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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)
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)
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)
If I didn't remembered it wrongly, Androo123 missed out 433.(3.141592653589793238462643383279...) Visit me at Ftbhrygvn ( Talk| Contribs| Log| Userboxes) 07:05, 29 May 2009 (UTC)
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:
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)
I reverted the following addition to the article:
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)
As my simple edit ( http://en.wikipedia.org/?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)
"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)
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)
[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)
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)
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\invented Pi?-- 64.79.177.254 ( talk) 18:08, 22 July 2008 (UTC)
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)
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)
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)
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)
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)
WRONG. π should always be italic, for the following reasons..
“ | These traditions are hundreds of years old. Italics help distinguish between variables and other things like numbers and operators. For instance cosine of x is written "cos()". (This issue comes up in other symbolic systems; programmers need that distinction too, but today almost universally use color coding instead.) But like any centuries-old tradition, there are a lot of quirks, for example vector variables are sometimes bold, non-italic. Also which letters you use for which variables is important. A lot of today's traditions were introduced by Descartes, like using the end of the alphabet for unknowns and the beginning for known quantities. At one point people used vowels vs. consonants, I think, but no longer. | ” |
“ | One of the things that Euler did that is quite famous is to popularize the letter for pi--a notation that had originally been suggested by a character called William Jones, who thought of it as a shorthand for the word perimeter. | ” |
So I'm thinking about going back and italicizing the pi's. An objections? ~~ Ropata ( talk) 05:38, 17 June 2009 (UTC)
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)
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)
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)
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)
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)
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)
Same applies to e in 5-digit vs. e in 3-digit groups. Dicklyon ( talk) 22:51, 7 October 2008 (UTC)
The digital value of Pi at 5 digits is 3.1416 and is pretty accurate (ratio = 1.000002+ on my calculator). And it's interesting to note that some other values related to Pi are pretty close to 4 digit numbers. Like Pi/4 =0.785398+ (= .7854 x 0.9999976), and Pi/6 = .523598+ (=.5236 x .9999976). So its pretty obvious that extended decimal digit numbers of the Pi value are not going to add much to the accuracy that would be accomplished by their usage. However, I am intrigued by what an extended binomial value of Pi would show in the array of 1's and 0's involved. That's because a binomial numbering system is better at showing the value of extended numbering than a decimal numbering system because each extension number is an indication of whether it is more or less than 1/2 of what is left. And a study of that might more significantly show the accuracy accomplishing value of the calculation than just inspecting the decimal digit notation. WFPM ( talk) 23:23, 17 August 2009 (UTC) I'll bet that if we used a binomial numbering system where instead of writing down all the 1's and 0's, we just counted them each time they occurred and wrote that number down we would soon arrive at a more accurate determination of the Pi value (with fewer numbers) than we could using a standard decimal number method of notation. WFPM ( talk) 23:46, 17 August 2009 (UTC)
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)
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)
I know 10,000 digits of pi, if it helps. Disli ker of human ities 08:53, 12 October 2008 (UTC)
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)
Pi day 2009 has long passed. Can we unprotect it now? 146.115.34.7 ( talk) 22:31, 31 March 2009 (UTC)
Is it worthwhile to mention the following derivation?
for the principal value of log(–1). | Loadmaster ( talk) 16:20, 9 December 2008 (UTC)
Just a thought.
Could´nt the fact that : be used to prove whether e and pi are algebraic indenpedent ? The formula clearly shows a relation between e and pi 86.52.155.97 ( talk) 15:03, 6 October 2009 (UTC)
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)
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)
70.233.173.118 is a nerd. —Preceding unsigned comment added by 68.202.97.110 ( talk) 00:48, 13 April 2009 (UTC)
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)
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 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.
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)
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)
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)
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*p_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)
or
The article says:
The ratio C/d is constant, regardless of a circle's size. [...] This fact is a consequence of the similarity of all circles.
Since pi is such a fundamental number, I mean its constancy deserves a more thorough explanation (and proof) than just stating that it follows from the similarity of all circles. Will somebody with mathematical insight please consider taking a look at this? —Preceding unsigned comment added by 62.107.206.120 ( talk) 20:54, 30 March 2009 (UTC)
What does this sentence explain?: "However it is known that at least one of πe and π + e is transcendental (see Lindemann–Weierstrass theorem)."
Both this and the e article claim the numbers are trancendental. It it not therefore obvious that the sum or multiple of both would be too? If not, can someone explain it in the article and also explain why this is of importance to Pi? The Lindemann theorum seems to prove Pi is trancendental by using e, but as both have better independant proofs, i don't think it really says anything about Pi. Yob Mod 11:28, 2 April 2009 (UTC)
I had a question. Did not Newton prove (implicitly) in Lemma 28 of Principia the fact about transcendentality of pi? I felt that the proof is a stone throw away from this Lemma and whats best is that its very elementary (and elegeant of course!), Someone please confirm. I cannot post the content of Lemma 28 right now. —Preceding
unsigned comment added by
Akashssp (
talk •
contribs)
03:51, 10 October 2009 (UTC)
The FFT has nothing to do with performing arithmetic on extremely large numbers - either in terms of magnitude, such as 3 x 1037 or in terms of the number of digits. FFT computes the FFT of a series of data points, which can have large magnitudes, but that does not determine FFT performance, the number of data points does.
