Talk:History of π

Why is Shanks listed here twice, with the same number of digits, with two different dates? Jaysbro 18:50, 2 November 2005 (UTC)


 * Possibly a mixup because "it took him 15 years to calculate"? The year I get when I look elsewhere is 1874, so I'll take out the other one. -- Rmrfstar 08:30, 3 November 2005 (UTC)

Who said Archimedes did it?
Can anybody tell me something about this 211875/67441 = 3.14163...? Where it comes from? --JustUser 17:11, 28 November 2005 (UTC)

There's an excellent history of maths resource here: http://members.aol.com/jeff570/ the constants page (which includes pi) is http://members.aol.com/jeff570/constants.html -- Bad_germ 20:25, 12 February 2006 (UTC)

Table removed to page Chronology of computation of π, including this blow! Still, its just copied. --JustUser 12:46, 9 November 2006 (UTC)

Page title
I feel that 'History of Pi' would have been sufficient as it implies 'human knowledge' (History is, after all, a field of human knowledge).Zero sharp 00:39, 15 March 2006 (UTC)


 * "History of pi" sounds to me like info regarding how pi came into existence, which I find to be strange because pi is a mathematical constant and mathematical constants are discoveries, not inventions. Georgia guy 00:40, 15 March 2006 (UTC)


 * History of pi was good enough for Petr Beckmann; it's good enough for me. On the metaphysical point, if history of North America and history of physics exist, why not history of pi? the ontology is much the same. Septentrionalis 00:52, 15 March 2006 (UTC)


 * I like the shorter title more. The long title may imply that pi is also known to extraterrestrials and God, and we only discuss what is known about pi to human beings. I would suggest the article be moved back to the short title. Oleg Alexandrov (talk) 00:53, 15 March 2006 (UTC)


 * "History of pi" is better, for reasons that have been articulated well enough above. Melchoir 03:14, 15 March 2006 (UTC)


 * I have moved this article and talk page to History of pi. -lethe talk [ +] 03:17, 15 March 2006 (UTC)

stubby new section
I've just added a new section, so that this article contains at least some information on its topic. More is needed. Michael Hardy 02:41, 21 March 2006 (UTC)


 * I like the contents you put, instead of just copy-pasting from history of numerical computations of &pi;. It shows very well that the two aspects are not the same, although of course related. I am quite sure that enough material can be found to make this page a "big" and interesting one, without focussing too much on the "hunt for digits". &mdash; MFH:Talk 14:03, 21 March 2006 (UTC)

Page title
Is there any objection against moving this to History of &pi;?

(I vaguely remember a related discussion on Talk:pi but I cannot find it anymore; and maybe some "special character" issues have changed context over the past years.) &mdash; MFH:Talk 14:06, 21 March 2006 (UTC)


 * The software now allows history of &pi; to be used as the title. Again.  An earlier software change made that impossible.  I'll move the article back to history of &pi;. Michael Hardy 22:09, 21 March 2006 (UTC)

Madhava
The article says:


 * The Indian mathematician and astronomer Madhava of Sangamagrama in the 14th century found this infinite series expansion of &pi;:


 * $$\pi = \sqrt{12}\left(1 - {1 \over 33} + {1 \over 532} - {1 \over 733} + \cdots\right).$$

There is a comment in the series that says. That is a good question. I strongly suspect that there is an error here, since the value of the expression given is actually 3.3609. One would expect the 532 term to be more like 150 or so. -- Dominus 01:31, 28 March 2006 (UTC)


 * Yes, it turns out it was incompetently transcribed, and should have been:


 * $$\sqrt{12}\sum_{i=0}^\infty {{(-1)}^i \over 3^i(2i+1)}$$


 * giving the first few terms as:


 * $$\sqrt{12}\left(1-{1\over 3\cdot3}+{1\over5\cdot 3^2}-{1\over7\cdot 3^3}+\ldots\right)$$


 * so you can see how the error occurred. I will fix it shortly. -- Dominus 01:43, 28 March 2006 (UTC)

25/8
The article says:


 * As early as the 19th century BC, Babylonian mathematicians were using π = 25/8, which is within 0.5% of the exact value.

