imaginatorium, your edit summary was simply false, the term not strictly accurate is an euphemism, at best, that I love to use, too. I took your revert as in need of the explanation, which I gave in my summary. Generally, I perceive \dots as not having an invariant meaning, it depends on their context, and includes finite sequences, repetitions, ... (see what I mean?). In my life, the equal with a dot above denoted Taylor approximation to the first non-zero degree, and a second dot below made up a definition, forgetful about definiens and definiendum.

Summing it up, I oppose to reintroducing dots for the given reasons, I would agree to any other \approx, if LaTeX wouldn't render it as it does, and I would go on living without any further edit on this, if there is consensus against my preferences. Cheers. Purgy (talk) 16:48, 7 December 2018 (UTC)

Addendum: Afaik, the PDG does identify the last agreed upon digit. Purgy (talk) 16:53, 7 December 2018 (UTC)

In passing by: How about ${\displaystyle \pi \approx 3.1416\cdots }$? Imho, the use of dots may be convenient, but is underserving ill-befitting the profession of a mathematician. ;) Purgy (talk) 07:25, 8 December 2018 (UTC)

And one more: How about ${\displaystyle \pi =3.14159\cdots }$? See also 0.999... Purgy (talk) 07:33, 8 December 2018 (UTC)

(Side note: we use ldots in this context, not cdots.)

• ${\displaystyle \pi \approx 3.1416\ldots }$ – absolutely not. But we would not put ${\displaystyle \pi \approx 3.1415\ldots }$ either (combining ... with ≈).
• ${\displaystyle \pi =3.14159\ldots }$ – fine, but I'm confused about what you're suggesting.

—Quondum 00:24, 10 December 2018 (UTC)

I have to admit that (because I try to avoid them) I am not versed in when to use which dots, and when to apply specific tokens denoting ellipsis. Furthermore, these finesses emerged later than I lost my interest in them. Nevertheless, I feel the duty to be bound by the general habit, and so I promise that I'll try to adhere to the local rules.

I also confess that none of my examples containing any dots corresponds to my liking. I am fully serious in claiming that dots require some agreement on their meanings in their respective appearances (thus my claim of them being ill-befitting the profession of an mathematician).

I do see both combinations of dots with approx and equal as suboptimal, but a combination of dots and approx could be taken as a hint to the impossibility of denoting irrational quantities as decimal numbers: the decimal number stays an approximation, disregarding how many decimals one adds. The "approx with dots" is sort of dual to "equal with dots".

My last suggestion was intended as an example to suggest the possibility of a fundamental misunderstanding of dots in this specific context. It is not compulsory to take x = 3.14159... as x = 3.1416, maybe even farfetched for those in the know, but my black-hearted intention was again to hint to this vague possibility, excluded by ... ?presupposed knowledge? only. Maybe the Dozenal Society disallows their members to think of π, when seeing 3.14159...?

BTW, I see a fine use of dots in the statement that someone used π for 6.28..., because stating that someone used π for 2π is really confusing.

Summing up again, I see only disadvantages in changing the status quo by adding any dots, possibly in exchange for an approx. Cheers! Purgy (talk) 09:55, 10 December 2018 (UTC)

This appears to be a debate about preferences. On the suggestion that 3.14159... might mean 3.14159, surely it should be clear that by {x₀, x₁, x₂, ...} we do not necessarily mean {x₀, x₁, x₂, x₂, x₂, x₂, ...} ? You will find the ellipsis being used in many articles, papers, etc., in the sense you seem to object to. Look at, for example, The article e. —Quondum 13:40, 10 December 2018 (UTC)

Sure, it's about preferences. I conceded convenience to dots, I tried to argue why I prefer alternatives to dots, I gave examples of (possible!, not necessary) confusions, I still see no valid resaon for dots here, because I refuted (rarely) given advantages for dots, but I announced not to act against dots, if re-introduced based on consensus, ... What else can I do? I certainly won't hunt dots for elemination, nor state that I agree that dots are better here. BTW, dots in other articles are a deprecated argument in WP (and with me). :) Purgy (talk) 14:46, 10 December 2018 (UTC)

The ellipsis is not deprecated in WP (see example 3.14159265358979323846... at MOS:DIGITS) —Quondum 22:40, 10 December 2018 (UTC)

I wanted to call any argument in favor of "something", that is based on its use "elsewhere", deprecated. I did not want to claim that "something" were deprecated, but rather that any argument based on "elsewhere" is. I am quite sorry for my clumsy formulations. Purgy (talk) 08:27, 11 December 2018 (UTC)

I agree that dots are better, for the reasons stated by Quondam in the original post (and by D Lazard in a followup comment). As to which dots, I have no strong opinion between three individual dots, ellipsis, or ldots (in contexts where ldots exist). I prefer any of those to cdots. --Trovatore (talk) 18:11, 12 December 2018 (UTC)

The ellipsis character in article text is deprecated in favor of three periods ("...", not "…"). That has nothing to do with whether we should use ellipses in mathematical formulas to indicate truncation of non-terminating decimals; I agree that we should. —David Eppstein (talk) 18:32, 12 December 2018 (UTC)

Certainly "dots" are better. I prefer the ellipsis character. Paul August ☎ 18:37, 12 December 2018 (UTC)

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Pi value is approximately 3.1428571428 106.215.124.34 (talk) 06:58, 4 March 2019 (UTC)

 Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. Also, no it's not.  DiscantX 07:32, 4 March 2019 (UTC)

I'd like to suggest two additions:

• This would need to be researched, but anecdotally I believe the infamous "Indiana Pi Bill" (which we reference in the article) gained notoriety because of it being cited by the Guinness Book of World Records for many years as "Most inaccurate value of pi". Since the bill is already included in the popular culture section, citing Guinness would be appropriate. (Though an argument could be made that since it was an attempt at passing an actual law, not, say, a reference in a movie or novel, the discussion of the Indiana Pi Bill might be more appropriate for the history section.)
• Again in Popular Culture, a very famous fictional use of pi as an actual weapon occurs in the Star Trek: The Original Series episode "Wolf in the Fold" when the evil noncorporeal entity "Redjac" (who, in the continuity of Star Trek, was once Jack the Ripper) takes over a computer and Mr. Spock drives it out of the device it by ordering that computer to calculate pi to the last digit. 136.159.160.5 (talk) 14:44, 12 March 2019 (UTC)

https://www.cbc.ca/news/technology/pi-day-emma-haruka-iwao-1.5056603 I've not added it to the page. Legacypac (talk) 03:43, 15 March 2019 (UTC)

Section "Describing physical phenomena" currently contains (approximate representation)

In electromagnetics, the vacuum permeability constant μ0 appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation. It is defined as exactly

   μ0 = 4π×1e7 H/m ...

That will need to be changed on 2019-05-20 - see in https://en.wikipedia.org/wiki/2019_redefinition_of_SI_base_units#Ampere

94.30.84.71 (talk) 14:10, 17 March 2019 (UTC)

This section includes the statement "Iterative methods were used by Japanese mathematician Yasumasa Kanada to set several records for computing π between 1995 and 2002. This rapid convergence comes at a price: the iterative algorithms require significantly more memory than infinite series." This conflicts with the cited reference which states "This resulted in a scheme that is roughly competitive in efficiency compared to the Salamin-Brent and Borwein quartic algorithms they had previously used, yet with a significantly lower total memory requirement.". Also the Kanada scheme used two Machin like formulas, one to generate, one to verify, and also Spigot_algorithm to verify the last few bits. Machin series don't converge as fast as the later series, but can take advantage of parallel calculations. In Kanada's paper, it mentions they used "64 nodes of 144 nodes of a HITACHI SR8000/MPP supercomputer.^[1] Rcgldr (talk) 00:42, 11 April 2019 (UTC)

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change "3.1415926 < π < 3.1415627" to "3.1415627 < π < 3.1415926" i.e. swap order, in History-->Polygon Approximation Era 137.195.59.181 (talk) 14:36, 26 June 2019 (UTC)

I'd rather be sure this is what was intended, and not that "...627" should really be "...927". Can anyone track this down? –Deacon Vorbis (carbon • videos) 14:48, 26 June 2019 (UTC)

Partly done. I found the appropriate page in Boyer & Merzbach, and indeed, it was just copied incorrectly. I've changed it to ...927 instead. Thanks for pointing this out! –Deacon Vorbis (carbon • videos) 15:10, 26 June 2019 (UTC)

What's the use of π²? Exessia (talk) 08:46, 30 June 2019 (UTC)