RSzoc ( talk) 02:06, 22 April 2009 (UTC)
Open Questions states that a plausible conjecture of chaos theory would imply that pi is normal base 2. However, the citation is to a subscription-only site, could someone state what conjecture within the article and link to it? —Preceding unsigned comment added by 141.209.170.158 ( talk) 17:28, 12 May 2009 (UTC)
It was a sidebar in the article:
Proof of the normality of pi may come from a link between number theory and chaotic dynamics. While this link is too complicated to explain briefly for pi, the example of log 2 (the logarithm of 2 to base e, where e is the fundamental con- stant 2.718281828 .... ) illustrates the mathematicians' new approach. Log 2 can be obtained to any desired number of decimal places from the ex- pression given below: log 2 = 1/2 + 1/8 + 1/24 + 1/64 + where each term has the form 1/k2 k starting at k = 1 This value works out to 0.6931471805599453 .... Bailey and Crandall have proposed that the normality of log 2 to base 2 is linked to a particular iterative process, or dynamical map, that gen- erates a sequence of numbers be- tween 0 and 1. Here's the mathemati- cal form for this dynamical map: Xn = (2xn - 1 + I/n)mod 1 Starting with xo = 0, each iteration, n, uses the previous result, xn - 1, as the in- put for calculating the next number, xn. The term "mod 1" is an instruction to use only the fractional remainder of each iteration's result as input for the next iteration. In other words, no input is ever larger than 1. The process generates the following sequence: xo = 0, xl = 0, x2 =1/2, x3 =1/3, x4 = 11/12, x5 = 1/30, x6 = 7/30, x7 = 64/105, x8 = 289/840 .... If it could be proved that the erratically fluctuating numbers xn are evenly distributed between 0 and 1, log 2 would be deemed normal to base 2. Establishing the same equidistribution property for a different, more complicat- ed dynamical map would lead to a proof that pi is normal to base 16 (or, equiva- lently, to base 2). That would be a signifi- cant step toward the long-sought goal of proving pi's absolute normality. —Preceding unsigned comment added by 141.209.34.49 ( talk) 17:54, 12 May 2009 (UTC)
How were the values of Pi in hexadecimal and binary calculated? Have these values been verified as being correct? 203.211.74.185 ( talk) 02:48, 19 May 2009 (UTC)
The last digit of pi was discovered. Here is the link. [3] —Preceding unsigned comment added by 69.225.243.9 ( talk) 01:39, 23 May 2009 (UTC)
Yeah, and a space alien filed a paternity suit against Hilary Clinton.
Just in case any innocent person is reading this page: see Proof that π is irrational.
And, BTW, the terminology in the joke article is clumsily and stupidly incorrect. Michael Hardy ( talk) 05:41, 26 May 2009 (UTC)
When a clear and simple understanding of Pi is presented, a 10 year old can probably grasp it with minimal guidance. This is such an explanation of Pi. The Main page is unnecessarily complex.
There were 3 steps to Archimedes determination of Value (3:14..) for Pi
1. Determine the angle at which Arc length equals Radius length.
This angle was determined to be 57.2958.. and it was given the term “Radian”
2. Divide Radian value (57.2958..) into Circle value (360) to produce a Radian / Circle ratio.
As Radian Arc length equals Radius length, the ratio produced (6.28..)is also a Radius/Circumference ratio.
3. Correct the Radius/Circumference ratio to a Diameter/Circumference ratio.
As 2 Radius equal 1 Diameter, the value 6.28.. is divided by 2 to produce value 3.14..
To determine Arc length for 1 degree of Arc, divide Radian value (57.2958..) into Radius length value. Then multiply that determined value by the degrees of Arc under consideration, to determine the length of the Arc.
It should be noted that Pi 3.14.. is also a ratio for Radius / Semi-Circle.
The image of Radian can be found by searching Wiki, Radian. If I have erred in Posting this as a new section, I offer my apology. -- Layman1 ( talk) 17:51, 8 July 2009 (UTC)
Hoax? —Preceding unsigned comment added by 86.132.229.81 ( talk) 14:23, 12 July 2009 (UTC)
i am mark kevin tom —Preceding unsigned comment added by 203.87.176.2 ( talk) 09:00, 13 July 2009 (UTC)
Under the subsection "Calculating pi" it currently says
In addition, this series [Gregory--Leibniz series] converges so slowly that 300 terms are not sufficient to calculate π correctly to 2 decimal places.[23]
Nevertheless 300 terms is certainly sufficient. It seems to me that 294 terms is enough to be precise. Also the reference to Lampret's article (ref no 23) is a bit weird. There is nothing in the article that supports the claim about 300 terms.
Could someone with an account correct these things, please. -- 91.156.39.161 ( talk) 10:17, 15 July 2009 (UTC)
The "300 terms" citation appears to be nearly a word-for-word quote from Petr Beckmann's A History of Pi (1971-75 with numerous reprints) on page 140. Beckmann wrote about the Gregory--Leibniz series, "its convergence was so slow that 300 terms were insufficient to obtain even two decimal places." Unfortunately, it was not pointed out to him the exact progression, otherwise he would have corrected this before his death in 1993:
Term Adjustment Pi Estimate
291 +4/581 3.1450291 292 -4/583 3.1381680 293 +4/585 3.1450061 294 -4/587 3.1381913 295 +4/589 3.1449825
Clearly the sum of the first 293 terms rounds to 3.15, while the sum of the first 294 or more terms always rounds to 3.14, as pointed out above. Glenn L ( talk) 16:03, 15 July 2009 (UTC)
source: iamned.com math page
These lines appear in the article:
π ≈ A3072 | = 3 ⋅ 28 ⋅ √(2 − √(2 + √(2 + √(2 + √(2 + √(2 + √(2 + √(2 + √(2 + 1))))))))) |
≈ 3.14159 |
I tried to indent this by putting a colon in front of it. That doesn't work. The failure to indent violates WP:MOSMATH. Is there some simple way to fix this? Michael Hardy ( talk) 20:22, 23 August 2009 (UTC)
Can someone fix citation [17]? Here is a suggested formatted reference
{{cite news |title = Statistical estimation of π using random vectors|author = S. C. Bloch|coauthor = R. Dresler|journal =American Journal of Physics|volume =67|number = 4|pages =298-303 |year = 1999| doi = 10.1119/1.19252}}
which renders as
S. C. Bloch (1999). "Statistical estimation of π using random vectors". American Journal of Physics. Vol. 67, no. 4. pp. 298–303.
doi:
10.1119/1.19252. {{
cite news}}
: Unknown parameter |coauthor=
ignored (|author=
suggested) (
help)
Thanks. 12.164.217.162 ( talk) 12:45, 1 September 2009 (UTC)
I don't really have a working knowledge of editing wikipedia, but I came across this article recently and thought that it addresses at least partially the question of digit distribution and occurence in pi. Maybe someone could edit this in?
The first digit frequencies of primes and Riemann zeta zeros tend to uniformity following a size-dependent generalized Benford's law by Bartolo Luque, Lucas Lacasa —Preceding unsigned comment added by 142.157.215.139 ( talk) 04:21, 4 September 2009 (UTC)
It is an interesting historical fact that there is a reference to the ratio of the circumference of a circle to its diameter being 30/10 = 3 when the bible was written.
