Talk:Pi

Pi in the Bible

By some people, pi is believed to be encoded in 1 Kings 7:23. The plain text gives a diameter D (1.5 foot) and a circumference 3D (4.5 foot), which would seem to indicate a value of 3 for pi (supposing both measures measure the same circle). However, the word for line/circumference, סָבִיב, is misspelled as סְבִיבָה. These two words have a gematric value of 106 and 111, respectively, so the word for circumference is "inflated" by 111/106. If one inflates the given value (3D) for the actual circumference, inflated the same amount, yields 3D×111÷106 = 3.1415..D 2A02:A45C:FF55:1:2F71:58D8:FF2D:3D8 (talk) 11:09, 21 June 2024 (UTC)

The use of gematric values is to some extent arbitrary and has little, if any, scientific basis. You need a reliable source, not original research, if you want to include this information in the article. Murray Langton (talk) 12:33, 21 June 2024 (UTC)

The תַּנַ״ךְ‎ Tānāḵ (Hebrew Bible) is a work of ethics, history, morality, poetry and tradition; it is not, nor does it pretend to be, a Geometry text. Further, the value given are only to one figure, and they are correct to one figure. Were the text to accurately give the measurements to 20 figures, they would still be incorrect, since π is irrational (in fact, transcendental). This is a long standing rebuttal of a claim that the text never made.

However, there might be a case for including various spurious claims in the popular culture section, including the notorious Indiana pi bill #246 of 1897. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:50, 21 June 2024 (UTC)

Mispelled? I checked online and the text says סָבִיב, not סְבִיבָה. :: -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:50, 21 June 2024 (UTC)

3.1415926535… 192.150.155.229 (talk) 21:35, 3 July 2024 (UTC)

References

Mistake in infinite series

In 1844, a record was set by Zacharias Dase, who employed a Machin-like formula to calculate 200 decimals of π in his head at the behest of German mathematician Carl Friedrich Gauss.

Looking at Arndt & Haenel 2006, pp. 194–195:

The Austrian mathematician Lutz von Strassnitzky (1803-1852) exploited an unusual opportunity which came his way. In 1840, the "famous mental computer" Zacharias Dase (1820-1861) visited him in Vienna and attended his lectures on elementary mathematics. [...] Strassnitzky persuaded him to do perform some research which "at least he would be able to use", namely the calculation of π to 200 decimal places. [...] Dase chose the following arctan formula which does not converge as well as Machin's formula[...]: ${\frac {1}{4}}\pi =\arctan {\frac {1}{2}}+\arctan {\frac {1}{5}}+\arctan {\frac {1}{8}}$

[...] He offered to calculate some mathematical tables, so Gauss suggested he should expand the existing prime factorisation tables. Dase took up this suggestion and, with financial support from the Hamburg Academy of Sciences, he calculated the prime numbers in all the numbers between 7 and 9 million.

Vinickw‍✉ 17:40, 27 June 2024 (UTC)

Should it be categorized as a Welsh invention

Two very well-known mathematical symbols, "=" (equality) and "π" (pi) originate from Cymru in the 16th and 18th century respectively. Only the equality sign is classified as a Cymru invention. The concept, calculation, and approximation methods for π far predate the actual symbol for π which we all know today. I am thinking about categorizing "π" as a Cymru invention, but I am unsure because the number, not the symbol, was discovered in antiquity, and much of the discussion concerns about this transcendental number of its decimal expansion.

Additionally, lowercase π could mean something entirely different depending on context, most notably that of the prime-counting function, which I don't recall any of them being introduced by a Cymro. Moreover, some formulas, notably that of the Riemann zeta function, involve multiple occurrences of π with different meanings!

--MULLIGANACEOUS-- (talk) 00:47, 24 July 2024 (UTC)

If π was "invented" by anyone, it was God. If you think God is Welsh, it's fine for you to think so, but you need an RS to put it in the article.

As for the symbol, that comes from the ancient Greeks (though they didn't use it with this meaning).

What you seem to be talking about is that it was a Welsh mathematician who is first recorded to have used π by itself (as opposed to something like ${\frac {\pi }{\delta }}$ or ${\frac {\pi }{\rho }}$) to denote the number.

That's ludicrously far from making π a Welsh invention.