It's really not clear what your question means; it's not very different from asking the equivalent energy of the number 5 in barrels of oil. As the article says, Legendre proved it was irrational in 17-something, but that also follows from the fact that it is transcendental. And there's evidently not much more notable to say... But what sort of answer were you looking for? Do you want more or less about it in the article? Imaginatorium (talk) 09:49, 30 June 2019 (UTC)

The most famous result about ${\displaystyle \pi ^{2}}$ is probably the Basel problem, which asserts that

${\displaystyle \pi ^{2}=6\sum _{n=1}^{\infty }{\frac {1}{n^{2}}}.}$

This is mentioned in sections § Irrationality and transcendence and § Number theory and Riemann zeta function. D.Lazard (talk) 10:54, 30 June 2019 (UTC)

@Exessia:, just as π is the area of a unit circle in two dimensions, π² is twice the 4-dimensional volume of the unit 4-ball in four dimensions, see Volume of an n-ball. —Kusma (t·c) 13:10, 30 June 2019 (UTC)

Where does "py" come from? the link offers no example of py --Backinstadiums (talk) 12:56, 17 March 2019 (UTC)

The link takes me to H:RESPELL, where under the vowels column, "y" is listed with the expected pronunciation. –Deacon Vorbis (carbon • videos) 14:07, 17 March 2019 (UTC)

I've been always wondering about english pronunciation of "π". Anywhere in the world, including origin/Greece, it is pronounced as is, i.e. "pi" or "pí" (in english pronunciation the "pee" is probably the closest). Why in english, and it seems only in english, is it pronounced differently? Kmarty (talk) 15:50, 5 May 2019 (UTC)

P is a letter. Pea is a vegetable. Pee is a urinating term. Georgia guy (talk) 17:25, 5 May 2019 (UTC)

The „might be homphonic to …“ is not an argument. Pie is a type of pastry.

You can check the Wiktionary „Etymology“ section. -- K (T | C) 22:03, 5 May 2019 (UTC)

Yeah, but π is a letter and P is a letter, and if they were pronounced the same, that would be extra confusing. (In some sense I suppose you can say they're the same letter, but that's not always a useful way of looking at things.)

On the original point, it looks like the respelling is no longer there, but if we were to have a respelling, in my opinion it should be "pie". I'm aware that there's a table somewhere that probably would explain the use of "py", but in my view that table misses the whole point of using respelling at all. If the reader has to look up the phonemic correspondences of the letters used in a table, then we might as well just use IPA; the reason to use respelling is so that competent English-language readers don't need a table. --Trovatore (talk) 23:35, 5 May 2019 (UTC)

It's there, just in the first section down, not in the lead. It also gives "pie" as a homophone along with IPA and respell, which can't hurt I guess. –Deacon Vorbis (carbon • videos) 01:22, 6 May 2019 (UTC)

@Kmarty: The Great Vowel Shift is responsible for both the pronunciation of "π" as /paɪ/ and the pronunciation of the letter "P" as /piː/. Before it happened, "π" was pronounced /piː/ (exactly as the letter "P" in contemporary English), whereas the letter "P" was pronounced /peː/ (as contemporary "pay" pronounced by someone from Scotland or Canada), a pronunciation which is used in contemporary German and Dutch. Kbb2 (ex. Mr KEBAB) (talk) 10:41, 5 July 2019 (UTC)

In other words, in Scotland and Canada the long a sound is a monophthong, not the diphthong it generally is. Georgia guy (talk) 12:23, 5 July 2019 (UTC)

@Kbb2: The question is why english mispronounce widely known constant "π" as /paɪ/. It is not english letter therefore any english pronunciation should not be applied regardless of any shifting (as well as for letter "ch" where is no "k" in pronunciation. But that's different story). Kmarty (talk) 09:17, 9 July 2019 (UTC)

@Kmarty: /paɪ/ is an established English pronunciation of "π" and it was caused by the Great Vowel Shift. It's not a mispronunciation. Kbb2 (ex. Mr KEBAB) (talk) 15:01, 9 July 2019 (UTC)

@Kbb2: I definitely won't argue how pronounce "pi" syllable in english. But since letter "π" is not english, one would at least try not to mispronounce it. Nothing more, nothing less. Kmarty (talk) 22:17, 9 July 2019 (UTC)

@Kmarty: Again, the reason for this pronunciation is the Great Vowel Shift. It's not a mispronunciation. Kbb2 (ex. Mr KEBAB) (talk) 23:25, 9 July 2019 (UTC)

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Consider two objects of masses 10^m and 10^n, where the lighter object is kept between a wall, which is on the left and the heavier object, which is on the right. The right of the larger object extends towards infinity. If the object of mass 10^m is sent towards the other stationary object of mass 10^n, such that m ≥ n, all collisions are elastic and there is no friction or drag, the total number of collisions including those of the two blocks as well as those between the lighter block and the wall is surprisingly, the digits of pi without the decimal. The number of digits of pi that show up is the ratio (m-n) For example, if the masses are 100 kg and 1 000 000 kg, the number of collisions will be 3141 as 6-2 = 4 digits

Original paper along with proof :Galperin's paper Thank you. https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf 27.34.68.12 (talk) 16:17, 20 July 2019 (UTC)

 Not done. Edit requests need to be precise – you need to give the exact text you want to add and where you want to add it. But more importantly here, I don't see a good place for this (admittedly very cute) result in this article. –Deacon Vorbis (carbon • videos) 17:15, 20 July 2019 (UTC)

An IP is edit waring at template {{Pi box}} for adding direct links to irrational number and transcendental number. IMO these links are irrelevant, as the links to the proofs of trancendence and irrationality suffices. I have already reverted them too many times. So action by other editors would be useful. (I am posting this here, because I suspect that the template has few watchers). D.Lazard (talk) 12:29, 20 November 2019 (UTC)

Complex dynamics π can be computed from the Mandelbrot set [...] The point (0.25, ε) at the cusp of the large "valley" on the right side of the Mandelbrot set behaves similarly[...]

This is wrong. It looked wrong so I checked it programmatically. (0.25, ε) should be (0.25+ε, 0)

2001:56A:71BA:6800:A1D1:3F93:8CF1:84D3 (talk) 14:13, 19 January 2020 (UTC)

Fixed. The source says the same; it was probably just a copying error. –Deacon Vorbis (carbon • videos) 14:20, 19 January 2020 (UTC)

Perhaps something like this would resolve the question of nested parens:

π is an irrational number, meaning that it cannot be written as the ratio of two integers—fractions such as ⁠22/7⁠ and ⁠355/113⁠ are commonly used to approximate π, but no common fraction (ratio of whole numbers) can be its exact value.

or

π is an irrational number, meaning that it cannot be written as the ratio of two integers. Fractions such as ⁠22/7⁠ and ⁠355/113⁠ are commonly used to approximate π, but no common fraction (ratio of whole numbers) can be its exact value.

I agree that the square brackets are awful. Johnuniq (talk) 23:08, 16 March 2020 (UTC)

The square brackets are awful, but so is having nested parenthetical clauses in any formatting. I prefer your second alternative, with two sentences. —David Eppstein (talk) 23:19, 16 March 2020 (UTC)

There is an insane method of estimating pi given by one R. Chartres in Philosophical Magazine from 1840 based on the probability of coprimality. SpinningSpark 08:24, 20 May 2020 (UTC)

to 10.1134/S0001434610090294 because SciHub only gives correct article on THAT DOI. 2A00:1FA0:44DF:31F8:C1A6:49C:82FC:FAA8 (talk) 16:53, 1 July 2020 (UTC)

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Please add the missing word (in bold):
The invention of calculus soon led to the calculation of hundreds of digits of π, enough for all practical scientific computations. 95.49.71.94 (talk) 16:25, 3 July 2020 (UTC)

 Done, thanks! ‑‑ElHef (Meep?) 16:49, 3 July 2020 (UTC)

In his book, Remmert referred to integral definitions, not to the circumference definition. Not all definitions of π with circumference rely on integral calculus. You can use polygonal paths and then define arc length as a limit of a sum of certain lengths of line segments. This does not make use of derivatives and integrals. You can then prove that this definition is equivalent to the integral-derivative definition of arc length, but you do not have to. The "Definition" subsection should be edited accordingly. A1E6 (talk) 16:06, 9 July 2020 (UTC)

No paragraph to state the current record for the calculation of Pi?

(It appears in the footnote 7 link).

Haruka Iwao, Emma (14 March 2019); 31.4 trillion digits.