This is factually incorrect, since the error is actually 0.528%. -- Dominus 01:53, 28 March 2006 (UTC)


 * i think it useful/interesting to know that by the 19th century BC Babylonian mathematicians were within 0.5% of the correct value. i suggest that instead of deleting the reference to this, to change the number to the more precise one. i did not confirm the calculation, i am assuming that it was done in good faith and that it is correct. i will make the change to the article accordingly. uri budnik 08:49, 29 March 2006 (UTC)

Wow some of you need to learn to round... .528 rounds to .5... hence not "factually incorrect" more like "only accurate to one significant figure" does that extra digit really matter I mean heck anyone with the wherewithall could just go and calculate the error... it's not hard, the point was to accent that the Babylonian's got it darn close.


 * You're wrong. "Within 5%" means LESS THAN 5%. Michael Hardy 19:25, 24 April 2006 (UTC)

Kashani
The exact value of Kashani's approximation is only interesting if his value is given in base 60; we have the first 16 decimal digits already. Septentrionalis 00:37, 1 April 2006 (UTC)

Merge thease three together
Shouldn't articles

History of π and History of numerical approximations of π

be merged into the article of pi?

A lot of informations repeats.


 * I don't think so. There are lots of articles related to pi; see list of topics related to π. Michael Hardy 20:46, 22 May 2006 (UTC)


 * We need multiple articles to hold the detail, but the current structure with multiple overview articles is clearly redundant. I am working on a rewrite of the main &pi; article that incorporates 90% of the relevant information from all the separate history articles, as well as some information that is missing, in a smaller space. It should be ready for upload soon, but I'm in the middle of an exam period, etc... Fredrik Johansson 10:30, 23 May 2006 (UTC)

Series
It says in the article: $$\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots \pm \frac{1}{2n -1}$$ If so, then wouldn't that mean that $$\pi = 4\sum_{n=1}^\infty\frac{(-1)^{n-1}}{2n-1}$$ is correct? I hope someone answers! --EdBoy 04:31, 19 August 2006 (UTC)
 * Yes, of course it's correct. Septentrionalis 06:54, 19 August 2006 (UTC)
 * The first formula is not correct; the right-hand side ends after finitely many terms and hence only gives an approximation for &pi;, so the equals sign is wrong. Further, the $$\pm$$ sign is used carelessly, suggesting that it wouldn't matter which sign you choose for the terms. Fredrik Johansson 08:10, 19 August 2006 (UTC)
 * True, it needs terminal dots. I'm not sure the plus/minus is seriously misleading; EdBoy read it correctly. Septentrionalis 22:14, 19 August 2006 (UTC)

History of the notation
So how did people refer to the value of pi before the use of the symbol &pi;? Jake 22:01, 14 March 2007 (UTC)

Logical inconsistency
"In 1761, Johann Heinrich Lambert showed that π is an irrational number by showing that tana is irrational if a is rational, and since tanπ / 4 = 1, it follows that π is irrational."

There is a logical inconsistency in this statement. It has to be shown that tana is rational if a is irrational for the tanπ / 4 = 1 proof to work. Pi is an irrational number, 1/4 is rational. I'm not switching the wording around because I do not know what the original proof is. Can someone who does know change this?

--Danshil 01:02, 2 May 2007 (UTC)


 * You're mistaken. The article is right.  It says:
 * If a is rational then tan(''a') is irrational.
 * In other words:
 * If P then Q.
 * Not Q.
 * Therefore not P.
 * Michael Hardy 02:27, 2 May 2007 (UTC)
 * Not Q.
 * Therefore not P.
 * Michael Hardy 02:27, 2 May 2007 (UTC)
 * Michael Hardy 02:27, 2 May 2007 (UTC)

Somewhat controversial move
I discovered a well-written history of pi at User:Fredrik/Pi and put that into Pi. Given that it's more complete and better-written than this entire article (was), I simply redirected the article to that section. If someone at some point wants to write a more complete (and well-referenced) history of Pi than is featured in that article, I wouldn't be opposed to that. —Disavian (talk/contribs) 00:05, 28 October 2007 (UTC)