Talk:Pi

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A-class review

I've nominated this article for A-class review through Wikipedia:WikiProject Mathematics. I'm transcluding it below. Please help me address/respond to their concerns. I'd eventually like to nominate this article for FA. —Disavian (^talk/_contribs) 19:25, 12 December 2007 (UTC)

Baffling and unnessisary links in the External Links section

Such as the pi is wrong! link - amusing and irreverent as this may be, it's utterly unnessisary and reads like the type of dross that me and my friends used to write at the back of Math class when we were 14. It doesn't really deserve a place on this page because it adds nothing to the discussion of what Pi is, does or is useful for. —Preceding unsigned comment added by 87.194.49.123 (talk) 19:00, 4 May 2008 (UTC)

I agree, the links need to be sorted, some just repeat themselves (Bonzai273 (talk) 04:39, 24 May 2008 (UTC))

The "π Is Wrong!" article makes a serious point, and the link to it should be kept. —Preceding unsigned comment added by 86.130.60.154 (talk) 15:55, 6 June 2008 (UTC)

Redirect to Pi

3.1415926535897932384626515 redirects to Pi. Although this is not the actual value of Pi, it may seem so at the beginning, but 515 is to be replaced with 832 (3.1415926535897932384626832795) Androo123 (talk) 00:41, 23 May 2008 (UTC) I eat PI

Well I decided to see if I could figure out exactly what pi was and figured everyone is doing it wrong... it shouldn't be explained in a decimal try explaining a rational number... rationally... but sadly google's calculator ran out of compatibility and then my calculator did the same but the closest I was able to get it was somewhere in between (352/(squareroot(12554.09993))) and (352/(squareroot (12554.09995))) if anyone needs explanation squareroot - means to take the square root of the following character or number in a shiny set of ()'s / - means divided by or also making a fraction of the characters or numbers before and after it —Preceding unsigned comment added by 206.74.75.177 (talk) 02:37, 13 January 2009 (UTC)

Hex

Hexadecimal 3.243F6A8885A308D31319, as stated in article does appear as Hex. I have seen Hex. when programming. 0, I believe is a null, the lowest value; not zero as in a number line; and should not appear in a decimal series. Coding of Hex., e.g, on OS MVS/XA uses a letter and number on the bit-map, no series of numbers. Please check. Your table might only apply to ASCII?

ASCII:

http://www.asciitable.com/

EBCDIC:

http://www.legacyj.com/cobol/ebcdic.html

Notice, in EBCDIC there are two for the bit, usually expressed using two lines, one line over the other line. To confirme check with a mainframe system programmer.

Thanks. —Preceding unsigned comment added by 58.110.206.219 (talk • contribs) 11:11, 28 May 2008; moved from Talk:Pi/to do by —Disavian (^talk/_contribs) 02:09, 29 May 2008 (UTC)

0 exists in all bases. The way it's expressed in COBOL is irrelevant to the purposes of this article. —Disavian (^talk/_contribs) 02:11, 29 May 2008 (UTC)

Unsourced addition

I reverted the following addition to the article:

However, by computing this series in a somewhat more clever way by taking the midpoints of partial sums, it can be made to converge much faster. Let

$\pi _{0,1}={\frac {4}{1}},\pi _{0,2}={\frac {4}{1}}-{\frac {4}{3}},\pi _{0,3}={\frac {4}{1}}-{\frac {4}{3}}+{\frac {4}{5}},\pi _{0,4}={\frac {4}{1}}-{\frac {4}{3}}+{\frac {4}{5}}-{\frac {4}{7}},\cdots \!$

and then define

$\pi _{i,j}={\frac {\pi _{i-1,j}+\pi _{i-1,j+1}}{2}}$ for all $i,j\geq 1$

then computing $\pi _{10,10}$ will take similar computation time to computing 150 terms of the original series in a brute force manner, and $\pi _{10,10}=3.141592653\cdots$, correct to 9 decimal places.

