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July 23, 2006Good article nomineeNot listed
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November 30, 2007Peer reviewReviewed
April 18, 2012Peer reviewReviewed
June 4, 2012Featured article candidatePromoted
Current status: Featured article

Semi-protected edit request on 26 October 2022[edit]

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

Not done – please clarify please cite and provide more clarification on edit request Wesoree (Talk) 13:24, 26 October 2022 (UTC)Reply[reply]
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 (talk) 07:28, 27 October 2022 (UTC)Reply[reply]

Calculation Using Cosine, Inverse Cosine, and Phi[edit]

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)Reply[reply]

Suspicious Unexplained removal of references[edit]

On 3 October 2022, two references[1][2] were removed and were replaced by Martini, Montejano, Oliveros (2019) by User:David Eppstein ( Why? Removal≠consolidation. A1E6 (talk) 00:21, 30 November 2022 (UTC)Reply[reply]

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)Reply[reply]
Thanks for the response. Why do you think it's a violation of WP:AGF? A1E6 (talk) 00:36, 30 November 2022 (UTC)Reply[reply]
"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)Reply[reply]
I decided to use the word "suspicious" because of this:[1][2][3][4][5][6] (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)Reply[reply]
"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)Reply[reply]
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)Reply[reply]
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)Reply[reply]
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)Reply[reply]
Yes. It was a joke (in the service of making a serious point). XOR'easter (talk) 18:12, 4 December 2022 (UTC)Reply[reply]


  1. ^ Lay, Steven R. (2007). Convex Sets and Their Applications. Dover. Theorem 11.11, pp. 81–82. ISBN 9780486458038.
  2. ^ Gardner, Martin (1991). "Chapter 18: Curves of Constant Width". The Unexpected Hanging and Other Mathematical Diversions. University of Chicago Press. pp. 212–221. ISBN 0-226-28256-2.

Removal of references pt. 2[edit]

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; 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)Reply[reply]

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)Reply[reply]
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)Reply[reply]
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)Reply[reply]
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)Reply[reply]
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)Reply[reply]
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)Reply[reply]
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)Reply[reply]
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)Reply[reply]
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)Reply[reply]
Ok, but it's also a WP:PRIMARYSOURCE, and we prefer secondary when possible. —David Eppstein (talk) 20:10, 4 December 2022 (UTC)Reply[reply]
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)Reply[reply]
OK, I give up. A1E6 (talk) 20:48, 4 December 2022 (UTC)Reply[reply]
Often, yes. Always, no. XOR'easter (talk) 18:15, 4 December 2022 (UTC)Reply[reply]

Rabinowitz reference is missing[edit]

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)Reply[reply]

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)Reply[reply]
Calm down. A1E6 (talk) 20:32, 5 December 2022 (UTC)Reply[reply]

Observable Pi vs calculated Pi isn't clearly differentiated in the current article.[edit]

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. (talk) 16:08, 23 December 2022 (UTC)Reply[reply]

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)Reply[reply]

Do not start article with a legacy definition of Pi but progress from abstract to historical?[edit]

> 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)Reply[reply]

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". (talk) 18:17, 24 December 2022 (UTC)Reply[reply]
Agreed. The lead is fine, and changing it as suggested would seriously damage the article. Meters (talk) 20:30, 24 December 2022 (UTC)Reply[reply]
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)Reply[reply]


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)Reply[reply]

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)Reply[reply]
youtube is blocked on my device Allaoii talk 14:39, 14 March 2023 (UTC)Reply[reply]

Confusing organization[edit]

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)Reply[reply]

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)Reply[reply]

1991 Guinness Book of Records[edit]

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? Serendipodous 08:54, 28 February 2023 (UTC)Reply[reply]

@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)Reply[reply]

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)Reply[reply]

incorrect phrase in "Rapidly converging series" subsection?[edit]

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)Reply[reply]