Leave the nationalism where it belongs, which I probably shouldn't say where that is lest I violate the current WP proprieties. --Trovatore (talk) 05:31, 24 July 2024 (UTC)

If Jones was the first user of "π" in this particular way, which he does not claim and is in doubt, the usage originated in London. NebY (talk) 07:19, 24 July 2024 (UTC)

That seems pretty ridiculous to me, to be honest. People had some concept of the ratio between circumference and diameter of a circle going back to ancient Mesopotamia, Egypt, China, etc., and since then there have been hundreds if not thousands of small developments in conceptual/practical understanding and use of this idea. Plucking out the first published appearance of the symbol π used in precisely this way is quite arbitrary. –jacobolus (t) 08:56, 24 July 2024 (UTC)

Wrong symbol used for π

At the end of the "In computer culture" section, the last sentence uses τ instead of π.

Here is an excerpt that begins with the exact issue:

τ has been added to several programming languages as a predefined constant.

I believe this should be π instead. 7agonczi (talk) 19:18, 17 August 2024 (UTC)

 Not done: τ (tau) is correct. See the ref[1] you did at first include with this request and the description of τ (tau) two paras up from the passage you quote.

small typo in first section

π is found in many -->formula(e)<-- in trigonometry and geometry, 160.179.102.212 (talk) 01:40, 20 August 2024 (UTC)

There's no typo there. "Formula" is singular, "formulae" plural, and "many formulae in trigonometry" is correct. NebY (talk) 01:54, 20 August 2024 (UTC)

Are we exaggerating the claim about Weierstrass?

This article says "An integral such as this was adopted as the definition of π by Karl Weierstrass", citing Remmert (2012), but what Remmert explicitly says is "This identity is pointed out by Weierstrass as a possible definition for π" which is a weaker claim. And I don't read German but glancing at Weierstrass (1841) even that seems like it might be a mild exaggeration. In the place where I see this integral what Weierstrass says is (via Google translate) "The integral ⁠$\textstyle {\color {Sepia}\int _{0}^{\infty }{\frac {d\lambda }{1+\lambda ^{2}}}}$⁠ is known to be equal to ⁠$\color {Sepia}{\tfrac {\pi }{2}}$⁠; but it is sufficient to know that it has a finite value, which can be shown as follows." And then later on the page says, "If we now denote the definite integral ⁠$\textstyle \color {Sepia}\int _{-\infty }^{+\infty }{\frac {d\lambda }{1+\lambda ^{2}}}=4\int _{0}^{1}{\frac {d\lambda }{1+\lambda ^{2}}}$⁠ by ⁠$\color {Sepia}\pi$⁠, the value of ⁠$\textstyle \color {Sepia}\int x^{n}dx$⁠ in the sense explained above is equal to ⁠$\color {Sepia}2\pi i$⁠ for ⁠$\color {Sepia}n=-1$⁠ and equal to zero for any other integer value of ⁠$\color {Sepia}n$⁠." I guess this is sort of a definition of π, but it seems a lot more off-hand than implied by our language. (The claim was added in July 2015 by Slawekb/Sławomir Biały.) –jacobolus (t) 19:26, 25 August 2024 (UTC)

This seems consistent with the language in the article, but perhaps the definite article should be replaced by the indefinite: "...adopted as a definition...". For what it's worth, Hardy (1908, Course in pure mathematics) explicitly says "If we define $\pi$ by the equation $\textstyle {\frac {1}{2}}\pi =\int _{0}^{\infty }{\frac {dt}{1+t^{2}}}$", without sourcing this to Weierstrass. Tito Omburo (talk) 20:14, 25 August 2024 (UTC)

I guess the way I read Weierstrass's paper is more like "here's an integral which equals π, which I assume every reader already knows how to define, so where convenient we can substitute the symbol π for the integral". I don't get the implication of something like "We shall define the constant π to be the result of this integral ...". YMMV. –jacobolus (t) 20:20, 25 August 2024 (UTC)

New algorithm for calculating Pi

While I'm competent in math, I'll leave this here for others to digest and incorporate into this article:

https://www.scientificamerican.com/article/string-theorists-accidentally-find-a-new-formula-for-pi

--Hammersoft (talk) 13:05, 4 September 2024 (UTC)

What do you mean? 69.166.117.13 (talk) 13:47, 15 September 2024 (UTC)