1 Kings 7:23 He [Solomon] made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it.
There are a number of ways people react to this: (1) How could an infallible God have an inaccurate approximation? (2) If one interprets the Hebrew word for circumference as a number (using the natural way of doing so) and the Hebrew word for diameter as a number then the ratio, times 3 is an extraordinarily accurate approximation for Pi (given the date that the bible was written. [2]
I am not sure how much of this adds rather than distracts. Personally, I think at least some of this is interesting. Wikinewbie123 ( talk) 15:15, 9 September 2009 (UTC)
Good and interesting points all around
Wikinewbie123 (
talk)
03:02, 10 September 2009 (UTC)
I have created an alternative formula for calculating Pi (which I would like to put on this wiki). It is based on Calculating Pi via Polygons and comes under the sub-section of Calculating π. Would it be okay with everyone to put it on the wiki; and do you all think I have chosen the right sub-section to put it in? The formula is as follows (also on my user page):
I have also create a reciprocal formula (which may also be posted - undecided as of yet):
Read My User Page for more information. If no one relpies within a few weeks I will assume there is no problem with it and go ahead. I just wanted to check with everyone first; and please comment with any additional ideas.
Jaymie 20:40, 16 September 2009 (UTC)
I have read that |pi - p/q| is never smaller than c*{q^(-42)}, where c is a fixed real number. Perhaps this should be put in the article, but by a more knowledgeable person than me. For all I know, the exponent may have since been improved to something greater than (- 42), that is, even harder to approximate than an algebraic number of degree 42. Rich ( talk) 02:27, 7 October 2009 (UTC)
If a circle has a circumference of 30 then pi=3 circumference divided by squareroot of 12, a constant, equals to the lenghts of triangle. the length of the triangle * 3 is the sum of the perimeter then divided by square root of 12 equals to the heights of the triangle.30 divided by 12=2.5 2.5*4=10 the diametere of the circle.Can't be done without calculator. the circumference of the circle divided by the perimeter of the triangle=1/sin60. three divided by square root of 12 equals to sin60. Twentythreethousand ( talk) 16:53, 11 October 2009 (UTC)
pi —Preceding unsigned comment added by 74.198.10.74 ( talk) 22:23, 18 October 2009 (UTC) mesfin mengistu gemechu(that's me) Twentythreethousand ( talk) 14:09, 27 October 2009 (UTC)
Good luck I'm a Prophet,I have seen the Lord from psalm 18(which they call him the dragon from the book of job chapter 41,everything under heaven is his)The king of the north and the King of the south.Greeks verses Persia.
To say pi equals three is changing all the textbooks in the classroom,and it can't be done whithout a calculator machine.the eye and the pupil of the human eye contains an equilateral triangle and two circles for a proof that pi =3 —Preceding unsigned comment added by Twentythreethousand ( talk • contribs) 19:48, 30 November 2009 (UTC)
:Sides of polygons inscribed in a circle. :60 degree, Sides of polygons 3 sides=30/radical 12 *3 :30 degree, Sides of polygons 6 (30/radical 12 *sin(30))Square + 2.5 square=5, *6=30 :15 degree; polygons 12 sides 2.5823769308862773429589687286191*12=30.988523170635328115507624743429 :7.5 degree polygons 24 sides :3.75 degree polygons 48 sides :conclusion:
5 the radius times ((sin60,sin30,sin15,sin7.5,sin3.75,sin1.875...)...3*22.... times sides of polygons reaches to the ratio of pi . Twentythreethousand ( talk) 17:33, 3 January 2010 (UTC)
Twentythreethousand ( talk) 22:47, 25 December 2009 (UTC)
Twentythreethousand ( talk) 16:47, 3 January 2010 (UTC)
Based upon a discussion at Wikipedia talk:WikiProject Mathematics#"Infoboxes" on number articles, I've removed the infobox from the article. If anyone disagrees, could you please join the discussion there. Thanks, Paul August ☎ 12:36, 18 October 2009 (UTC)
Just a comment: It really doesn't do much good to discuss the issue here. There is an entire community of editors over at Wikipedia talk:WikiProject Mathematics who contribute to the upkeep and improvement of all of the mathematics articles. Since this is an issue that affects seven or eight different articles, it makes more sense to discuss it on the wikiproject page.
In addition to this philosophical argument, it is also simply a reality that the WikiProject Mathematics community does have the power to change this article as it sees fit. For example, the project includes several administrators, who will presumably respect any consensus reached on the project page.
Right now, there is not a consensus on the project page, and if you continue to participate in the discussion there I suspect that you will manage to forge a compromise that everyone can live with. What you need to do right now is read over the objections that have been raised to the infoboxes and propose an alternate form that they could take that addresses some of these concerns. The strategy of trying to move the discussion back here is not going to work out for you. Jim ( talk) 16:40, 19 October 2009 (UTC)
I think some of the remarks above are a tad unfair or misleading. Here are some facts:
I've said elsewhere that I handled this badly, and I apologized saying "It would have been better if I had waited for more editors to comment before I removed the infoboxes, and it would have been better if I had publicized the discussion I started ... more widely": [21]. In a second post I accepted responsibily for causing this mess saying that the situation had gotten off to a bad start "for which I [was] willing to accept the blame". [22] So if anyone feels a need to assign blame or "address ... behavior" please assign it to me or address mine. But I think it goes too far to castigate other editors in the Mathematics project, or the project as a whole. And as for Jim's comment "they were reverting your reverts" I would just point out that only one editor was reverting and as I've indicated above a reasonable argument can be made to justify those edits. I understand that reasonable people might disagree with this. In any case I think we should dispense with any more recriminations.
Paul August ☎ 19:38, 21 October 2009 (UTC)
The page is semi-protected and I cannot alter it. Please improve the outcome of Liu Hius formula to 3.1415894, the present outcome is too rough. Weia ( talk) 23:09, 14 December 2009 (UTC)
Soon there will be 3,141,592 Wikipedia-Articles, right? ;-) Grey Geezer 21:06, 27 December 2009 (UTC) —Preceding unsigned comment added by Grey Geezer ( talk • contribs)
Every now and then I run into a science fiction novel that supposes the value for pi can vary according to a gravitational constant, or a local "curvature" in the universe. Um, I don't think so, but it is getting kind of predictable that this sort of thing keeps popping up in science fiction literature.