As no reference is given, this appears to be original research. If someone can find a source, please feel free to re-instate with reference. Gandalf61 (talk) 19:48, 31 May 2008 (UTC)

It is somewhat OR in that I'm not sure whether it has ever been published. I posted an article giving this result on Usenet many years ago--you can find it by going to Google Groups and searching on "ash@sumex-aim.stanford.edu sci.math". I sent a proof via private email to Noam Elkies; we agreed that the result is valid and I'm trying to ping Noam now to see if he remembers the correspondence or can point us to a published reference.--Dash77 (talk) 20:45, 31 May 2008 (UTC)

Per a note from Noam, it appears that this is not OR but is an example of the Van Wijngaarden transformation. I am about to reinstate the deleted text with a link to that Wikipedia article, which in turn contains a link to another article that is well referenced.--Dash77 (talk) 01:05, 1 June 2008 (UTC)

Avoid peacock terms

As my simple edit ( http://en.wikipedia.org/w/index.php?title=Pi&diff=216691447&oldid=216456829 ) was reverted by someone who 'disagreed'. Allow me to explain. I didn't state than I don't think Pi is 'important', just that claiming 'importantance' is not, by itself, encyclopedic.

Please refer to Wikipedia:Avoid_peacock_terms

I leave it to someone else to now be bold.

Dr. Zed (talk) 17:58, 6 June 2008 (UTC)

In this case, the term is justified because it has been often said; so I copied the source from e for it. Dicklyon (talk) 00:10, 7 June 2008 (UTC)

Question about not being immediately obvious

"While that series is easy to write and calculate, it is not immediately obvious why it yields π." - in the discussion of 4/1 - 4/3 + 4/5 - 4/7

Why does it say this? The result is easily derived from the expansion of arctanx. I will add this in unless someone objects. Helenginn (talk) 16:32, 7 June 2008 (UTC)

I think the point is that 4/1-4/3+... is a conditionally convergent series, which means you have to be careful when manipulating it (for example it can become divergent, or converge to a different limit, if you reorder its terms). The easy derivation of the series for tan⁻¹(x) is valid for |x|<1, the region where the series is absolutely convergent, and it doesn't follow instantly that it works for x=1, even though the series does converge (conditionally) at x=1. --Trovatore (talk) 09:15, 12 October 2008 (UTC)

SVG

For anyone who can be bothered, it would be good to replace the gif at the top with an SVG. —[semicolons]— 21:18, 14 June 2008 (UTC)

Semicolons, I disagree. SVG with animation has incomplete support in browsers while GIF animations are universal and recommended.Cuddlyable3 (talk) 06:54, 25 June 2008 (UTC)

Wikipedia doesn't directly serve SVG images to the browser, they are rendered to PNG using rsvg. Animation is thus out of question, as it is supported neither by rsvg nor by PNG. — Emil J. (formerly EJ) 15:08, 25 June 2008 (UTC)

Pi calced at 3 when figuring the circ/dia ratio of a thin walled vessel.

[Re: Biblical value of Pi]

Wrong. That would make Pi exceed 3.14. As wall thickness increases, the ratio goes up, not down. —Preceding unsigned comment added by 69.122.62.231 (talk) 15:59, 18 June 2008 (UTC)

No. If the circumference C is measured on the inside edge of the brim and the diameter D is measured from the outside edge, then the ratio C⁄D is exactly π if the brim had zero thickness. But as the brim thickness increases, assuming that the outer diameter D stays the same, the inner circumference C decreases, so the ratio decreases as well. If instead we say that the inner circumference C remains the same and the outer diameter D increases, the ratio still decreases. So when measured this way, a non-zero brim thickness produces a ratio less than π. Therefore at some thickness (where the brim is about 4 inches wide), the ratio is exactly 3.0. | Loadmaster (talk) 16:49, 16 January 2009 (UTC)

Pi cropcircle

As the article is locked, I'll add it here: Crop circle repesenting pi 86.150.97.50 (talk) 17:13, 20 June 2008 (UTC)

I see the Telegraph has gone downhill.... No, it shouldn't be added to the article. — Arthur Rubin (talk) 17:55, 20 June 2008 (UTC)

Cosmological constant

Does anybody know where the formula for the cosmological constant came from? In particular, the c² denominator is not in the listed source (and not in any of the other sources I checked). Also, is ρ supposed to be the vacuum energy density? Thank you.—RJH (talk) 18:12, 22 July 2008 (UTC)

Who discovered it?

