Talk:Pi

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Significant digits in engineering calculations

The article says, practical science and engineering will rarely require more than 100 digits. Can anybody cite anything to support the claim that anywhere near that many digits are ever used in engineering calculations? The moon is about 10^9 feet away from the Earth. If NASA worked the Apollo calculations to 10 digits, they would have hit the moon within one foot of their target, which is clearly far higher precision than was needed. If you told me they used 12 or even 15 digits, I would believe you. But 100? That's absurd. -- RoySmith (talk) 00:55, 25 February 2007 (UTC)

No claim that "anywhere near that many digits are ever used" is made in the article, and therefore there is no need to support such a hypothetical claim. The sentence you quote asserts that the required number of digits for almost everything is less than 101. Last time I checked, 12 and 15 were both indeed less than 101. –Henning Makholm 01:09, 25 February 2007 (UTC)

The word rarely isn't nearly strong enough. Something is rare when 5% of the instances do it that way. I would say, practical science and engineering will rarely require more than 6 digits -- RoySmith (talk) 03:01, 25 February 2007 (UTC)

You might as well say that practical science and engineering only uses the first Million digits of Pi, or that the Earth is bigger than a proton. It may be true, but it's not useful. Paladinwannabe2 18:17, 27 February 2007 (UTC)

I'd agree with Roy that the statement does suggest that there are computations which require 50-100 digits. However, I appreciate it won't be easy to reformulate it in an acceptable (i.e., attributable) way. That won't stop me from giving it a try though. How about

While the value of pi has been computed to billions of digits, practical science and engineering computations typically use only 16 digits. It is hard to envisage a situation where more than a hundred digits will be needed for this purpose.

The 16 digits refers to standard double precision. I think it's fair to say that is the precision typically used, though perhaps we do officially need a reference to back this up. -- Jitse Niesen (talk) 03:29, 25 February 2007 (UTC)

You could say something like, The roughly 16 decimal digits of precision supplied by the ubiquitous IEEE 754 floating point format is more than sufficient for almost all practical scientific and engineering calculations -- RoySmith (talk) 04:20, 25 February 2007 (UTC)

I agree, this is very silly. 5 digits of Pi gets us within 0.0001 inches at my work, and it looks like we got men to the moon on 5 digits as well, but I can't find an authoritative source yet. I'm going to change it, since I can always supply my own reference in the form of mathematics. Paladinwannabe2 17:18, 27 February 2007 (UTC)

Hardly an attributable source, but there's a scene in Apollo 13 where the guys in mission control are working calculations with slide rules, which are typically good to 3 digits. -- RoySmith (talk) 17:27, 27 February 2007 (UTC)

I changed the example to something sensible. Millimeters are something we can see, we know the earth is huge, this will hopefully get the point across better. Plus, I can provide my own numbers for anyone to see and double-check.

(Using 6,378.137km as the Earth's radius (r) at the equator, 2*(r*3.1415926536 - r*pi) ~= 0.130mm.)Paladinwannabe2 18:03, 27 February 2007 (UTC)

I am unhappy that the "circle the size of the galaxy" example has disappeared. It gave a nice direct demonstration that a realtively small number of digits is sufficient for anything anybody in their wildest dreams could imagine computing. The "six digits for an Earth-sized circle" does not impress this as vividly. Non-matematician readers who don't deeply grok how accuracy in a positional system improves exponentially with the number of digits might end up with a fuzzy expectation that to calculate a circle that encompasses a thousand earths, one would need six thousand digits – and the point that computing millions of digits is practically useless would not be driven home as efficiently. –Henning Makholm 21:05, 27 February 2007 (UTC)

This discussion and the current statement in the text that "practical science and engineering will rarely require more than 10 decimal places. As an example, computing the circumference of the Earth's equator from its radius using only 10 decimal places of pi yields an error of less than 0.2 millimeters" smacks of ill informed WP:original research. First of all there are many measurements in physics and astronomy that are accurate to better than one part in 10^10. More importantly, numerical solutions of differential equations and the like are often very sensitive to small errors and must be carried our at much higher precision than the final answer. So the Earth radius to millimeter calculation prove nothing. This sentence should go.--agr 10:18, 14 October 2007 (UTC)

This is exactly what I've been thinking every time these "you only need 5 digits" discussions pop up, but I've never seemed to have any evidence that high precision is commonly used, or even first hand knowledge (in my own calculations I often require thousands of digits, but these are not for what would be called "practical purposes"). I have modified the offending paragraph for now, but if you have any sort of reference it could be useful. -- Meni Rosenfeld (talk) 00:02, 1 November 2007 (UTC)

I agree, a reference to ever needing more digits for "specialized applications" would be nice, or at least, an article on how many digits are acceptable. —Disavian (^talk/_contribs) 01:40, 1 November 2007 (UTC)

I'd say that the comment could have stayed as I have put it in the meantime, but I understand that you are probably sensitive to those things because of the GA nomination. -- Meni Rosenfeld (talk) 10:11, 1 November 2007 (UTC)

You would be correct :) —Disavian (^talk/_contribs) 12:50, 1 November 2007 (UTC)

Is there an error here?