The main article could be improved if somebody put a link in there, connecting it to another Wiki article about Pi in science fiction literature. For instance, The Infinite Man by Daniel F. Galouye is one such novel that uses this as an essential part of its plot. His story proposes that computers using standard calculations, according to a standard formula, suddenly start spitting out a different sequence of decimal digits, because the whole universe starts changing its density levels, apparently in response to a supreme being deciding to change the amount of mass in the universe.
It isn't my purpose to argue against one plot in support of another, in terms of science fiction literature employing plausible plot lines, merely that this kind of thing apparently keeps happening, and among different writers around the world. Science fiction authors keep arguing that the formulas for calculating pi, as applied, produces results that are consistent with observable data. Dexter Nextnumber ( talk) 07:50, 1 January 2010 (UTC)
Perhaps in the open questions part of the article would be a reasonable place to place this type of conjectural suggestions of variant values for Pi. Even though they are not really open questions it is the place where the case might be explored. It is certainly interesting to imagine what other universes might be like if they had sufficiently different conditions that their values of Pi could be unique. What would it mean if Pi<1, or Pi=1, or Pi=Infinity? What would it mean if Pi were not a constant? What would it mean if Pi could change its sign? —Preceding unsigned comment added by 76.11.118.129 ( talk) 03:41, 21 February 2010 (UTC)
While this is historically the correct way, and quite possibly the way the article should go, it is also dangerous, because it gives the layman the wrong impression. It is much more fruitful to consider pi an abstract constant (possibly defined through exp(i*pi)=-1), which happens to also give a certain relationship in a circle.
I would advice that, at a minimum, the introduction stresses that the "traditional" definition is a historical left-over and ultimately only a secondary characterization of pi. 188.100.196.8 ( talk) 00:26, 7 January 2010 (UTC)
I don't know why my edit to this page was removed. I have never seen the removal of constructive information from a talk page before. I relevantly submit that a useful definition for pi is as the only root of the sin function between 1 and 4, where sin is defined by its power series. The existence of such a root is guaranteed by the intermediate value theorem. This is the method by which pi is defined in at least two well known math volumes I'm familiar with (Principles of Mathematical Analysis by W. Rudin; Functions of One Complex Variable by Conway). —Preceding unsigned comment added by 75.140.4.134 ( talk) 07:20, 17 August 2010 (UTC)
Manually collapsing WP:OR |
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The following discussion has been closed. Please do not modify it. |
Polygons inscribed in a circleA simplest way to calculate pi is to observe polygons (polygons from three sides, to polygons increasing by multiple of two) inscribed in a circle and watch the height and the base of the sides of the polygons and use the theorem of Pythagoras to find the degree of the angles. The more sides there are in the polygons and the less the degree of the angle of the triangles. Since the angles start with 60 degree and diminish by multiple of two and the sides increase by multiple of two we have an equation: Sin (60/2^x) * 2^x *3=pi Angles of triangles of polygons.
…… Twentythreethousand ( talk) 20:57, 11 January 2010 (UTC) Twentythreethousand ( talk) 00:25, 15 January 2010 (UTC) you can check what it looks like on a graph with radians and degrees and the graph is a constant on pi and on 180. you can make a graph with this equation. Twentythreethousand ( talk) 00:06, 22 January 2010 (UTC) Twentythreethousand ( talk) 19:30, 31 January 2010 (UTC) Twentythreethousand ( talk) 01:13, 2 February 2010 (UTC) 1degree,0.1degree,0.001degree,0.0001degree, Twentythreethousand ( talk) 16:24, 12 February 2010 (UTC)
dear Arthur Rubin you said you know,but your equation is not even in the article and what I have stated in this discussion group is not hard trigonometry and not even hard integral calculus If the calculator machine allowed an irrational number without any increase or a decrease of the number which is a straight line and a measure of a distance that require only two or three digits,what's the use of calculating pi to the billions of digits. Twentythreethousand ( talk) 18:09, 13 February 2010 (UTC)
one other thing Plato the republic and criticism the major statement by Charles Kaplan about the creator and the imitator there was a movie called Coming to America that was made relating to the book.For the last generation.I am not the creator of math.We all live in a circle. —Preceding unsigned comment added by Twentythreethousand ( talk • contribs) 18:39, 14 February 2010 (UTC) New Interesting FormulaI suggest adding formulas 1.1 and 2.13 from http://iamned.com/math/infiniteseries.pdf to the main article They are interesting —Preceding unsigned comment added by 71.139.200.147 ( talk) 06:14, 17 January 2010 (UTC)
Extremely Accurate Approximation
—Preceding unsigned comment added by 67.161.40.148 ( talk) 05:44, 19 January 2010 (UTC)
The often quoted ramanujan approximation uses 13 digits to get 10 places: http://mathworld.wolfram.com/images/equations/PiApproximations/Inline49.gif there's a bunch of them here: http://mathworld.wolfram.com/PiApproximations.html The only really good one is http://mathworld.wolfram.com/images/equations/PiApproximations/Inline77.gif but it's a coincidence due to the continued fraction expansion of pi^4
@RDBury From the work I;ve done those approximations are either coincidences or in the case of Ramanujan derived using elliptic integrals. All expressions that don't involve logarithms are constructable, but obtaining the approximation probably done though trial and error via a computer without an underlying theory. As for computation, you wouldn't use a pi approximation, but a pi formula. —Preceding unsigned comment added by 67.161.40.148 ( talk) 16:25, 20 January 2010 (UTC) |
The text currently says that Einstein was the first to suggest that rivers have a tendency towards an ever more loopy path because the slightest curve will lead to faster currents on the outer side, which in turn will result in more erosion and a sharper bend. He may well have been the first to discover the connection with pi but I cannot believe he was the first to explain the process, even though the cited source claims this. Martin Hogbin ( talk) 18:44, 30 January 2010 (UTC)
Strangely enough π is also used in economics to represent profit. l santry ( talk) 16:11, 4 February 2010 (UTC)
The ploufe formulas need to go. You wouldn't use them to actually compute pi. They don't seem to fit in with the overall flow of the article. —Preceding unsigned comment added by 67.161.40.148 ( talk) 05:38, 17 February 2010 (UTC)
Furthermore, the physicist using 39 digits to draw a circle of known universe is highly ambiguous, fully unsourced, and seems to be one of those 78% of all statistics that are made up. —Preceding unsigned comment added by 71.180.59.107 ( talk) 05:15, 24 March 2010 (UTC)
I think adding a chapter named "computing pi" addressing historical and computational aspect of this number would have a stand in this article. As it's been a difficult topic for a long time in history. Also I noticed that it's been already addressed in other articles like,