MBG02 (talk) 05:00, 1 November 2020 (UTC)

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The caption to the photo of a pi pie says "pe pie". That must be a mistake, right? 80.71.142.50 (talk) 13:58, 13 December 2020 (UTC)

 Not done - I do not see the error, caption reads "pi pie"... - Adolphus79 (talk) 16:16, 13 December 2020 (UTC)

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I prove pi to be 2.72 here: https://1drv.ms/w/s!AmwYc90gKnVxgzErx9Y120Q2gV8z?e=yNKRGs also here https://commons.wikimedia.org/wiki/File:Calculating_Pi_To_Be_2.72.pdf I want this page to be updated to reflect this. IAmTobiOne (talk) 13:00, 15 December 2020 (UTC)

 Not done: please provide reliable sources that support the change you want to be made. Melmann 13:24, 15 December 2020 (UTC)

The links you provide are not of high enough quality to allow me to see what is going on. In particular I can't work out where the points L and K are. Can you provide something of better quality? As Melman says, you do need to get this published in a reliable source before it can be considered for inclusion in Wikipedia, since Wikipedia is not a publisher of original research. Murray Langton (talk) 17:14, 15 December 2020 (UTC)

L = (0.2, 1.0) and K = (1.0, 0,2). The alleged proof starts with an unproven and clearly wrong claim: "The line LK is the best transmutation of the circles edge to a straight line for the purpose of calculating the area of the circle". Just looking manually at the drawing, the line removes a large part of the circle in the first quadrant and only adds two tiny parts. PrimeHunter (talk) 22:08, 15 December 2020 (UTC)

In any case, your alleged result has been proved to be wrong since more than 2,000 years. D.Lazard (talk) 17:46, 15 December 2020 (UTC)

D.Lazard, I agree with you, but I want to try and see what is wrong with the 'proof'. Murray Langton (talk) 21:05, 15 December 2020 (UTC)

I did understood that, and it is why my post is less indented than yours. D.Lazard (talk) 21:12, 15 December 2020 (UTC)

Hi IAmTobiOne. Here is a simple test you can do yourself to empirically show that you claimed value for pi (2.72) is incorrect. Get a tape measure and a reasonably large circular dinner plate. Measure the diameter of the dinner plate (271 mm in my case). Measure the circumference of the dinner plate (850 mm in my case). Divide circumference by diameter to get an approximate value for pi (in my case 850/271 = 3.14). PrimeHunter has already pointed out the problem with your 'proof'. Murray Langton (talk) 12:08, 18 December 2020 (UTC)

A discussion is taking place to address the redirect 3.1415926535897932384626433832795. The discussion will occur at Wikipedia:Redirects for discussion/Log/2021 March 14#3.1415926535897932384626433832795 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. O.N.R. ^(talk) 04:21, 14 March 2021 (UTC)

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HI people pi is a eniterity of numbers starting with...... 3.1415968529552956104620561957201510561947201064018649036710684086010181498870091680913460141010794194105170956159073838056138610659.

No edit requested, closing. ScottishFinnishRadish (talk) 20:47, 17 March 2021 (UTC)

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24.45.239.147 (talk) 08:05, 23 April 2021 (UTC)

Giro Lazala

No edit requested, closing. D.Lazard (talk) 08:19, 23 April 2021 (UTC)

Should there be some information about Barbier's theorem? ${\displaystyle \pi }$ pops up very naturally there and it is understandable by non-mathematicians as well. I wonder why there's no mention of it in the Pi article. A1E6 (talk) 22:52, 19 May 2021 (UTC)

Apparently, you have added it to the article. I support this addition. D.Lazard (talk) 09:56, 20 May 2021 (UTC)

The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion:

• Pi-unrolled-720.gif

Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 22:55, 14 July 2021 (UTC)

In the Pop Culture section regarding Pi Day in the US, "In the United States, Pi Day falls on 14 March (written 3/14 in the US style)..." can the sentence be updated to "...on 14 March (written 3/14 in middle-endian format)..."? It is a little redundant in its current form. 96.33.102.34 (talk) 19:46, 27 August 2021 (UTC)

How is it redundant? The vast majority of readers would not know what middle-endian means, and would have to follow that link to find out. (And even that link is a little cryptic.) Most readers WILL know that the practice of writing dates with the month before the year is a US one. HiLo48 (talk) 02:22, 28 August 2021 (UTC)

I agree that "in the US style" is clearer and better. The fact that someone somewhere has created a joke name for the US date format is merely a distraction. TooManyFingers (talk) 03:03, 28 August 2021 (UTC)

A photo caption here claims that the circular shape of pie makes it a frequent subject of pi puns. But that reasoning is faulty; there are many other circular-shaped items, and they are not frequently the subject of pi puns. Pie is the subject of pi puns because in English their names sound the same. Pie's circular shape may often be of coincidental benefit to the puns created, but it isn't a primary reason for their creation. TooManyFingers (talk) 03:15, 28 August 2021 (UTC)

(A case could be made that if pies were some other shape the puns would be fewer and not as clever; but if pie was called "beel" or "sturvel", there would be none of the puns at all.) TooManyFingers (talk) 03:37, 28 August 2021 (UTC)

Reworded to "A pi pie. Pies are circular, and "pie" and π are homophones, making pie a frequent subject of pi puns" (with appropriate links).Meters (talk) 03:50, 28 August 2021 (UTC)

That's better than I would have come up with. Thanks! TooManyFingers (talk) 04:45, 28 August 2021 (UTC)

I reverted this change, because the original is better. The reasoning is not faulty at all: to make a pun, you have to have (near-)homophones -- that is what "pun" means. So talking about "homophones" is superfluous; it's sort of "de-explanation", telling the reader that a simple word ('pun') can be described using a more complicated word ('homophone'). But the reason "pie" often appears in a pun is indeed that (at least some) pies are circular. (In my experience many pies are not circular...) Imaginatorium (talk) 07:21, 28 August 2021 (UTC)

Yes, it's a bit of an over explanation, but I can understand why TooManyFingers thought the way they did. The caption did read as if roundness was the only criterion. The objection was raised. I resolved the issue the user raised. Let's see what other editors think. Meters (talk) 07:29, 28 August 2021 (UTC)

I do see the way in which my complaint is potentially "operating at the wrong level" if that's a valid way of describing Imaginatorium's point. I think each "level" is worth something, but whichever way it ends up is OK with me. (A bit of a rebuttal though: In my opinion, Imaginatorium's reasoning can easily lead to the conclusion that giving it any caption at all is to miss the point.) TooManyFingers (talk) 15:43, 28 August 2021 (UTC)

Hello Editors,

Under the section 'Polygon approximation era', there is a grammatical error in the last sentence. It says:

"Christiaan Huygens was able to arrived at 10 decimals places in 1654 using a slightly different method equivalent to Richardson extrapolation."

A simple error I thought needed addressing.

Kind Regards ~~~

Wildpumpkin (talk) 06:16, 5 September 2021 (UTC)

Corrected. A1E6 (talk) 11:10, 5 September 2021 (UTC)

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Pi was discovered by Aryabhatta. add these points. 2409:4043:102:10E1:0:0:9A5:90AC (talk) 16:20, 22 October 2021 (UTC)

 Not done As the article states, good approximations for pi were known to ancient civilizations, centuries before Aryabhata was born. Mindmatrix 16:47, 22 October 2021 (UTC)

Can you please add a redirect at the front of the page for Pi Day — Preceding unsigned comment added by 68.50.116.194 (talk) 21:00, 17 November 2021 (UTC)

Pi day is already linked in the infobox at the top of the page, and discussed in § In popular culture. This is sufficient. D.Lazard (talk) 21:09, 17 November 2021 (UTC)

Sourced from Wolfram|Alpha Ir should be added AniiiCo (talk) 11:17, 25 November 2021 (UTC)

No. This is out of scope for Wikipedia, and there are plenty of websites dedicated to mathematics that provide this information. Mindmatrix 17:15, 25 November 2021 (UTC)

@D.Lazard: Per the change to the caption and WP:BRD, see here. For example, when epsilon is 0.0000001, the iteration count is 31415928. So, you do indeed have to multiply the iteration count by epsilon in order to get the approximation of Pi. The caption, saying π can be computed from the Mandelbrot set, by counting the number of iterations required before point (−0.75, ε) diverges. is misleading, because the number of iterations is an integer and cannot approximate pi. The body text of the article correctly explains it as If points with coordinates (−0.75, ε) are considered, as ε tends to zero, the number of iterations until divergence for the point multiplied by ε converges to π. I don't think it is "nonsensical" to add this to the image caption. Especially since the image is far away from the article body text. I found the caption alone to be quite confusing, so I think it is better to add "then multiplying by epsilon", as here. What do you think? Leijurv (talk) 19:45, 25 November 2021 (UTC)

I agree that the current caption requires to be improved, but your edit is not an improvement, as your sentence ... by counting the number of iterations required before point (−0.75, ε) diverges then multiplying by ε is not grammatically correct, and I am unable to give it any meaning. D.Lazard (talk) 21:54, 25 November 2021 (UTC)

@D.Lazard: I am not sure why you say that is grammatically incorrect. You count the iterations, then, multiply that number (the quantity of iterations) by epsilon. What is the issue? Maybe there needs to be a comma before "then"?