Under the section Analysis, the second example begins with the sentence: Half the circumference of the unit circle: but the formula states it's equal to Pi; which is the whole circumference, not half of it! What am I missing here? -- Daniel B. Sedory 67.150.121.211 21:57, 25 February 2007 (UTC)

The unit circle has radius 1. Therefore its diameter is 2, and its total circumference is $2\pi$. –Henning Makholm 23:17, 25 February 2007 (UTC)

Neat thing about pi

Pi x 10^9 is equal to the number of seconds in 99.55319 years or 99 and 55319/100000 years. 24.4.131.142 05:09, 7 October 2007 (UTC)

Pi also is...

• the circumference of a circle divided by its raduis —Preceding unsigned comment added by Lairtnogaw (talk • contribs) 21:52, 15 October 2007 (UTC)

No, it is not. -- Meni Rosenfeld (talk) 21:58, 15 October 2007 (UTC)

Pi in Popular Media

Does this article need a section on this? (Or similar) --Earin 16:16, 20 October 2007 (UTC)

No. We used to have one, but it got unwieldy, had questionable encyclopedic value, and needed constant care and trimming because people tended to add listings for every offhand reference to pi in any fictional context whatsoever. I would support adding fictional references to the current article only if some literary use of pi is of high internal importance within the work of fiction and has this importance has been noted by a respectable secondary source. –Henning Makholm 23:12, 21 October 2007 (UTC)

Quick-failed "Good Article" nomination

Per the the GA reviewing guidelines, if "The article has any cleanup banners, including but not limited to {{cleanup}}, {{wikify}}, {{NPOV}}, {{unreferenced}}, etc..." it must be quick-failed. As there are multiple merge banners now present, and the completion of any merges would very significantly alter its content, I cannot in good faith allow a GA review to take place. Please feel free to remedy this and renominate the article, or alternatively seek a reassessment if you feel this decision was in error. Thank you for your work so far, VanTucky ^Talk 04:40, 25 October 2007 (UTC)

Okay then. I'll work on that stuff. this looks useful. —Disavian (^talk/_contribs) 04:57, 25 October 2007 (UTC)

Before I renominate it, I'd like the following accomplished:

1. At least 20 in-line references used in the article. We're not far from that.
2. Less than half of the external links currently on the article

Those two tasks can be combined if you wish, by using ELs to cite a specific portion of the text. Anyone want to chip in with this task? Also, thank you to those of you who have been copyediting the new prose for style/spelling/formatting, etc. :) —Disavian (^talk/_contribs) 05:49, 29 October 2007 (UTC)

Sources

I was going to review the article for its GA nom, and have read the article completely, but I think it needs more sources/references. Until that is accomplished, this won't pass GA. Lex^{94 Talk Contributions Signatures} 19:19, 3 November 2007 (UTC)

Is there anything in particular you'd like to see cited, or are you looking for a specific number of sources? —Disavian (^talk/_contribs) 05:21, 4 November 2007 (UTC)

GA review

Hello, I am the reviewer of this article. If you have anything to ask, please do so. You can leave a message here or you can leave one on my talk page. Regards, Daimanta 01:46, 6 November 2007 (UTC)

How does the sourcing look so far? —Disavian (^talk/_contribs) 01:53, 6 November 2007 (UTC)

Up to "Advanced properties" the sources are good, but after that, no sources appear. Can somebody explain that to me? Regar~ds, Daimanta 12:24, 6 November 2007 (UTC)

I've been going through the article referencing things; that's the only section I haven't appreciatively cited since the last reviewer came along. —Disavian (^talk/_contribs) 13:20, 6 November 2007 (UTC)

Ok, how long do you think this will take? Daimanta 15:20, 6 November 2007 (UTC)

I don't know... I just got sick, and have some projects due on monday/wednesday, but I'll work on it when I can. —Disavian (^talk/_contribs) 03:39, 8 November 2007 (UTC)

Ok, that's fine with me. I hope the GA committee won't be angry with :( Regards, Daimanta 12:33, 8 November 2007 (UTC)

I see that new sources are inserted. That's great! Another problem I saw was this: "As a practical matter, this approximation is poor and converges very slowly." Can someone elaborate a little bit on that. Is it possible to give a mathematical deviation from pi? Regards, Daimanta 12:21, 9 November 2007 (UTC)

I haven't been able to find one, so I removed that sentence. If someone comes across one for it at a later point, it can be added back. —Disavian (^talk/_contribs) 13:37, 9 November 2007 (UTC)

What is the relationship between the principles of the universe and the nature of the circle?

The following excerpt from the article talks about the nature of the circle, while I contend that the prevalence of π in physics formulas is due solely to trigonometric coordinate systems. Can anyone expound?

The number π appears routinely in equations describing fundamental principles of the Universe, due in no small part to its relationship to the nature of the circle and, correspondingly, spherical coordinate systems.

Michael.Urban 20:08, 8 November 2007 (UTC)

I think "its" refers to π, so the relationship in the title is not implied. -- Meni Rosenfeld (talk) 20:43, 8 November 2007 (UTC)

Pronunciation

A small point: the article says, " "π" is usually pronounced as pie when referring to the constant, although the letter is properly pronounced pee otherwise. " This wording is misleading. Pi in English is always "properly" pronounced "pie". It is only correct to say that it is "properly pronounced pee" in modern Greek. See the article on the letter pi which gets this right.