Computation of π
In one of his numerical approximations of π, he correctly computed 2π to 9 sexagesimal digits.[9] This approximation of 2π is equivalent to 16 decimal places of accuracy.[10] This was far more accurate than the estimates earlier given in Greek mathematics (3 decimal places by Archimedes), Chinese mathematics (7 decimal places by Zu Chongzhi) or Indian mathematics (11 decimal places by Madhava of Sangamagrama). The accuracy of al-Kashi's estimate was not surpassed until Ludolph van Ceulen computed 20 decimal places of π nearly 200 years later.[1] in the Kashi's article. Repsieximo ( talk) 19:45, 14 March 2010 (UTC)
why not writing something about pi's pronounciation ? (i am french, we pronounce it like pea) —Preceding unsigned comment added by 77.200.68.70 ( talk • contribs) 17:29, March 14, 2010
It's pronounced like the Greek letter pi. Only pronunciation in the OED is /paɪ/. — kwami ( talk) 16:10, 30 January 2011 (UTC)
{{ editsemiprotected}}
There is a minor error in the section titled "Decimal Representation", third paragraph, first sentence. It says, "Because π is an irrational number, its decimal representation does not repeat, and therefore does not terminate." This does not make sense because repeating and terminating are mutually exclusive concepts. A number must either repeat or terminate. It must do one or the other and it cannot do both. I would suggest rewriting this to say "Because π is an irrational number, its decimal representation does not terminate, and therefore repeats indefinitely."—Preceding unsigned comment added by Fkento ( talk • contribs) 14:15, 15 March 2010 (UTC)
Yes, you are correct. I realized my mistake a few hours later but not soon enough to delete the comment. You can remove the edit request if you so desire. Thanks Fkento ( talk) 18:45, 15 March 2010 (UTC)
A bunch of stuff has been deleted uncessarily from he pi discussion pages—Preceding unsigned comment added by 67.161.40.148 ( talk • contribs)
{{tn| The value of PI was first calculated by an Indian mathematician Budhayan, and he explained the concept of what is known as the Pythagorean Theorem. He discovered this in the 6th century, which was long before the European mathematicians.
Amitsinghsodha ( talk) 05:03, 26 March 2010 (UTC)
Not done
{{tn| Please remove repetitive information from the following consecutive sentences:
Robert Pollard ( talk) 17:50, 5 May 2010 (UTC)
In the section "Numerical approximations", it reads:
But 103933/33102 is NOT the next good approximation, because:
Thus, 52163/16604 is closer to than 355/113. Since both the numerator and denominator of this are smaller than 103933/33102, the latter cannot be the next good fraction.
If what "good" means here is the number of correct decimal places, then compare:
Again, there is a fraction, namely 86953/27678, which is correct to more decimal places than 355/113, but has numerator and denominator both smaller than 103993/33102. So, again, this latter fraction cannot be the next good fraction.
The explanation in the Wiki page reads:
That's the culprit. Continued fraction is not the sole method of finding fractions close to . The "better" fractions that I give above were found using Stern-Brocot tree.
219.79.176.121 ( talk) 15:36, 21 April 2010 (UTC)
On average, the number of significant places of the "best" approximation will be close to the sum of the digits of the numerator and the denominator of the approximating fraction. This can be understood as reasonable by thinking of throwing darts so they "stick" in a line 1 unit long. If there are 10000 darts then the average distance between pairs of darts is going to be 1/10000. Likewise when you think of the number of choices of possible fractions using arbitrary numerators and denominators, the estimate is simply the product of the numerator times the denominator, thus giving us a rough estimate of what to expect. This works very well except we now have the problem that 355/113 is more accurate than we would usually find for the number of digits. This is easily explained by the dart analogy because occasionally the darts will strike considerable closer to each other than what is average, and that is exactly how the 292 comes up. As the digits of Pi seem to be more or less random I'm sure a good probabilistic analysis of the likelihood of the 292 coming up would not be any earth shaking profundity.
What the article calls "Rational Approximations", are derived directly from what the article calls "continuing fraction" (I prefer to think of these as the terms of a continuing fraction, they are a series, not a fraction). In fact, given the terms of a continuing fraction series as far as it has been calculated, along with the residue left over from deriving the terms thus far, we have the complete and "lossless" description of PI because one can be exactly derived from the other in either direction (e.g. they contain exactly equivalent information).
Without proving the rational approximations derived from the continuing fraction series of Pi produce the best approximations of Pi, it is easy to show that it is reasonable that they are. In particular, any candidate fractional approximation of Pi that is not equal in value to any of the approximations of Pi derived from continuing fraction series of Pi, must itself have its own continuing fraction series. That series will be different from the continuing fraction series of Pi and if that series is extended in attempt to approximate Pi, it will fail to do so because it must converge to a different value than Pi. This is because process is reversible and if it approximates Pi it would exactly produce the unique continuing fraction series of Pi, contradicting the condition which said it was not derived from the continuing fraction series of Pi.
Stronger arguments can be made, but this one is more fun.
99.22.92.218 ( talk) 10:35, 30 April 2010 (UTC)
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![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
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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)
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)
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)
If I didn't remembered it wrongly, Androo123 missed out 433.(3.141592653589793238462643383279...) Visit me at Ftbhrygvn ( Talk| Contribs| Log| Userboxes) 07:05, 29 May 2009 (UTC)
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:
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)
I reverted the following addition to the article:
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)
As my simple edit ( http://en.wikipedia.org/?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)
"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)
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)
[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)
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)
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\invented Pi?-- 64.79.177.254 ( talk) 18:08, 22 July 2008 (UTC)
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)
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)
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)
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)
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)
WRONG. π should always be italic, for the following reasons..