Regardless, there could be a better way, if you don't like the way I had it.

How about: π can be computed from the Mandelbrot set, by multiplying some ε by the number of iterations required before point (−0.75, ε) diverges.

Or: π can be computed from the Mandelbrot set, by counting the number of iterations required before point (−0.75, ε) diverges, then multiplying that quantity by ε. Leijurv (talk) 22:10, 25 November 2021 (UTC)

I understand now; the comma makes the difference. However, π can be computed from the Mandelbrot set, by counting the number of iterations required before point (−0.75, ε) diverges, and then multiplying the result by ε is slightly better. However this sentence remains confusing, as π seems depend on ε (product of ε and an integer), and a "point that diverges" is not a common concept. D.Lazard (talk) 22:26, 25 November 2021 (UTC)

@D.Lazard: I would agree on the point that diverges, as it is specific to the mandelbrot/julia sets and not general to anything else in the Pi article. How about: π can be computed from the Mandelbrot set, by counting the number of fractal iterations required before point (−0.75, ε) diverges, and then multiplying the result by ε.? That way it is clear that this is an operation specific to that fractal. Then if it's confusing you can click the link to Mandelbrot set which will explain it further. Perhaps it also needs a , as ε approaches zero. at the end, but I'm not sure if that would make it more or less confusing to read. Leijurv (talk) 22:31, 25 November 2021 (UTC)

How about: "The Mandelbrot set can be used to approximate π by counting the number of fractal iterations it takes for point (−0.75, ε) to diverge. When the number of iterations is multiplied by ε, the result approaches π as ε approaches zero." I also think it's fine to just have the caption be "The Mandelbrot set can be used to approximate π" and let readers find the longer explanation in the text. Danstronger (talk) 03:07, 26 November 2021 (UTC)

That first one sounds good to me! Leijurv (talk) 05:35, 26 November 2021 (UTC)

The second is much better, because, as I pointed above, the first is either inaccurate or requires to be an expert in Mandelbrot set to be understood. D.Lazard (talk) 09:24, 26 November 2021 (UTC)

The first is good enough as captions go. Can you point out where the inaccuracy is? No expert knowledge is needed. We cannot explain the entire mandelbrot set in the Pi article, so we have to be somewhere between complete vagueness and a full explanation. I think the first one is good because the part that it explains is the connection between the mandelbrot set and pi. Which is what it should explain.

The second one is too vague. If it were used, I would say that the image would need to be moved up a section to be adjacent to the text in the article talking about mandelbrot set. Well, perhaps that should be done in any case. Leijurv (talk) 09:57, 26 November 2021 (UTC)

Again, a "point that diverges" is nonsensical for most readers. I guess that the intended meaning is "divergence of the iteration process starting from the point". For this guess, I have used the text in the body, which is less cryptic, although still confusing. So the first suggestion is definitively not convenient.

MOS:CAPTION says Captions should be succinct; more information can be included [...] in the main text. As the "more information" is already in the article, this is a strong argument in favor of the second suggestion.

On my laptop, the image is on the right of the text. Be care that moving an image may have different effects on different devices. So, I have changed the section heading for clarifying the relationship of the image and the text. D.Lazard (talk) 11:19, 26 November 2021 (UTC)

Okay, after playing with my zoom and window size, I see that the image is optimistically placed next to the next. However there are too many images in quick succession, so it gets pushed downwards. If you're curious what I see, it is this. If I log out of Wikipedia to see how it would look to someone also using firefox on a similar monitor to mine, it looks like this. The issue of too many images making them not line up with the text to which they refer is perhaps an issue for another day. If it works for some/most people, that is fine. Leijurv (talk) 19:12, 26 November 2021 (UTC)

I agree the short caption is better. No need for the caption to repeat a technical explanation that’s in the main text. Danstronger (talk) 14:29, 26 November 2021 (UTC)

All right, fine. What you wrote The Mandelbrot set can be used to approximate π. is good enough. Perhaps a little bit more detail, such as π can be approximated from analyzing the fractal behavior of specific points in the Mandelbrot set. Leijurv (talk) 19:12, 26 November 2021 (UTC)

I don't think that the short description Number, approximately 3.14 is accurate enough. It's approximately 3.14, and what? There are lots of numbers which are approximately 3.14. I think it can be made more accurate while still being simple. Do you agree?

Cf. the short description of e (mathematical constant): 2.71828..., the base of the natural logarithm (bolding mine). A1E6 (talk) 20:14, 22 January 2022 (UTC)

See WP:SDNOTDEF. Greater accuracy is not an end to seek in itself in this context; the point is to make clear to people what topic the article is about in searches on mobile devices, where all they see in the search results will be the title and short description. What searches do you have in mind where "Pi: Number, approximately 3.14" is going to be an ambiguous search result that needs more information to disambiguate it? —David Eppstein (talk) 21:18, 22 January 2022 (UTC)

@David Eppstein: The level of accuracy is quite inconsistent, then. It seems to me that you imply that rather the e article is in the wrong here; that 2.71728... alone is a sufficient short description, and that what follows is superfluous (if I understand correctly). A1E6 (talk) 21:56, 22 January 2022 (UTC)

I don't think consistency is really the main point here. It should be the most familiar, common, and recognizable form of the number, whichever number of digits that ends up being. For e, I think there are too many digits; 2.718 would probably be fine. For pi, abbreviating to three digits as 3.142 is not a good choice, because that's not a common way of writing it. —David Eppstein (talk) 22:04, 22 January 2022 (UTC)

Alright :) A1E6 (talk) 22:08, 22 January 2022 (UTC)

The three Monte Carlo methods described are all great, but it seems like the third is described in a very different style from the first two. Is there any reason for this? I think it could be described in an equally plain/straightforward way, without removing any of its content. As it is, I suspect that many/most readers are unable to understand it. In particular, I am looking at its unexplained use of 'expectation' notation, the ${\displaystyle n\to \infty }$ formulation being unlike the previous ${\displaystyle \pi \approx }$ formulation, and the unnecessary use of jargons like "random variable" and "discrete stochastic process" which are just as applicable to the other two Monte Carlo methods. Gumshoe2 (talk) 09:07, 28 January 2022 (UTC)

I don’t have any objection to making that section more accessible, but wanted to point out that it is fundamentally different from the other two methods. Because it is the limit of an expression with expected value, if you do n trials with k flips each, n and k have to both approach infinity for the value to approach pi. As opposed to Buffon where you can simply keep dropping needles and the running average approaches pi, you can’t just take one infinite random walk, at any point |W_k| is not guaranteed to be anywhere near its expected value. Danstronger (talk) 14:02, 28 January 2022 (UTC)

Incidentally, "monte carlo methods" feels out of place in the middle of "modern quest for more digits". Maybe "modern quest..." should be renamed "modern calculation methods" and "monte carlo methods" should be moved to the start of it. Danstronger (talk) 14:18, 28 January 2022 (UTC)

This edit request to Pi has been answered. Set the |answered= parameter to no to reactivate your request.

Can you let me edit this webpage? 60.246.144.234 (talk) 13:06, 13 February 2022 (UTC)

 Not done: this is not the right page to request additional user rights. You may reopen this request with the specific changes to be made and someone may add them for you, or if you have an account, you can wait until you are autoconfirmed and edit the page yourself. Cannolis (talk) 13:55, 13 February 2022 (UTC)

An editor has identified a potential problem with the redirect 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706 and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 February 22#3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. TartarTorte 21:37, 22 February 2022 (UTC)

The article contains two mentions of a 'Richard Baltzer', which actually link through to a German soldier, who is not the person intended. The correct Richard Baltzer was a German mathematician, who lived 1818-1887. At the very least the erroneous links should be deleted. — Preceding unsigned comment added by 82.35.203.20 (talk) 12:25, 15 March 2022 (UTC)

Links removed. D.Lazard (talk) 14:09, 15 March 2022 (UTC)

This article has become far more complex than the version promoted (), mostly due to unnecessary additions that make the article confusing to the layperson, and which are often uncited. I honestly wouldn't be opposed to reverting most of the sections to the promoted version. Particularly suspect sections are "Modern quest for more digits" (which should be a quick summary of Approximations of π), the analytical definitions in "Definition", the inclusion of long approximations in binary and ternary, and the sections on modular forms and the gamma function. It's a very arbitrary collection. Ovinus (talk) 02:09, 26 April 2022 (UTC)