Who discovered\invented Pi?--64.79.177.254 (talk) 18:08, 22 July 2008 (UTC)

See Pi#History. The concept was known at least about 4000 years ago. No single known personal inventor can be nominated. The use of the symbol π was introduced by William Jones (mathematician) A.D. 1706, Rgds / Mkch (talk) 00:24, 24 July 2008 (UTC)

Suggestion to the registered users

Since the page is protected, I cant changes it myself. There is another identity for calculating Pi which I did not find (almost) anywhere else - not even on Mathworld. I have talked about it on my blog: http://blog.hardeep.name/math/20080725/value-of-pi/. Please consider if a link to my blog entry can be posted here. —Preceding unsigned comment added by Hardeeps (talk • contribs) 08:05, 28 July 2008 (UTC)

This formula is called a Machin-like formula, because it is a variation on the following formula discovered by John Machin in 1706:

${\frac {\pi }{4}}=4\arctan {\frac {1}{5}}-\arctan {\frac {1}{239}}$

The particular formula quoted in your blog is formula (22) at this MathWorld page. Your blog would probably not be considered a reliable source, and so linking it from a Wikipedia article would not be appropriate. You could source the formula by referencing the MathWorld page or another reliable source. However, I am not sure that this particular formula will pass the notability test, because there are so many similar formulae. I think you would have to show that this particular formula has some property that distinguishes it from other Machin-like formulae. Gandalf61 (talk) 08:39, 28 July 2008 (UTC)

History

In the History section, it says:

Geometrical period

That the ratio of the circumference to the diameter of a circle is the same for all circles, and that it is slightly more than 3, was known to ancient Egyptian, Babylonian, Indian and Greek geometers. The earliest known approximations date from around 1900 BC; they are 25/8 (Babylonia) and 256/81 (Egypt), both within 1% of the true value.[2] The Indian text Shatapatha Brahmana gives π as 339/108 ≈ 3.139. The Tanakh appears to suggest, in the Book of Kings, that π = 3, which is notably worse than other estimates available at the time of writing (600 BC). The interpretation of the passage is disputed,[24][25] as some believe the ratio of 3:1 is of an exterior circumference to an interior diameter of a thinly walled basin, which could indeed be an accurate ratio, depending on the thickness of the walls...

I believe the last sentence should have the positions of the adjectives "exterior" and "interior" reversed. I. e., the last sentence should read:

The interpretation of the passage is disputed,[24][25] as some believe the ratio of 3:1 is of an interior circumference to an exterior diameter of a thinly walled basin, which could indeed be an accurate ratio, depending on the thickness of the walls. --AjitDongre (talk) 01:09, 7 August 2008 (UTC)

Why did you not mention the name of Aryabhat from India? He is very famous for his contribution to 'pi' much before William Jones and Lambert. He was the first to realize that Pi (π) is irrational. —Preceding unsigned comment added by Dsg512 (talk • contribs) 08:20, 6 March 2009 (UTC)

Pi vs. π

This article waffles on using "pi" and using "π". This should be remedied. —Preceding unsigned comment added by Tastemyhouse (talk • contribs) 15:49, 25 August 2008 (UTC)

      I am in agreement.  Though this may not be the right place to say this, however the Greek pronunciation of "pi" needs to be updated.  Greek does not have an "i" (or "eye") in it.  iota, eeta, upsilon are all the "ee" sound making the proper pronunciation "pee".  —Preceding unsigned comment added by 199.253.174.9 (talk) 19:10, 4 December 2008 (UTC) 

Pi

Hello, sir. I happen to know the first 32 digits of Pi, if it helps the article. Any comments, feel free to leave messages on my talk page. Chris Wattson (talk) 18:25, 11 September 2008 (UTC)

We have all of the digits we need, thanks. —Disavian (^talk/_contribs) 20:21, 11 September 2008 (UTC)

Italicization

The Greek letter pi is italicized in some parts of the article, and roman in others. That needs to be fixed, but which is correct?