“ | These traditions are hundreds of years old. Italics help distinguish between variables and other things like numbers and operators. For instance cosine of x is written "cos()". (This issue comes up in other symbolic systems; programmers need that distinction too, but today almost universally use color coding instead.) But like any centuries-old tradition, there are a lot of quirks, for example vector variables are sometimes bold, non-italic. Also which letters you use for which variables is important. A lot of today's traditions were introduced by Descartes, like using the end of the alphabet for unknowns and the beginning for known quantities. At one point people used vowels vs. consonants, I think, but no longer. | ” |
“ | One of the things that Euler did that is quite famous is to popularize the letter for pi--a notation that had originally been suggested by a character called William Jones, who thought of it as a shorthand for the word perimeter. | ” |
So I'm thinking about going back and italicizing the pi's. An objections? ~~ Ropata ( talk) 05:38, 17 June 2009 (UTC)
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)
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)
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)
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)
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)
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)
Same applies to e in 5-digit vs. e in 3-digit groups. Dicklyon ( talk) 22:51, 7 October 2008 (UTC)
The digital value of Pi at 5 digits is 3.1416 and is pretty accurate (ratio = 1.000002+ on my calculator). And it's interesting to note that some other values related to Pi are pretty close to 4 digit numbers. Like Pi/4 =0.785398+ (= .7854 x 0.9999976), and Pi/6 = .523598+ (=.5236 x .9999976). So its pretty obvious that extended decimal digit numbers of the Pi value are not going to add much to the accuracy that would be accomplished by their usage. However, I am intrigued by what an extended binomial value of Pi would show in the array of 1's and 0's involved. That's because a binomial numbering system is better at showing the value of extended numbering than a decimal numbering system because each extension number is an indication of whether it is more or less than 1/2 of what is left. And a study of that might more significantly show the accuracy accomplishing value of the calculation than just inspecting the decimal digit notation. WFPM ( talk) 23:23, 17 August 2009 (UTC) I'll bet that if we used a binomial numbering system where instead of writing down all the 1's and 0's, we just counted them each time they occurred and wrote that number down we would soon arrive at a more accurate determination of the Pi value (with fewer numbers) than we could using a standard decimal number method of notation. WFPM ( talk) 23:46, 17 August 2009 (UTC)
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)
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)
I know 10,000 digits of pi, if it helps. Disli ker of human ities 08:53, 12 October 2008 (UTC)
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)
Pi day 2009 has long passed. Can we unprotect it now? 146.115.34.7 ( talk) 22:31, 31 March 2009 (UTC)
Is it worthwhile to mention the following derivation?
for the principal value of log(–1). | Loadmaster ( talk) 16:20, 9 December 2008 (UTC)
Just a thought.
Could´nt the fact that : be used to prove whether e and pi are algebraic indenpedent ? The formula clearly shows a relation between e and pi 86.52.155.97 ( talk) 15:03, 6 October 2009 (UTC)
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)
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)
70.233.173.118 is a nerd. —Preceding unsigned comment added by 68.202.97.110 ( talk) 00:48, 13 April 2009 (UTC)
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)
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 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.
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)
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)
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)
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*p_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)
or
The article says:
The ratio C/d is constant, regardless of a circle's size. [...] This fact is a consequence of the similarity of all circles.
Since pi is such a fundamental number, I mean its constancy deserves a more thorough explanation (and proof) than just stating that it follows from the similarity of all circles. Will somebody with mathematical insight please consider taking a look at this? —Preceding unsigned comment added by 62.107.206.120 ( talk) 20:54, 30 March 2009 (UTC)
What does this sentence explain?: "However it is known that at least one of πe and π + e is transcendental (see Lindemann–Weierstrass theorem)."
Both this and the e article claim the numbers are trancendental. It it not therefore obvious that the sum or multiple of both would be too? If not, can someone explain it in the article and also explain why this is of importance to Pi? The Lindemann theorum seems to prove Pi is trancendental by using e, but as both have better independant proofs, i don't think it really says anything about Pi. Yob Mod 11:28, 2 April 2009 (UTC)
I had a question. Did not Newton prove (implicitly) in Lemma 28 of Principia the fact about transcendentality of pi? I felt that the proof is a stone throw away from this Lemma and whats best is that its very elementary (and elegeant of course!), Someone please confirm. I cannot post the content of Lemma 28 right now. —Preceding
unsigned comment added by
Akashssp (
talk •
contribs)
03:51, 10 October 2009 (UTC)
The FFT has nothing to do with performing arithmetic on extremely large numbers - either in terms of magnitude, such as 3 x 1037 or in terms of the number of digits. FFT computes the FFT of a series of data points, which can have large magnitudes, but that does not determine FFT performance, the number of data points does.
RSzoc ( talk) 02:06, 22 April 2009 (UTC)
Open Questions states that a plausible conjecture of chaos theory would imply that pi is normal base 2. However, the citation is to a subscription-only site, could someone state what conjecture within the article and link to it? —Preceding unsigned comment added by 141.209.170.158 ( talk) 17:28, 12 May 2009 (UTC)
It was a sidebar in the article:
Proof of the normality of pi may come from a link between number theory and chaotic dynamics. While this link is too complicated to explain briefly for pi, the example of log 2 (the logarithm of 2 to base e, where e is the fundamental con- stant 2.718281828 .... ) illustrates the mathematicians' new approach. Log 2 can be obtained to any desired number of decimal places from the ex- pression given below: log 2 = 1/2 + 1/8 + 1/24 + 1/64 + where each term has the form 1/k2 k starting at k = 1 This value works out to 0.6931471805599453 .... Bailey and Crandall have proposed that the normality of log 2 to base 2 is linked to a particular iterative process, or dynamical map, that gen- erates a sequence of numbers be- tween 0 and 1. Here's the mathemati- cal form for this dynamical map: Xn = (2xn - 1 + I/n)mod 1 Starting with xo = 0, each iteration, n, uses the previous result, xn - 1, as the in- put for calculating the next number, xn. The term "mod 1" is an instruction to use only the fractional remainder of each iteration's result as input for the next iteration. In other words, no input is ever larger than 1. The process generates the following sequence: xo = 0, xl = 0, x2 =1/2, x3 =1/3, x4 = 11/12, x5 = 1/30, x6 = 7/30, x7 = 64/105, x8 = 289/840 .... If it could be proved that the erratically fluctuating numbers xn are evenly distributed between 0 and 1, log 2 would be deemed normal to base 2. Establishing the same equidistribution property for a different, more complicat- ed dynamical map would lead to a proof that pi is normal to base 16 (or, equiva- lently, to base 2). That would be a signifi- cant step toward the long-sought goal of proving pi's absolute normality. —Preceding unsigned comment added by 141.209.34.49 ( talk) 17:54, 12 May 2009 (UTC)
How were the values of Pi in hexadecimal and binary calculated? Have these values been verified as being correct? 203.211.74.185 ( talk) 02:48, 19 May 2009 (UTC)
The last digit of pi was discovered. Here is the link. [3] —Preceding unsigned comment added by 69.225.243.9 ( talk) 01:39, 23 May 2009 (UTC)
Yeah, and a space alien filed a paternity suit against Hilary Clinton.