What is "arbitrary" about modular forms and the gamma function? A1E6 (talk) 15:00, 26 April 2022 (UTC)

"Arbitrary" isn't the right word, sorry. They just seem to be explained in far more detail than is necessary for the main "pi" article. Most of the sections can be easily covered in respective articles (Gamma function and Stirling's approximation are the place). Ovinus (talk) 18:31, 26 April 2022 (UTC)

For example, some people prefer the gamma function to be defined directly in the "Pi" article ("for reading comfort"), while others would suggest only a link to the "Gamma function" article where it is defined. I'm afraid that the kind of changes you are proposing could be viewed as controversial. A1E6 (talk) 18:51, 26 April 2022 (UTC)

Fair enough; I think that's true for math articles on Wikipedia in general. I don't think the article is bad, just of FA quality (mainly 2(c) and 4 in WP:WIAFA). Ovinus (talk) 19:49, 26 April 2022 (UTC)

@David Eppstein: The text It is a transcendental number and cannot be produced with a finite sequence of algebraic operations is misleading since many algebraic numbers also cannot be produced with a finite sequence of algebraic operations. I don't believe that including a definition of transcendental in that text, e.g., It is a transcendental number, meaning that it is not a zero of any polynomial with rational coefficients, and thus cannot be produced with a finite sequence of algebraic operation, is pedantic. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:58, 28 April 2022 (UTC)

You are omitting an important part of the text. It says "It is a transcendental number and cannot be produced with a finite sequence of algebraic operations (sums, products, powers, and roots)." So it is already unambiguous. You have a different version of what it means to be an algebraic operation in mind than the one used here, but the one used here is not misleading. —David Eppstein (talk) 16:13, 28 April 2022 (UTC)

I'm in a hurry and haven't looked over the two versions in detail, but I would point out that many readers are likely to interpret "root" as meaning "n^th root for some positive integer n", or possibly even "square root". The implication given, of course, is still true, but it doesn't define "transcendental", and some readers may take the text as implying that it does. --Trovatore (talk) 16:39, 28 April 2022 (UTC)

So change it to "polynomial roots"? —David Eppstein (talk) 17:55, 28 April 2022 (UTC)

This was a good change. A brief definition of transcendental would likely help the average reader. And the original wording, while technically true, is somewhat confusing about the relationship between the two properties. It's not pedantic to clarify that the second property follows as a consequence of the first, rather than being independent or worse, an incorrect characterization of the definition of it. 35.139.154.158 (talk) 16:31, 28 April 2022 (UTC)

Pedantic clarifications do not belong in article leads. —David Eppstein (talk) 17:55, 28 April 2022 (UTC)

I made this change recently (from the original phrasing, which indeed characterized it more precisely), so I should probably comment. I don't think "and" implies equivalence in the same way a dash or colon would, just a connection of some sort, hence why I wrote it that way. But I agree it's possible for someone to think they are equivalent. That being said, the current version of the lead (with "roots of integer polynomials") contains redundancy, since transcendental numbers are precisely those numbers which are not roots of integer polynomials. I want to avoid "root" (in the polynomial sense) in the first paragraph per WP:ONEDOWN. I put something a bit more carefully worded in. Ovinus (talk) 22:20, 28 April 2022 (UTC)

Your modified wording hints that being transcendental means not being constructible using arithmetic operations and nth roots. This is incorrect. —David Eppstein (talk) 00:35, 29 April 2022 (UTC)

That's why I used "implying" rather than "meaning". What phrasing do you propose? Ovinus (talk) 00:47, 29 April 2022 (UTC)

If you want to avoid polynomial roots, turn the relation around. It is a transcendental, meaning that no way of summing nonzero integer multiples of its powers can produce zero. —David Eppstein (talk) 06:50, 29 April 2022 (UTC)

"Nonzero" is unneeded here, and possibly confusing. Otherwise, this formulation is fine.

I have boldy edited the article, with the formulation "meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers". I have no clear opinion on the best formulation. This may depend on which is more technical between "solution of an equation" or "integer multiple". In favour of my formulation: people who have already encountered the definition of transcendental may recognize it more easily. D.Lazard (talk) 07:14, 29 April 2022 (UTC)

@D.Lazard: The current formulation "it cannot be a solution of an equation involving only sums, products, powers, and integers" is incorrect, since ${\displaystyle \pi }$ is a solution of the equation ${\displaystyle 0x=0}$. A1E6 (talk) 10:24, 29 April 2022 (UTC)

This is how technical articles become unreadable. I suppose you could insert "non-trivial equation" or "the value of pi cannot be" but that wouldn't help any reader who wanted to know what transcendental meant. Johnuniq (talk) 10:29, 29 April 2022 (UTC)

I think D.Lazard's new phrasing is reasonable. But maybe I'm misguided in trying to remove "root" from the first paragraph. I guess there's a discussion to be had on the intended audience for the lead. Ovinus (talk) 14:45, 29 April 2022 (UTC)

Maybe "it cannot be calculated by solving an equation involving only sums, products, powers, and integers"? I feel like anyone who understands the mathematician's use of "non-trivial" is likely to know what "transcendental" means already. Perhaps "a finite number of" should be inserted somewhere to foreclose the possibility of infinite series. XOR'easter (talk) 16:00, 29 April 2022 (UTC)

Good point about infinite series/infinite products... Also everyone understands what "non-zero" means. A1E6 (talk) 16:37, 29 April 2022 (UTC)

I think the purpose of explaining that pi is a transcendental number is to help the reader understand why we use π to represent the ratio of a circle's circumference, so the current lead sentence seems good. For example, ${\displaystyle {\sqrt {2}}}$ is represented by "root" and the "integer" 2.--SilverMatsu (talk) 17:50, 29 April 2022 (UTC)

The text reads "Another spigot algorithm, the BBP digit extraction algorithm, was discovered in 1995 by Simon Plouffe". But, unless I missed it, both indicated references give credit to Bailey, Borwein, and Plouffe, not to Plouffe. I am aware that Plouffe has made some public claims that Bailey and Borwein deserve no credit. Is it a conscious choice to be agreeing with him? I could not find any commentary on the talk page here, including the archives. Gumshoe2 (talk) 09:28, 28 January 2022 (UTC)

If there is no argument against it I will edit to credit Bailey–Borwein–Plouffe instead of Plouffe. Gumshoe2 (talk) 06:08, 12 May 2022 (UTC)

Bailey's account says that Borwein and Plouffe found a similar method for binary digits of log 2, they both began working on pi, using search software created for the purpose by Bailey, and that Plouffe's search runs succeeded. I agree that crediting Plouffe alone does not seem warranted. —David Eppstein (talk) 06:25, 12 May 2022 (UTC)

This is in reference to this section:

Let V be the set of all twice differentiable real functions ${\displaystyle f:\mathbb {R} \to \mathbb {R} }$ that satisfy the ordinary differential equation ${\displaystyle f''(x)+f(x)=0}$. Then V is a two-dimensional real vector space, with two parameters corresponding to a pair of initial conditions for the differential equation. For any ${\displaystyle t\in \mathbb {R} }$, let ${\displaystyle e_{t}:V\to \mathbb {R} }$ be the evaluation functional, which associates to each ${\displaystyle f\in V}$ the value ${\displaystyle e_{t}(f)=f(t)}$ of the function f at the real point t. Then, for each t, the kernel of ${\displaystyle e_{t}}$ is a one-dimensional linear subspace of V. Hence ${\displaystyle t\mapsto \ker e_{t}}$ defines a function from ${\displaystyle \mathbb {R} \to \mathbb {P} (V)}$ from the real line to the real projective line. This function is periodic, and the quantity π can be characterized as the period of this map.

[ref: section 1.3 of Ovsienko and Tabachnikov "Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups"]

I find this section baffling. Removing the needlessly complicated language and setup, it amounts to the following: given a real number t let ${\displaystyle P_{t}}$ denote the set of functions ${\displaystyle x\mapsto c\sin(x-t)}$, the set defined by c ranging over all real numbers. The mapping ${\displaystyle t\mapsto P_{t}}$ has period π. (And there is a vector space V for which each ${\displaystyle P_{t}}$ is a point of the projectivization ${\displaystyle \mathbb {P} (V).}$)

To me as a reader of this page, this is totally arbitrary content of questionable significance. The given reference of Ovsienko–Tabachnikov does not seem to even mention pi at all in the entire chapter, their purpose being to associate an equivalence class of curves in ${\displaystyle \mathbb {RP} ^{1}}$ to any Sturm–Liouville operator. I agree that the curve associated to ${\displaystyle f\mapsto f''+f}$ has period π but from available evidence, only the editor who added this material to wikipedia thinks this is worth pointing out. (The specific Sturm–Liouville operator ${\displaystyle f\mapsto f''+f}$ is not even singled out for any comment by Ovsienko–Tabachnikov)

Could someone clarify? If not, perhaps this section should be removed. Gumshoe2 (talk) 06:50, 12 May 2022 (UTC)

What an amazing example of pedantry!!

