Talk:Pi

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)

Propose for the change of Description

As we know π is an Irrational number meaning it cant be expressed in a ratio.Therefore I propose to change to change the article description to "Irrational Number, approximately 3.14" Uncharted 430 (talk) 06:49, 23 December 2024 (UTC)

It's a real number. It's a complex number with imaginary part 0. It's an irrational number. It's a transcendental number. But see WP:SDNOTDEF: the short description is not the place to give as precise a definition as we can. Short descriptions are mainly used for disambiguating searches on mobile devices: when you search for a term like pi, you will get a lot of results, and it's helpful to have a brief and easy-to-read blurb that clarifies which topic each search term is about. So the current description "Number, approximately 3.14" does that, because it tells you it's the article about the number and not say the article about the Greek letter or Pi (film) or any number of other topics with the letters pi in them. Putting the word "irrational" doesn't make it easier to tell which search result you want. It might be confusing to non-mathematicians who don't know about irrational numbers. It might cause pedants to tell us that well actually it's transcendental and we should say that instead, and then be even more confusing to non-mathematicians. And merely for the reason that it makes the short description less short, it makes it less quick to read and find among the other short descriptions of all the other pi search results. So I don't think this would be an improvement. —David Eppstein (talk) 07:01, 23 December 2024 (UTC)

@David Eppstein Thanks for your efforts.But shouldnt it be at the least categorized as Irrational number Uncharted 430 (talk) 07:04, 23 December 2024 (UTC)

In the categories at the bottom of the page? No. There, it is categorized as a real transcendental number. The way Wikipedia's category system works, when an article would belong to both a more general category and a more specific subcategory, we only put it into the more specific subcategory. Category:Real transcendental numbers is a subcategory of Category:Irrational numbers, so articles in Category:Real transcendental numbers should not be placed in Category:Irrational numbers. Instead, people looking at the irrational number category should explore all its subcategories to find the articles in them. —David Eppstein (talk) 07:09, 23 December 2024 (UTC)

@David Eppstein Thanks.Much appreciated Uncharted 430 (talk) 07:11, 23 December 2024 (UTC)

First sentence of the article already contains potential weasel word.

> The number "Pi" is a mathematical constant that is the ratio of a circle's circumference to its diameter ...

The opening sentence already implies a statement that would require extraordinary proof to stand.

Has there been conclusive astronomy / satellite observation of the farthest / oldest reaches of our Universe, to confirm the constancy of Pi thoughout the cosmic ages, from Big Bang to this day? [Note that significant effort was made in satellite astronomy just to confirm the constancy of Speed of Light and the Fine Structure Constant - indeed finding them to be constant to the full extent of achiveable instrument accuracy.]

After all, Pi is fundamentally an empirical ratio, as there was no circle in the heads of philosophers and mathematicians before they saw one in the dust of Babylon and Athens.

Thus the abstraction of Pi as a constant ratio of an abstract circle's diameter vs circumference can only follow after the circle as a pyhsical reality is confirmed to be based on a constant Pi throughout the cosmic ages. The burden to provide that confirmation / proof is on those who make the claim of constancy. 94.21.237.182 (talk) 13:47, 31 December 2024 (UTC)

Pi can be defined without reference to geometry, as the last paragraph of the lede mentions. Tito Omburo (talk) 14:50, 31 December 2024 (UTC)

π is not dependent on physical reality. Our discussion of circumferences and diameters of circles in this context is related to abstract Euclidean space. It is incorrect to say that "π is fundamentally an empirical ratio". –jacobolus (t) 16:58, 31 December 2024 (UTC)

There are no weasel words there. π is a mathematical object in analysis and Euclidean geometry. Its utility in physics is a separate issue. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 20:00, 31 December 2024 (UTC)

Certainly no weasel words, but arguably a lack of context. As it says in the subsection "Definition":

This definition of π implicitly makes use of flat (Euclidean) geometry

However, I strongly believe this is exactly as it should be. Lay readers will generally understand the first sentence quite easily, and including e.g. "in Euclidean geometry" in that sentence would make it less, not more, understandable. Nø (talk) 10:49, 1 January 2025 (UTC)