Just in case any innocent person is reading this page: see Proof that π is irrational.
And, BTW, the terminology in the joke article is clumsily and stupidly incorrect. Michael Hardy ( talk) 05:41, 26 May 2009 (UTC)
When a clear and simple understanding of Pi is presented, a 10 year old can probably grasp it with minimal guidance. This is such an explanation of Pi. The Main page is unnecessarily complex.
There were 3 steps to Archimedes determination of Value (3:14..) for Pi
1. Determine the angle at which Arc length equals Radius length.
This angle was determined to be 57.2958.. and it was given the term “Radian”
2. Divide Radian value (57.2958..) into Circle value (360) to produce a Radian / Circle ratio.
As Radian Arc length equals Radius length, the ratio produced (6.28..)is also a Radius/Circumference ratio.
3. Correct the Radius/Circumference ratio to a Diameter/Circumference ratio.
As 2 Radius equal 1 Diameter, the value 6.28.. is divided by 2 to produce value 3.14..
To determine Arc length for 1 degree of Arc, divide Radian value (57.2958..) into Radius length value. Then multiply that determined value by the degrees of Arc under consideration, to determine the length of the Arc.
It should be noted that Pi 3.14.. is also a ratio for Radius / Semi-Circle.
The image of Radian can be found by searching Wiki, Radian. If I have erred in Posting this as a new section, I offer my apology. -- Layman1 ( talk) 17:51, 8 July 2009 (UTC)
Hoax? —Preceding unsigned comment added by 86.132.229.81 ( talk) 14:23, 12 July 2009 (UTC)
i am mark kevin tom —Preceding unsigned comment added by 203.87.176.2 ( talk) 09:00, 13 July 2009 (UTC)
Under the subsection "Calculating pi" it currently says
In addition, this series [Gregory--Leibniz series] converges so slowly that 300 terms are not sufficient to calculate π correctly to 2 decimal places.[23]
Nevertheless 300 terms is certainly sufficient. It seems to me that 294 terms is enough to be precise. Also the reference to Lampret's article (ref no 23) is a bit weird. There is nothing in the article that supports the claim about 300 terms.
Could someone with an account correct these things, please. -- 91.156.39.161 ( talk) 10:17, 15 July 2009 (UTC)
The "300 terms" citation appears to be nearly a word-for-word quote from Petr Beckmann's A History of Pi (1971-75 with numerous reprints) on page 140. Beckmann wrote about the Gregory--Leibniz series, "its convergence was so slow that 300 terms were insufficient to obtain even two decimal places." Unfortunately, it was not pointed out to him the exact progression, otherwise he would have corrected this before his death in 1993:
Term Adjustment Pi Estimate
291 +4/581 3.1450291 292 -4/583 3.1381680 293 +4/585 3.1450061 294 -4/587 3.1381913 295 +4/589 3.1449825
Clearly the sum of the first 293 terms rounds to 3.15, while the sum of the first 294 or more terms always rounds to 3.14, as pointed out above. Glenn L ( talk) 16:03, 15 July 2009 (UTC)
source: iamned.com math page
These lines appear in the article:
π ≈ A3072 | = 3 ⋅ 28 ⋅ √(2 − √(2 + √(2 + √(2 + √(2 + √(2 + √(2 + √(2 + √(2 + 1))))))))) |
≈ 3.14159 |
I tried to indent this by putting a colon in front of it. That doesn't work. The failure to indent violates WP:MOSMATH. Is there some simple way to fix this? Michael Hardy ( talk) 20:22, 23 August 2009 (UTC)
Can someone fix citation [17]? Here is a suggested formatted reference
{{cite news |title = Statistical estimation of π using random vectors|author = S. C. Bloch|coauthor = R. Dresler|journal =American Journal of Physics|volume =67|number = 4|pages =298-303 |year = 1999| doi = 10.1119/1.19252}}
which renders as
S. C. Bloch (1999). "Statistical estimation of π using random vectors". American Journal of Physics. Vol. 67, no. 4. pp. 298–303.
doi:
10.1119/1.19252. {{
cite news}}
: Unknown parameter |coauthor=
ignored (|author=
suggested) (
help)
Thanks. 12.164.217.162 ( talk) 12:45, 1 September 2009 (UTC)
I don't really have a working knowledge of editing wikipedia, but I came across this article recently and thought that it addresses at least partially the question of digit distribution and occurence in pi. Maybe someone could edit this in?
The first digit frequencies of primes and Riemann zeta zeros tend to uniformity following a size-dependent generalized Benford's law by Bartolo Luque, Lucas Lacasa —Preceding unsigned comment added by 142.157.215.139 ( talk) 04:21, 4 September 2009 (UTC)
It is an interesting historical fact that there is a reference to the ratio of the circumference of a circle to its diameter being 30/10 = 3 when the bible was written.
1 Kings 7:23 He [Solomon] made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it.
There are a number of ways people react to this: (1) How could an infallible God have an inaccurate approximation? (2) If one interprets the Hebrew word for circumference as a number (using the natural way of doing so) and the Hebrew word for diameter as a number then the ratio, times 3 is an extraordinarily accurate approximation for Pi (given the date that the bible was written. [2]
I am not sure how much of this adds rather than distracts. Personally, I think at least some of this is interesting. Wikinewbie123 ( talk) 15:15, 9 September 2009 (UTC)
Good and interesting points all around
Wikinewbie123 (
talk)
03:02, 10 September 2009 (UTC)
I have created an alternative formula for calculating Pi (which I would like to put on this wiki). It is based on Calculating Pi via Polygons and comes under the sub-section of Calculating π. Would it be okay with everyone to put it on the wiki; and do you all think I have chosen the right sub-section to put it in? The formula is as follows (also on my user page):
I have also create a reciprocal formula (which may also be posted - undecided as of yet):
Read My User Page for more information. If no one relpies within a few weeks I will assume there is no problem with it and go ahead. I just wanted to check with everyone first; and please comment with any additional ideas.