67.171.43.170 (talk) 02:37, 17 September 2008 (UTC)

Pi should be italicized; π should not be. Septentrionalis PMAnderson 16:58, 20 September 2008 (UTC)

Not exactly consensus, but I agree and boldly made the change throughout (in celebration of this glorious day), but e still appears italicized. Note that, as a constant, this is different from the several variables that appear italicized (d, r, etc.), although I'm not 100% sure what's proper there, either. Out of curiosity, would $\pi$ be an option for the article body? Or $e$? /Ninly (talk) 16:04, 14 March 2009 (UTC)

The rationality of Pi sequence

I have removed this material again: it is probable WP:OR, WP:PEACOCK terms, unsourced and contentious (pi is not rational). I have asked the author to discuss it here before trying to add it in again. Richard Pinch (talk) 11:36, 20 September 2008 (UTC)

Use of the symbols \approx and \approxeq

The symbols \approx and \approxeq are used apparently with the same meaning. Also, \approxeq does not appear in the list of mathematical symbols. I could not find an explanation for \approxeq, while \approx is explained in the list of mathematical symbols. I suggest to use only one symbol: \approx. An alternative is to include an explanation for \approxeq in the list of mathematical symbols. —Preceding unsigned comment added by Xelnx (talk • contribs) 07:36, 24 September 2008 (UTC)

Also, at several places = needs to be replaced by \approx (or \approxeq). —Preceding unsigned comment added by Xelnx (talk • contribs) 07:43, 24 September 2008 (UTC)

Yes, "approximately equal" should always be \approx, not \approxeq. I have replaced \approxeq with \approx in the Geometrical period section of the article. Gandalf61 (talk) 10:34, 24 September 2008 (UTC)

Misleading numeric value of 50 digits

It is misleading to show Pi to only 50 decimal places. Note the red digits, below, show how the zero (the last digit shown in black) would actually be a 1 were such a 50-decimal-place expression of Pi actually be properly written down. For instructional purposes such as here on Wikipedia, truncated expressions of Pi should ideally end on a digit where the following (hidden) digit would fall in the range of 0 to 4. This issue is resolved by expressing Pi here on Wikipedia another three digits because the digit after the 2 (shown) is a 1 (hidden).

Specifically,

Here is the value to 53 decimal places:

3.14159265358979323846264338327950288419716939937510582

Greg L (talk) 20:55, 7 October 2008 (UTC)

Noted. — Arthur Rubin (talk) 22:06, 7 October 2008 (UTC)

If the quark-splitting research at CERN is based on Wikipedia, this could be of vital importance!! ;) Ropata (talk) 08:10, 16 January 2009 (UTC)

Ropata please explain your statement. Cuddlyable3 (talk) 13:45, 16 January 2009 (UTC)

Sorry, just being sarcastic. Actually on second thought Greg_L has a point, but I think it is "tidier" to truncate at 50 digits, than to round the last digit or extend to 53. There are many many sources on the web for longer expansions of $\pi$. -- Ropata (talk) 10:40, 26 January 2009 (UTC)

Ropata, perhaps in your effort to regale us with your quarkish humour you have missed Greg_L's point. It is simply wrong to truncate at any number of places where if correctly rounded the last digit would be different. Correctness trumps over your idea of "tidiness". Neither Greg_L nor anyone else is proposing to extend the value in the article to 53 digits. Cuddlyable3 (talk) 11:35, 27 January 2009 (UTC)

Cuddlyable3, Greg_L really is proposing exactly that: "This issue is resolved by expressing Pi here on Wikipedia another three digits". Which I consider quite pointless, hence the sarcasm. Who cares about a theoretical rounding of the last digit.. -- Ropata (talk) 01:59, 31 January 2009 (UTC)

I read Greg's words "is resolved..here" to mean on this Talk page, but Greg may correct me if I have misread his post. Ropata, maybe you care more about justifying your sarcasm than whether the digit is correct or wrong but Greg and I certainly agree that it must be correct. Our purpose is improving the main article so why are you posting at all if you think that is pointless?