The part of the content of section § Projective geometry that is relevant for this article is simply: The solutions of the differential equation ${\displaystyle f''+f=0}$ form a real vector space of dimension two, with sine and cosine as a basis. All functions in this vector space are periodic of half-period π. The second part of the section is nothing else than a pedantic way to say that if a solution f of the differential equation is 0 at t, the same is true for the scalar multiples of f, and the same is true at ${\displaystyle t+\pi .}$ The fact that this differential equation can be an example for an advanced theory (and many others) does not imply that this theory is sufficiently related to π for being mentioned here.

However the fact summarized in the quoted sentence is fundamental, since it explains the ubiquity of π in mathematics (this is a personal opinion). It appears partially in § Definition (Landau's definition) and in § Angle units. It should be made more visible.

In summary, OK for removing § Projective geometry, but a section on the solutions of ${\displaystyle f''+f=0}$ must be added. D.Lazard (talk) 08:07, 12 May 2022 (UTC)

It is already present in a slightly disguised form in the "Eigenvalues" section. But that section has (in my opinion) its own major obscurantist problems, with a completely unnecessary appeal to Sturm–Liouville theory, negative definite operators, and Wirtinger's inequality when a totally elementary approach is standard and works fine. Gumshoe2 (talk) 10:23, 12 May 2022 (UTC)

Yes. I knew I could calculate pi radius times two under perimeter

John Rowell 95.146.121.120 (talk) 10:23, 14 May 2022 (UTC)

It is well established now that the area of a circle is π*r^2 and that the circumference is 2*π*r; When was it first documented that the constant π is the same in both cases. What was the proof then (using modern, but simple, terms)? What is a simple, elegant modern proof, preferably accessible to ordinary school children.

I believe this would be interesting to many people, especially teachers of secondary school maths and their students. — Preceding unsigned comment added by CuriousMarkE (talk • contribs) 19:32, 29 April 2022 (UTC)

@CuriousMarkE: I think it is explained in the Area of a circle--SilverMatsu (talk) 15:52, 1 May 2022 (UTC)

Thanks, a useful reference. It shows how quickly we can get into deep material when we want to revisit basics! I’m still thinking of something more straightforward to read for school children, however am now less sure that will be easy to find. CuriousMarkE (talk) 04:01, 26 May 2022 (UTC)

"It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22/7 are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern." "Consequently" is the wrong word here. Just start with "Its decimal representation...." (and "nor" requires a precedent "neither". "nor does it enter ..." would be better. 142.163.194.232 (talk) 15:18, 6 July 2022 (UTC)

Better yet, move that text to the end of the next sentence:

It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22/7 are commonly used to approximate it. Consequently, its decimal representation never ends. It is a transcendental number, meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers; its decimal representation never enters a permanently repeating pattern.

possibly with some wordsmithing --Shmuel (Seymour J.) Metz Username:Chatul (talk) 18:37, 6 July 2022 (UTC)

I don't see anything wrong with [c]onsequently here. It might not be necessary, but it isn't wrong. 142.163.194.232, would you like to explain why you think it's the wrong word? --Trovatore (talk) 20:03, 6 July 2022 (UTC)

Also, never...nor is just fine in my estimation. --Trovatore (talk) 20:21, 6 July 2022 (UTC)

The second sentence of the article would read better split into two sentences by cutting the word "and," adding a period, and capitalizing a 'T':

BEFORE PROPOSED EDIT:

It appears in many formulas in all areas of mathematics and physics and the earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by Welsh mathematician William Jones in 1706.[1]

AFTER PROPOSED EDIT: It appears in many formulas in all areas of mathematics and physics. The earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by Welsh mathematician William Jones in 1706.[1]

— Preceding unsigned comment added by Scholarnick (talk • contribs) 14:44, 14 March 2021 (UTC)

The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion:

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Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 18:39, 2 October 2022 (UTC)

This edit request to Pi has been answered. Set the |answered= parameter to no to reactivate your request.

Add link to Emma Haruka Iwao in modern usage section 157.26.68.252 (talk) 13:20, 26 October 2022 (UTC)

Not done – please clarify please cite and provide more clarification on edit request Wesoree (Talk) 13:24, 26 October 2022 (UTC)

In section 3.3 - Rapidly convergent series, there's a mention of the current record holder for the most digits of Pi in the penultimate paragraph 157.26.68.252 (talk) 07:28, 27 October 2022 (UTC)

ϕ = (1 + √5)/2

ϕ = 2*cos(π/5)

π = 5*arccos(ϕ/2)

π = 5*arccos((1 + √5)/4)

Would there be any issue in calculating π through an inverse cosine? I think π is part of the inverse cosine function, is it not? It would be referencing itself in that case, yes?

Kaleb.G (talk) 05:26, 9 November 2022 (UTC)

On 3 October 2022, two references^[1][2] were removed and were replaced by Martini, Montejano, Oliveros (2019) by User:David Eppstein (https://en.wikipedia.org/w/index.php?title=Pi&diff=1113776184&oldid=1113772803). Why? Removal≠consolidation. A1E6 (talk) 00:21, 30 November 2022 (UTC)

They were redundant with the Martini, Montejano, Oliveros reference, which covers the same general topic better. Using one good reference in place of a greater number of references that do not cover the subject in as much depth (the Dover book) or that are popular-press works instead of more-reliable scholarship (Gardner) is an improvement, and what I meant by consolidation. Also, please explain how your use of the word "suspicious" is not a violation of WP:AGF. —David Eppstein (talk) 00:29, 30 November 2022 (UTC)

Thanks for the response. Why do you think it's a violation of WP:AGF? A1E6 (talk) 00:36, 30 November 2022 (UTC)

"Suspicious" casts doubt on my motives for making this edit. It is an accusation of dishonesty, with no evidence. WP:AGF prohibits doing that. —David Eppstein (talk) 00:37, 30 November 2022 (UTC)

I decided to use the word "suspicious" because of this: (new article)

I don't accuse you of a harmful motive. It just seemed suspicious. Don't take it too seriously. A1E6 (talk) 00:58, 30 November 2022 (UTC)

"Suspicious" implies dishonesty. Look up its definition. You need evidence to make such an accusation, you have provided none. I think you owe me an apology for this harmful accusation. I happen to own a copy of the Martini, Montejano, Oliveros book. I think it is a good book. But I have no connection to its authors or publisher and no reason to cite it other than my opinion that it is a good reference for this topic. As for the recent edits you list: I have been systematically going through a list of members of the Mexican Academy of Sciences and adding new articles on women in the list, as part of a multi-year project to improve Wikipedia's coverage of women in STEM more generally. One of those women happened to be an author of this book. When I add new articles on women in STEM, I also make sure to search for other articles that cite them, to make sure they do not become {{orphan}}s. That's all I did here. —David Eppstein (talk) 01:50, 30 November 2022 (UTC)

I'm very sorry for labeling it as "suspicious". I was very confused by your edit summary. A1E6 (talk) 02:16, 30 November 2022 (UTC)

I concur that Using one good reference in place of a greater number of references that do not cover the subject in as much depth (the Dover book) or that are popular-press works instead of more-reliable scholarship (Gardner) is an improvement. Moreover, having more (and worse) references than necessary to establish a comparatively minor point just makes for a more distracting^{[101][102][103]} reading experience.^{[99][101][105][106][114]} XOR'easter (talk) 17:09, 4 December 2022 (UTC)

I disagree. The references would look like this^[115][116] (which is not distracting at all), not like ^{[115][116][117][118][119]}. The example which you provided is extremely exaggerated on purpose. A1E6 (talk) 17:31, 4 December 2022 (UTC)

Yes. It was a joke (in the service of making a serious point). XOR'easter (talk) 18:12, 4 December 2022 (UTC)

On 20 May 2021, I added the references to the article. On 3 October 2022, they were removed by David Eppstein and replaced by the Oliveros reference on the basis that "the Oliveros reference covers the same topic better". When I tried to add the references back, David Eppstein accused me of "attacks on other editors" (see https://en.wikipedia.org/w/index.php?title=Pi&diff=1125217969&oldid=1125202267; this is ridiculous). What if someone removes the Oliveros reference and replaces it by a "better" reference? It's only a matter of opinion. Such thing would be just as unfair as David's edit. A1E6 (talk) 17:11, 4 December 2022 (UTC)

