Talk:Pi

message: Towards the end of the lead we say:
:In modern mathematical analysis, it is often instead defined without any reference to geometry; therefore, it also appears in areas having little to do with geometry, such as number theory and statistics.
That therefore makes no sense. Rather,
:Because it appears in areas having little to do with geometry, such as number theory and statistics, it is possible to define it without any reference to geometry, as is usually done in modern mathematical analysis.
However, I will not make that change; I hope someone else can come up with a better wording. Nø (talk) 08:42, 8 December 2023 (UTC)
replies: text: In that context, because makes as little sense as therefore. How about Because it appears in areas having little to do with geometry, such as number theory and statistics, it is convenient to define it without any reference to geometry, as is usually done in modern mathematical analysis.? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:49, 8 December 2023 (UTC)

text: I've edited it using "and" rather than asserting causation in either direction; the body of the article doesn't, as far as I can tell, assert one caused the other so our WP:LEAD summary shouldn't. I couldn't see that "often" was supported by the body of the article so I dropped that too, rather than replace it with "usually". NebY (talk) 14:49, 8 December 2023 (UTC)
replies: text: Good solution. Tito Omburo (talk) 16:16, 8 December 2023 (UTC)

text: This 'often' or 'usually' is probably a supportable claim, but "can be defined" also seems fine. –jacobolus (t) 19:07, 8 December 2023 (UTC)
replies: text: Yes indeed, quite possibly supportable but maybe not worth the trouble? Thanks, both, and to Nø for spotting the problem. NebY (talk) 17:56, 9 December 2023 (UTC)
thread_title:  Therefore ... 

message: Though pi has been mentioned in many Egyptian and Babylonian civilizations' sources, pi was first said to be discovered by the Archimedes of Syracuse in Greece more than 2200 years ago around 250BC. The Chinese mathematicians approximated π to seven digits, while Indian mathematicians (especially Aryabhata during the Gupta dynasty achieved a five-digit approximation using geometrical techniques. William Jones then devised the Greek symbol π to represent pi in 1706. It was then popularized by Leonhard Euler in 1737. Georges Buffon devised a method to calculate the value of pi based on probability.
The invention of calculus allowed the calculation of the digits of pi up to a hundred digits which was sufficient for scientific purposes. Aanchal.Mishra20 (talk) 04:37, 9 March 2024 (UTC)
replies: text: I don't understand what you are getting at. The article already discusses all of this in greater detail. –jacobolus (t) 06:52, 9 March 2024 (UTC)
thread_title:  Discovery and Invention of Pi 

message: In the section History->Infinite Series there is a mistake in the equation
$\pi/4=5 \arctan(1/7)+2\arctan(3/77)$.
This should be replaced by the correct version used by Euler
$\pi/4=5 \arctan(1/7)+2\arctan(3/79)$,
i.e. 79 instead of 77 in the denominator of the second arctan. 134.2.251.3 (talk) 18:11, 14 March 2024 (UTC)
replies: text: Tito Omburo (talk) 18:20, 14 March 2024 (UTC)
replies: text: Thank you! 2A02:3038:600:F6A4:1049:1828:E0EC:9F34 (talk) 18:25, 14 March 2024 (UTC)

text: Thanks. I believe I was responsible for that typo. –jacobolus (t) 18:25, 14 March 2024 (UTC)
thread_title:  Edit request: Mistake in arctan equation 

message: In the definition using integral, the function of the upper half of the circle is in the denominator. It should just be int_{-1}{1}sqrt(1-x^2)dx if I’m not mistaken. Marsi Viktor (talk) 22:14, 4 April 2024 (UTC)
replies: text: This is the integral for arc length of the circle, not area.  Tito Omburo (talk) 22:25, 4 April 2024 (UTC)
replies: text: You are right, sorry :) Marsi Viktor (talk) 08:06, 5 April 2024 (UTC)
thread_title:  Mistake in definition