Truncation is admissible with trailing ellipsis so this is correct: pi = 3.1415... Cuddlyable3 (talk) 10:55, 31 January 2009 (UTC)

I'm having a really hard time wondering why there is all this discussion. If the 50th digit is a zero, then so be it. As long as we don't say "rounded to 50 places", it should be no problem at all. "The first 50 digits of pi are:" or "the value of pi truncated at 50 decimal places is:" would be perfectly fine. Anybody who doesn't understand the difference between "rounded" and "truncated" isn't going to wonder about that zero; and anybody who does know the difference already knows that they're not going to rely on the value shown in this article anyway - most especially not if they have any reason to believe they even need 50 places. I would also note that this was re-opened several months after no discussion on the topic.  Frank  |  talk  00:37, 1 February 2009 (UTC)

The perfectly fine statements above are indeed correct. However stating a numerical value of pi carries the assumption and obligation that the digits printed are as accurate as they can be. That by default i.e. with no qualification such as "truncated" nor use of ellipses means correctly rounded at the last place. The subject of how many digits to show of an irrational number is moot since the consensus is what we have. Wikipedia has lots of information that someone may already know or never need to know, so no surprises here. See WP:TIND Cuddlyable3 (talk) 14:47, 5 February 2009 (UTC)

delimiting values every five digits

This technique of delimiting values every five digits is amateurish. The international standard (according to BIMP: 5.3.4 Formatting numbers, and the decimal marker, and NIST More on Printing and Using Symbols and Numbers in Scientific and Technical Documents: 10.5.3, Grouping digits is that digits should be grouped in threes. Greg L (talk) 21:05, 7 October 2008 (UTC)

It may not meet with professional standards, but it's much more sensible than threes. For what it's worth, I have never seen a number of more than 15 digits in threes. We should be dealing here with mathematical standards, rather than engineering or physics. — Arthur Rubin (talk) 21:58, 7 October 2008 (UTC)

It is the international standard and is extraordinarily common. Greg L (talk) 22:04, 7 October 2008 (UTC)

P.S. If you don’t believe me that physicists delimit numeric equivalencies every three digits, check out this at the NIST: Energy Equivalents Calculator . Try any other conversion; they’re all delimited the same way. And, these guys know physics. Greg L (talk) 22:08, 7 October 2008 (UTC)

This is a mathematics article. What care we for physics standards? And the number of physics articles which have more than 12 decimal places for a number which is not a defined constant is probably fewer than the number of decimal places we have in this article. — Arthur Rubin (talk) 22:11, 7 October 2008 (UTC)

For all purposes—especially mathematics—the international standard has always been to delimit every three digits. The only thing that varies is what sort of delimiter one uses and what the decimal marker is. Some countries use spaces before and after the decimal marker and the decimal marker is a comma. Regardless of whether it is commas or spaces for delimiting before the decimal marker, or spaces after the decimal marker, the delimiting—both before and after the decimal marker—is always every three digits. See BIMP: 5.3.4 Formatting numbers, and the decimal marker. Delimiting every five digits is thoroughly non-standard. Pi needs to follow the way numbers are used throughout Wikipedia. See also Natural logarithm. Greg L (talk) 22:25, 7 October 2008 (UTC)

Fixed, now, in natural logarithm. See e (mathematical constant). — Arthur Rubin (talk) 22:33, 7 October 2008 (UTC)

• Please don’t disrupt Wikipedia to make a point WP:POINT. What you are doing amounts of vandalism. The BIPM, the ISO, and the NIST all require three digits. You are wrong. Greg L (talk) 22:42, 7 October 2008 (UTC)

There are hundreds of books that list pi split into 5-digit groups. Also hundreds in 3-digit groups. I'd go with the majority. Dicklyon (talk) 22:47, 7 October 2008 (UTC)

Yes, Greg, please stop this. We follow usage in the literature, not what some standards body has arbitrarily promulgated. --Trovatore (talk) 22:50, 7 October 2008 (UTC)

Same applies to e in 5-digit vs. e in 3-digit groups. Dicklyon (talk) 22:51, 7 October 2008 (UTC)

39 digits is incorrect

Where the article currently says as follows:

For example, a value truncated to 11 decimal places is accurate enough to calculate the circumference of the earth with a precision of a millimeter, and one truncated to 39 decimal places is sufficient to compute the circumference of any circle that fits in the observable universe to a precision comparable to the size of a hydrogen atom.

…this is obviously in error regarding 39 digits. The supposed citations—if they really say as much—are in error. There is all sorts of bunk out there. Wikipedia’s own Universe article states as follows:

Astronomical observations indicate that the universe is 13.73 ± 0.12 billion years old and at least 93 billion light years across.