What is the need for the additional reference, when the references in the article verify the information already? I'm neutral on the issue but your comment doesn't really explain why the references should be added. - Aoidh (talk) 17:16, 4 December 2022 (UTC)

The reason is simple: it's always better to have two references instead of just one reference. A1E6 (talk) 17:27, 4 December 2022 (UTC)

I'm afraid I don't follow that reasoning. Why is it always better? Is the content controversial? Is the neutrality or reliability of the source in the article in question? Is the source already present somehow deficient in verifying the content? What does the second reference add that the first reference is lacking? Why is that particular reference something that should be considered? Why is an additional reference necessary? - Aoidh (talk) 17:36, 4 December 2022 (UTC)

You see, no one was asking "Why do we need the Oliveros reference?" "Is the source already present somehow deficient in verifying the content?" This is just unfair. A1E6 (talk) 18:52, 4 December 2022 (UTC)

False. You asked it, above. And I provided an answer: because it consolidates the references by providing a single source for all the claims about the connections between π and curves of constant width, rather than making readers who want to verify those claims look for each one piecemeal in multiple different sources. Also because it is more authoritative on this topic than, say, Gardner. —David Eppstein (talk) 19:40, 4 December 2022 (UTC)

There should have been "no one was asking "Why do we need the Oliveros reference?" on 3 October 2022". Even if it is a single source for all the claims, it doesn't give you the right to remove valid references. A1E6 (talk) 19:49, 4 December 2022 (UTC)

What gives you the idea that any special rights are required to perform such edits? And "it's valid" is not the same as "it's the best way we could be referencing this topic", especially for a Featured Article. —David Eppstein (talk) 19:56, 4 December 2022 (UTC)

If you're suggesting that the statement needs more sources, I don't think "what's wrong with the ones already there?" is an unfair or unreasonable question to ask. There are situations where more sources would be a good thing, my question was purely to figure out if this was one of those situations. It was and remains a legitimate question and a great opportunity to make the case for the inclusion of the source, which I personally would be more than open to considering if a good reason can be presented. If you could make the case for the source you'd have my support, but "two is better than one" isn't a case for why the source is needed. - Aoidh (talk) 19:57, 4 December 2022 (UTC)

Well, I can give you at least one such reason for including the Rabinowitz reference – it's freely available unlike the Oliveros reference. A1E6 (talk) 20:08, 4 December 2022 (UTC)

Ok, but it's also a WP:PRIMARYSOURCE, and we prefer secondary when possible. —David Eppstein (talk) 20:10, 4 December 2022 (UTC)

That would be a very good point in favor of using an additional source if one were offline and another available online, but the source currently in the article has a GBooks link and I was able to click the link and view the content freely and with no issues. While there may be a gratis versus libre distinction there that I'm not aware of in terms of what you mean by "freely available", what matters is the verifiability of the source and in that regard both can be easily accessed with a single click, so that's not an edge over what's in the article. - Aoidh (talk) 20:20, 4 December 2022 (UTC)

OK, I give up. A1E6 (talk) 20:48, 4 December 2022 (UTC)

Often, yes. Always, no. XOR'easter (talk) 18:15, 4 December 2022 (UTC)

One of the references says "The analytic curve of constant width due to Rabinowitz, pp. 111–112." but the Rabinowitz reference (with a link etc.) is actually nowhere in the article. A1E6 (talk) 16:16, 5 December 2022 (UTC)

Do you understand that the phrase you quote is the title of a section in a book? Do you think every person mentioned in a title in a reference must automatically be cited? How many new talk page sections are you going to create after your previous discussions go south? —David Eppstein (talk) 16:36, 5 December 2022 (UTC)

Calm down. A1E6 (talk) 20:32, 5 December 2022 (UTC)

I think the article should more strictly divide between the "platonic ideal" of the mathematical Pi vs physical-world Pi. It is possible that physical Pi was different during the earliest moments of our Universe, pico-seconds after the Big Bang, e.g. pi == sqrt2 + sqrt3, because physical Pi is tied to the speed of light and there is emerging clue that C hadn't necessarily always been the same as of now. 188.143.7.205 (talk) 16:08, 23 December 2022 (UTC)

There is no concept of a physical π. The mathematical constant π is accurately defined independently of any physical measurement. It appears in many formulas of physics, but the constant that appears there is always the mathematical constant. If a formula is not accurate is some context, this is the formula that must be changed, not π. For example, π is the ratio of the circumference of a circle and its diameter in classical geometry (the space of geometry is not the physical space but a mathematical model of the physical space). In spacetime of the general relativity, the ratio of the circumference of a circle and its diameter is not a constant and it is not called π. This is not contradictory with the fact that the (mathematical) π is commonly used in relativity. D.Lazard (talk) 16:47, 23 December 2022 (UTC)

> The number π (/paɪ/; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159

I feel this is an outdated view, akin to as if the article on Meter said it's the lenght of platinum-iridium etalon rod No.1. held in the vaults of Paris observatory (when measured at 20 deg C, exactly 1016hPa air pressure and 50% moisture, under ambient lightning and with the Moon at half-phase). Just to nitpick one issue: how many dimensional circle does the author mean and what are the geometry axioms chosen?

(Because of such variances, the Meter has long been abstracted and noone says any more that exactly 10 million meters span the distance from Equator to Pole, the aboriginal reason for the etalon rod's lenght. Definition of Meter has been converted to vibration wavelenght of excited caesium atoms by the 1970s and recently got even further abstracted by fixing it to c, the speed of light and Wikipedia's article says so right from the start.)

Similarly, this article about Pi could present the Ludolphine number in an abstracted manner upfront, e.g. Pi = 4 - 4/3 + 4/5 - 4/7 + 4/9 - .... (a formula using just elementary math) and elaborate further down the text on historical origins of Pi, regarding the circumference of an eucledian circle. Etomcat (talk) 17:12, 24 December 2022 (UTC)

No. Your analogy is inapt -- the meter is an invented physical unit, while pi is an exact numerical quantity. Defining it geometrically is probably *more* abstract than by an infinite series, and gives an intuitive notion first, as well as helps to indicate why the number is important, and follows how sources tend to treat the subject anyway. The definition as the circle constant follows how it was historically (and still is) used, and it's not "outdated". 35.139.154.158 (talk) 18:17, 24 December 2022 (UTC)

Agreed. The lead is fine, and changing it as suggested would seriously damage the article. Meters (talk) 20:30, 24 December 2022 (UTC)

Presenting it as an infinite series obscures the significance and would be unintelligible to a reader with no knowledge of convergence. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:28, 25 December 2022 (UTC)

Pi#Continued fractions is under Pi#Fundamentals but Pi#Infinite series is under Pi#History. Shouldn't they both be under History? Shmuel (Seymour J.) Metz Username:Chatul (talk) 16:04, 24 January 2023 (UTC)

No, the continued fraction expansion of pi is a fundamental property of pi, while there is no series that is naturally associated to pi (this is a big difference with e (mathematical constant)). The series that are presented in § History have been used historically for computing pi. If some of these series have another fundamental interest, they should be mentioned in another section, but, in any case, they belong to the history of pi. D.Lazard (talk) 12:58, 23 February 2023 (UTC)

I remember that the 1991 Guinness Book of Records listed the least accurate ever pi approximation (4). Does anyone know of a way to check that? Serendi^podous 08:54, 28 February 2023 (UTC)

@Serendipodous: I have Danish 1982 and 1996 editions with the alleged record for least accurate pi. They both say the Indiana legislature in 1997 set it to 4 in law number 246. This refers to the already mentioned Indiana Pi Bill. It gave or hinted at different values. Maybe one of them was 4 depending on interpretation. PrimeHunter (talk) 12:47, 28 February 2023 (UTC)

This reminded me of a discussion about what level of accuracy is "enough".^[1]George Rodney Maruri Game (talk) 02:13, 3 March 2023 (UTC)

i know there is a song that helps people remember 100 digits of pi, it's well known, shouldn't this be added to the "in popular culture" section? (ps: please tell me who wrote the song it is driving me crazy) Allaoii ^talk 21:49, 2 January 2023 (UTC)

Several versions with lyrics are on YouTube, check out Vi Hart while you're there. Happy Pi Day! — JimsMaher (talk) 12:21, 14 March 2023 (UTC)

youtube is blocked on my device Allaoii ^talk 14:39, 14 March 2023 (UTC)

Shouldn't "The fast iterative algorithms were anticipated in 1914" actually say, "Rapidly converging series were anticipated in 1914"? Rather than just make an edit on a well-curated page, I thought I would post here. If I'm correct, please make this change and feel free to delete this here. If I'm wrong, I think this needs some clarification. Thanks! Natkuhn (talk) 17:52, 15 March 2023 (UTC)

I did not realize the painfully polarizing effect of tau :)

Removing (not pop culture):

In 1958 Albert Eagle proposed replacing π by τ (tau), where τ = π/2, to simplify formulae,^[1] but this use of τ is otherwise unknown.