Any child can do the math: Circumference of universe 93×10⁹ ly × Pi = 292×10⁹ ly = 2.764×10²⁷ m divided by 1.15×10³⁷ = 2.4 Å (the diameter of hydrogen atom). Greg L (talk) 21:24, 7 October 2008 (UTC)

Given that the number you used is a lower bound on the size of the universe, 37 digits is almost certainly not enough. But 39 is almost certainly enough. No need to put your WP:OR into the article. Dicklyon (talk) 22:24, 7 October 2008 (UTC)

• Fallacious argument. The value for the size of the universe comes right out of our own Universe article. It’s pretty much the same value as in the Observable universe article. The Universe article makes it clear that sizes even twice this big are urban legends. If you can cite a much value that withstands scrutiny, cite it. Otherwise, accept that the measurements of the universe are certainly not in error by two orders of magnitude. Greg L (talk) 22:29, 7 October 2008 (UTC)

It's not our job to try to justify a tighter bound than the 39 digits found in a reliable source, even if we can. Dicklyon (talk) 22:35, 7 October 2008 (UTC)

• Your citation is demonstrably false and is beyond worthless. It would require a universe be 100 times larger than the values accepted for use in two of Wikipedia’s articles. Greg L (talk) 22:37, 7 October 2008 (UTC)

You haven't showed that it's false, only that you have found a tighter bound that you prefer. But that's WP:OR. Dicklyon (talk) 22:52, 7 October 2008 (UTC)

I have no opinion on 39 versus 37, but to change it to 37 while keeping the source which says 39 is contrary to the verifiability policy. What we have in the article should agree with the source we give. And, as Dicklyon says, if 37 works, then 39 works as well — leaving a comfortable margin for error. siℓℓy rabbit (talk) 22:57, 7 October 2008 (UTC)

Honestly I'd question whether it makes sense to include this silly calculation at all. The calculation really doesn't make much sense even on its own terms. Space may be asymptotically flat, but it isn't flat to 30 significant digits. So if you wanted to know the circumference of the observable universe to 30 significant figures, or even fifteen, you wouldn't do it by multiplying the diameter by π; you'd have to do something more complicated. --Trovatore (talk) 21:08, 10 October 2008 (UTC)

The main point of this argument is of course that there is no practical geometry-motivated application for computing millions of digits of pi. Perhaps we should just say this instead. Dcoetzee 00:09, 11 October 2008 (UTC)

That's the underlying point of the info from the cited source, yes, but is hardly the point of this argument. This argument is about WP:V vs. WP:RS. Dicklyon (talk) 04:55, 11 October 2008 (UTC)

By "this argument" I meant the argument described by the text under discussion. The idea was to suggest a compromise, since it's entirely irrelevant exactly how many digits of pi are needed for this particular application. Dcoetzee 09:31, 11 October 2008 (UTC)

10000 digits of Pi

I know 10,000 digits of pi, if it helps. Disliker of humanities 08:53, 12 October 2008 (UTC)

Not for me to say whether it might help something, but as far as this article goes, I'm afraid not. If we wanted to put in 10,000 digits, or even a million, we could easily look them up, or generate them. The consensus is that this would not be an improvement to an encyclopedia article. Impressive memory feat though! --Trovatore (talk) 09:00, 12 October 2008 (UTC)

Vandalism

This article is getting a depressing amount of vandalism from IPs. I thought it was semi-protected? Richard Pinch (talk) 21:55, 14 October 2008 (UTC)

It was, but the protection expired. I've renewed it. Thanks for the note. --Ckatz^chat_spy 22:23, 14 October 2008 (UTC)

Thanks for that. I was confused, as it still had the little padlock icon. Richard Pinch (talk) 05:45, 15 October 2008 (UTC)

Higher analysis

Is it worthwhile to mention the following derivation?

$e^{i\pi }+1=0$

$e^{i\pi }=-1$

$i\pi =log(-1)$

$\pi ={\frac {1}{i}}\,log(-1)$

$\pi =-i\,log(-1)$

for the principal value of log(–1).  | Loadmaster (talk) 16:20, 9 December 2008 (UTC)

Do you have a reliable source that puts it that way? If not, it's just your own trivial rearrangement, not really useful. Dicklyon (talk) 18:03, 9 December 2008 (UTC)

Yes, that's correct, it is my own trivial rearrangement, showing that π is equal to a complex log. Perhaps something like this more rightfully belongs at List of formulae involving π. | Loadmaster (talk) 21:27, 9 December 2008 (UTC)

This is not a valid derivation of the principal value of log. Try starting with $e^{3i\pi }+1=0$, do the same manipulations, and you'll end up with the same RHS and a different LHS. Fredrik Johansson 21:54, 9 December 2008 (UTC)

Not again!

A page constructed by total nerds for an encyclopeadic article for someone looking for the quick explanation, not 10 complex mathematical theories and formulas! Please, replace it. It is incredibly annoying for someone who could not understand the mathematical formula who is in Year 9 in the 2nd top group with one of the highest levels in the class. It is totally pointless and gawky. Koshoes (talk) 19:01, 25 January 2009 (UTC)

This page may be more use to you. Cuddlyable3 (talk) 21:59, 25 January 2009 (UTC)

Seconded. There is absolutely no need for you to attempt to justify your outrage at the "nerdiness" of this article with your dubious academic qualifications. I am sure there is a stylistic guideline somewhere against shameless self-aggrandizement. 70.233.173.118 (talk) 05:57, 29 January 2009 (UTC)

Carl Sagan

Why not including some reference to the presence of pi in Sagan's book "Contact"??? It's pretty important to the story! —Preceding unsigned comment added by 143.107.178.145 (talk) 18:03, 30 January 2009 (UTC)

You could add that under the heading Pi in popular culture, but I suggest only as a reference. WP:UNDUE. Cuddlyable3 (talk) 11:08, 31 January 2009 (UTC)

Error in statement of physics

The article states that Heisenberg "shows that the uncertainty in the measurement of a particle's position (Δx) and momentum (Δp) can not both be arbitrarily small at the same time". This is not true and is not derivable in quantum mechanics. The derivable result is that the product of Δx bar and Δp bar cannot both be arbitrarily small at the same time. This is true not just for QM but for any wave mechanics - this applies to all 'wavicles'.

Δx bar is the average of a set of measurements of position, either of the same particle in subsequent measurements or of a set of particles at the same time. It is easy to see that this cannot hold for a single particle. Prepare a beam of electrons with precise momentum. The beam is necessarily spread out because of the corresponding uncertainty of position. Then measure any one electron's position to arbitrary accuracy. At that time you have a precise momentum and position.

The article should state that Heisenberg showed that a set of measurements of position and momentum will have an accuracy not better than h / 4 pi. 212.167.5.6 (talk) 16:32, 4 February 2009 (UTC)

When you say "prepare a beam" and "measure...position to arbitrary accuracy" are you describing a physical demonstration or a thought experiment? If it's a physical demonstration please tell how you achieve the steps described. If yours is a thought experiment, have you offered anything more than a conjecture about how an uncertainty in position might arise? The article Uncertainty principle refers explicitly to a single particle thus:

When the position of a particle is measured, the particle's wavefunction collapses and the momentum does not have a definite value. The particle's momentum is left uncertain by an amount inversely proportional to the accuracy of the position measurement.

That supports the statement to which you object. Cuddlyable3 (talk) 15:55, 5 February 2009 (UTC)

In popular culture

In the In Popular Culture section, the following should be added: "On November 7, 2005, Kate Bush released the album, Aerial. The album contains the song "π" whose lyrics consist solely of Ms. Bush singing the digits of π to music, beginning with "3.14 . . ." —Preceding unsigned comment added by NE Voter (talk • contribs) 18:09, 15 February 2009 (UTC)

A few years ago, the article contained a very long list of such random "in popular culture" sightings. There are so many that a trying to create a list of them all is essentially useless -- each individual example does not contribute relevant encyclopedic information about pi. Rather, to avoid the slippery slope starting again, I think the two last sentences in the current "in popular culture" section should be culled. –Henning Makholm 21:22, 15 February 2009 (UTC)

As an inclusionist I respectfully disagree and say hang the slippery slope! Notable appearances of pi in popular culture are, by definition, not random but related in a specific way. If the list gets too long the solution is to fork it to its own article, like the many we have at [1]. Cuddlyable3 (talk) 21:36, 15 February 2009 (UTC)