Mentioning: Tau Day (the reason it's relevant to pop culture). That sentence should also note this usage started recently; "21st century" seems correct but vague, perhaps "since 2010"? – SJ + 14:09, 2 May 2023 (UTC)

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Change the pronunciation of "π' /paɪ/ to /pi/ (pee). The Greek letter "π" is pronounced "pee" or "pih" and not "pie" or "pai". Factchecker25and0 (talk) 18:49, 25 April 2023 (UTC)

"Pie" is by far the most common pronunciation in English. You can see the modern Greek pronunciation at Pi (letter). –jacobolus (t) 18:59, 25 April 2023 (UTC)

I agree. We should reflect the pronunciation that people actually use for this mathematical symbol in English, not the proper Greek pronunciation as a Greek letter. Although I suspect the reason for the change in pronunciation is merely an accident of history, it also has an important side effect: it makes it possible to distinguish p from π in spoken mathematical English. So anyway, we should not make this requested change. —David Eppstein (talk) 19:58, 25 April 2023 (UTC)

I added the ancient Greek pronunciation, but kept the common English pronunciation as well. I agree this should be stated, as /pi:/ (like in Ancient Greek) is the most common pronunciation used in other major languages. Besides, other constant articles (e.g. φ) contain both the common English and Greek pronunciations. — Preceding unsigned comment added by Fkitselis (talk • contribs) 06:46, 18 May 2023 (UTC)

I reverted your edit since only the pronunciation of the mathematical symbol is relevant here. Do not confuse Pi and Pi (letter). D.Lazard (talk) 08:19, 18 May 2023 (UTC)

I don't confuse the letter with the symbol. What is relevant and what is not is a matter of perspective in this case, an opinion. I see I am not the first person bringing this up here. I am not going to insist now, but if more people would comment on this in the future, adding it should be considered. Fkitselis (talk) 05:17, 20 May 2023 (UTC)

It would be fine for Wikipedia or some other Wikimedia project to elaborate about the history of pronunciation of the Greek letter π (e.g. on the page about the letter). It could cover classical, Koine, and modern Greek pronunciation of this letter, the pronunciation in a wide variety of other modern languages, etc. It's just not in scope for the article about the mathematical constant. Note that this symbol for the mathematical constant dates from early 18th century England, and doesn’t have anything directly to do with either ancient or modern Greek pronunciation. –jacobolus (t) 05:40, 20 May 2023 (UTC)

The article about φ makes no mention whatsoever of pronunciation. –jacobolus (t) 00:39, 19 May 2023 (UTC)

I think we should add why pi is used not tau with proof. Yuthfghds (talk) 02:45, 28 May 2023 (UTC)

Because people arbitrarily settled on π a few hundred years ago, and both are close enough to the same to make switching not worth the bother for practitioners today. –jacobolus (t) 03:33, 28 May 2023 (UTC)

Thanks for the explanation Yuthfghds (talk) 04:17, 28 May 2023 (UTC)

Obviously there are some people (such as Michael Hartl) who disagree and think switching would be well worth the trouble, arguing especially for a benefit to students and laypeople. YMMV. –jacobolus (t) 07:34, 28 May 2023 (UTC)

Ohh Yuthfghds (talk) 07:42, 28 May 2023 (UTC)

I have a doubt.Is there a separate mathematics committee in wiki Yuthfghds (talk) 07:48, 28 May 2023 (UTC)

The numbers π and τ are immutable, and one can meaningfully discuss proofs about their values. The choice of which to use in a text is arbitrary, and hence not subject to proof.

While such constructions as ${\displaystyle \hbar =h/{2\pi }}$ are shorter written with τ, others such as ${\displaystyle A=\pi R^{2}}$ are longer. So the case isn't clear even without taking into account the massive disruption caused by switching at this late date. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 13:14, 28 May 2023 (UTC)

The area formuala is a red herring and very poor example if you think a half-turn should be the named constant; the ${\displaystyle {\tfrac {1}{2}}}$ naturally should appear given our convention of using a square as the basic unit for area. However, if you start looking at volumes of balls, the most natural named constant is a quarter turn, say ${\displaystyle \kappa ={\tfrac {1}{2}}\pi }$ (this is not a standard symbol), and this formula should "really" be expressed as ${\displaystyle A={\tfrac {1}{2}}\kappa D^{2}}$ if you want to better understand what is going on. This then generalizes to higher dimensions as: ${\displaystyle V={\tfrac {(n-1)!!}{n!}}\kappa ^{\lfloor n/2\rfloor }D^{n}.}$ (If we used an isosceles right triangle for our unit for area – and more generally a simplex for hypervolume – the factors of ${\displaystyle {\tfrac {1}{n!}}}$ would disappear from such formulas.) –jacobolus (t) 15:55, 28 May 2023 (UTC)

About Michael Hartl: the "Tau manifesto" starts "No, really, pi is wrong..." - end of conversation. Imaginatorium (talk) 13:23, 29 May 2023 (UTC)

Actually in my vision π is more convenient than τ and that's it Yuthfghds (talk) 04:01, 31 May 2023 (UTC)

I recently realized that the formatting for this article changed to have every instance of the greek letter pi denoted as the capital pi instead of the lowercase pi. Capital pi has a specific meaning in mathematics as early as secondary education that denotes a multiplication from the index k to the upper integer limit of n (other letters may be used to denote the range of these indicies). This seems bizarre to me and every vector image used in the article still uses the lowercase pi. I think the article should be reformatted to refer to the irrational number 'pi' with the lowercase variant. — Preceding unsigned comment added by 2601:281:D781:7420:65A0:C766:AEDF:9FBC (talk) 04:43, 4 June 2023 (UTC)

The capital ${\textstyle \prod }$ only shows up in one formula in Pi § Number theory and Riemann zeta function. If you are seeing ${\displaystyle \Pi }$ elsewhere in the article then you have something going very wrong with your font configuration. ${\displaystyle \pi }$ and π should both be the lower-case letter. –jacobolus (t) 06:27, 4 June 2023 (UTC)

This is probably because your processing system uses the font Tinos as the default instead of Times New Roman. This is common on some Android devices. Tinos is more rectangular, so the lowercase pi might look a bit like the capital one. This doesn't change the images and vectors because you can't change their fonts, and it probably won't be the case for LaTeX equations because they're always in the font Latin Modern Math. The Old Macintosh (talk) 16:14, 11 June 2023 (UTC)

The greek language, where the letter π comes from, does not have a sound for /aɪ/. They pronouce the word πι as /pi:/. 91.240.227.220 (talk) 13:00, 7 July 2023 (UTC)

So? This is a term used in English in the English encyclopedia. We do not list all pronounciations in other languages. And this is an article about the mathematical term, not the Greek letter. It is definitely not pronounced pee in English (that would confuse it with the Roman letter p). See above discussion where there was no consensus for this change. —David Eppstein (talk) 16:13, 7 July 2023 (UTC)

You might notice that we just went over this 2.5 months ago: Scroll up to #Semi-protected edit request on 25 April 2023. –jacobolus (t) 16:44, 7 July 2023 (UTC)

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172.119.66.101 (talk) 22:32, 26 July 2023 (UTC)

As qualified, the numbers of pi are far more than could understand, some people just remember '3.141'

 Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. Dylnuge ^{(Talk • Edits)} 23:09, 26 July 2023 (UTC)

Also since I think you're asking that the number of digits listed in the first sentence, note that this has been discussed several times in the talk page archives (e.g. why the common '59' ending?, Digit creep: Why 3.14159 is the right approximation for the introduction) and current consensus is to keep 3.14159. One reason not to use 3.141, the number you suggested, is that the value of pi at four digits is different depending on whether you round it (3.142) or truncate it (3.141). There was a preference expressed towards using a number which is identical whether rounded or truncated, which holds for 3.14159 (the digit following 3.14159 is a 2). Dylnuge ^{(Talk • Edits)} 00:22, 27 July 2023 (UTC)

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change The number π is a to π is a. 2405:9800:B920:7F44:ECF6:5372:BB60:D02D (talk) 07:00, 30 July 2023 (UTC)

No. For one thing, we should not start a sentence with lowercase notation. For another, the extra context is helpful for readers. —David Eppstein (talk) 14:36, 30 July 2023 (UTC)