Who said we're dealing with "notable appearances of pi"? Most of the appearances that people typically want to add strike me as definitely not notable in their relation to the mathematical constant. The album referenced here may or may not be notable in its own right, but its connection to pi still isn't. Connections between two notable topics need not be equally notable from both ends. For example, it is a notable fact about John Lennon that he was killed in New York City, but it is not a notable fact about NYC that it is where John Lennon was killed. –Henning Makholm (talk) 16:12, 14 March 2009 (UTC)

I agree with Henning. — Emil J. 13:23, 16 February 2009 (UTC)

I'm all too aware of the tendency for a "___ in popular culture" section to degenerate into a list of every passing mention of a phenomenon in every trivial television episode, etc., but I do think that there should be a Popular Culture section, particularly for Pi which is, as the article rightly notes, just about unique in its hold on mathematicians and non-mathematicians alike (maybe the numbers 3 and 7 compare, but that's about it). A scholarly, encyclopedia-worthy discussion of the phenomenon of π and the non-mathematician world is well called for. We've just got to be vigilant about the "my reference, too" approach and remove the fluff.

And that "Pi Plate" is wonderful. I want one. --Minturn (talk) 17:11, 18 February 2009 (UTC)

What I object to is just the my-reference-too fluff. I agree that the general fact that many references to pi occur in popular culture is of encyclopedic interest, and there should be a section for it as soon as we can find reliable secondary sources for a discussion of it. It is just the particular examples we should avoid (except insofar as they in fact support a general point to be made). –Henning Makholm (talk) 16:13, 14 March 2009 (UTC)

history

there is this tale i've heard, several hundred years ago someone tempted to calculate pi with more decimals than have had been calculated before him (the number of which averaged 17). so he has drawn circles on the ground for like twenty years, and one day a soldier stepped on his work, so he burst out toward the ignorance of the soldier and was killed on the spot.

i think he had calculated around 600 decimals, but he had done an error after the 200th or so, so the decimals were all right except the ones coming after that last-good one.

p.s. sorry for the lack of references everyone, but i think it's better to start a discussion about it and claim such an history exists than to not give anything just because one hasn't the time to do it. Twipley (talk) 18:59, 7 March 2009 (UTC)

This is a garbled version of story of Archimedes who according to Plutarch was killed in similar circumstances during the Siege of Syracuse (214–212 BC). According to tradition, his last words are supposed to have been, Do not disturb my circles. Archimedes was one of the first to do systematic work on approximations on pi, but his best-known result is that pi lies between 223/71 and 22/7, which gives only 2 decimals. He definitely was not concerned with computing decimals, since decimal fractions were only invented long after his time. The one who spent decades of his life computing 600 decimals (of which 527 were right) was William Shanks, as described in the Numerical approximations of pi article. Shanks lived 2000 years later than Archimedes and died of old age in 1882 in England, not close to any military action. –Henning Makholm (talk) 22:47, 7 March 2009 (UTC)

Acttally, as his article notes, Shanks is famous for his calculation of π to 707 places, accomplished in the year 1873, which, however, was only correct up to the first 527 places. This error was highlighted in 1944 by D. F. Ferguson (using a mechanical desk calculator). Glenn L (talk) 05:33, 25 March 2009 (UTC)

Error in article

Digits of pi redirects to Numerical ... and does in fact NOT show the 10,000 first digits of pi. —Preceding unsigned comment added by 62.97.226.2 (talk) 12:38, 14 March 2009 (UTC)

 Done, it used to be the first 10,000 digits of pi, but it was redirected to an actual article. A new name 2008 (talk) 12:47, 14 March 2009 (UTC)

"The Cosine algorithm"

There is no mentioning of the cosine algorithm (or whatever it is called) for calculating pi. The one where p_0 = 1.5, p_(n+1) = p_n + cos(p_n), pi=2*pi_inf. I know hardly anything about it (more than how it works), so I can't write about it, but it trippels the number of decimals each step, so I think it should be mentioned. /Petter —Preceding unsigned comment added by 79.136.98.249 (talk) 14:04, 28 March 2009 (UTC)