Jaymie 20:40, 16 September 2009 (UTC)
I have read that |pi - p/q| is never smaller than c*{q^(-42)}, where c is a fixed real number. Perhaps this should be put in the article, but by a more knowledgeable person than me. For all I know, the exponent may have since been improved to something greater than (- 42), that is, even harder to approximate than an algebraic number of degree 42. Rich ( talk) 02:27, 7 October 2009 (UTC)
If a circle has a circumference of 30 then pi=3 circumference divided by squareroot of 12, a constant, equals to the lenghts of triangle. the length of the triangle * 3 is the sum of the perimeter then divided by square root of 12 equals to the heights of the triangle.30 divided by 12=2.5 2.5*4=10 the diametere of the circle.Can't be done without calculator. the circumference of the circle divided by the perimeter of the triangle=1/sin60. three divided by square root of 12 equals to sin60. Twentythreethousand ( talk) 16:53, 11 October 2009 (UTC)
pi —Preceding unsigned comment added by 74.198.10.74 ( talk) 22:23, 18 October 2009 (UTC) mesfin mengistu gemechu(that's me) Twentythreethousand ( talk) 14:09, 27 October 2009 (UTC)
Good luck I'm a Prophet,I have seen the Lord from psalm 18(which they call him the dragon from the book of job chapter 41,everything under heaven is his)The king of the north and the King of the south.Greeks verses Persia.
To say pi equals three is changing all the textbooks in the classroom,and it can't be done whithout a calculator machine.the eye and the pupil of the human eye contains an equilateral triangle and two circles for a proof that pi =3 —Preceding unsigned comment added by Twentythreethousand ( talk • contribs) 19:48, 30 November 2009 (UTC)
:Sides of polygons inscribed in a circle. :60 degree, Sides of polygons 3 sides=30/radical 12 *3 :30 degree, Sides of polygons 6 (30/radical 12 *sin(30))Square + 2.5 square=5, *6=30 :15 degree; polygons 12 sides 2.5823769308862773429589687286191*12=30.988523170635328115507624743429 :7.5 degree polygons 24 sides :3.75 degree polygons 48 sides :conclusion:
5 the radius times ((sin60,sin30,sin15,sin7.5,sin3.75,sin1.875...)...3*22.... times sides of polygons reaches to the ratio of pi . Twentythreethousand ( talk) 17:33, 3 January 2010 (UTC)
Twentythreethousand ( talk) 22:47, 25 December 2009 (UTC)
Twentythreethousand ( talk) 16:47, 3 January 2010 (UTC)
Based upon a discussion at Wikipedia talk:WikiProject Mathematics#"Infoboxes" on number articles, I've removed the infobox from the article. If anyone disagrees, could you please join the discussion there. Thanks, Paul August ☎ 12:36, 18 October 2009 (UTC)
Just a comment: It really doesn't do much good to discuss the issue here. There is an entire community of editors over at Wikipedia talk:WikiProject Mathematics who contribute to the upkeep and improvement of all of the mathematics articles. Since this is an issue that affects seven or eight different articles, it makes more sense to discuss it on the wikiproject page.
In addition to this philosophical argument, it is also simply a reality that the WikiProject Mathematics community does have the power to change this article as it sees fit. For example, the project includes several administrators, who will presumably respect any consensus reached on the project page.
Right now, there is not a consensus on the project page, and if you continue to participate in the discussion there I suspect that you will manage to forge a compromise that everyone can live with. What you need to do right now is read over the objections that have been raised to the infoboxes and propose an alternate form that they could take that addresses some of these concerns. The strategy of trying to move the discussion back here is not going to work out for you. Jim ( talk) 16:40, 19 October 2009 (UTC)
I think some of the remarks above are a tad unfair or misleading. Here are some facts:
I've said elsewhere that I handled this badly, and I apologized saying "It would have been better if I had waited for more editors to comment before I removed the infoboxes, and it would have been better if I had publicized the discussion I started ... more widely": [21]. In a second post I accepted responsibily for causing this mess saying that the situation had gotten off to a bad start "for which I [was] willing to accept the blame". [22] So if anyone feels a need to assign blame or "address ... behavior" please assign it to me or address mine. But I think it goes too far to castigate other editors in the Mathematics project, or the project as a whole. And as for Jim's comment "they were reverting your reverts" I would just point out that only one editor was reverting and as I've indicated above a reasonable argument can be made to justify those edits. I understand that reasonable people might disagree with this. In any case I think we should dispense with any more recriminations.
Paul August ☎ 19:38, 21 October 2009 (UTC)
The page is semi-protected and I cannot alter it. Please improve the outcome of Liu Hius formula to 3.1415894, the present outcome is too rough. Weia ( talk) 23:09, 14 December 2009 (UTC)
Soon there will be 3,141,592 Wikipedia-Articles, right? ;-) Grey Geezer 21:06, 27 December 2009 (UTC) —Preceding unsigned comment added by Grey Geezer ( talk • contribs)
Every now and then I run into a science fiction novel that supposes the value for pi can vary according to a gravitational constant, or a local "curvature" in the universe. Um, I don't think so, but it is getting kind of predictable that this sort of thing keeps popping up in science fiction literature.
The main article could be improved if somebody put a link in there, connecting it to another Wiki article about Pi in science fiction literature. For instance, The Infinite Man by Daniel F. Galouye is one such novel that uses this as an essential part of its plot. His story proposes that computers using standard calculations, according to a standard formula, suddenly start spitting out a different sequence of decimal digits, because the whole universe starts changing its density levels, apparently in response to a supreme being deciding to change the amount of mass in the universe.
It isn't my purpose to argue against one plot in support of another, in terms of science fiction literature employing plausible plot lines, merely that this kind of thing apparently keeps happening, and among different writers around the world. Science fiction authors keep arguing that the formulas for calculating pi, as applied, produces results that are consistent with observable data. Dexter Nextnumber ( talk) 07:50, 1 January 2010 (UTC)
Perhaps in the open questions part of the article would be a reasonable place to place this type of conjectural suggestions of variant values for Pi. Even though they are not really open questions it is the place where the case might be explored. It is certainly interesting to imagine what other universes might be like if they had sufficiently different conditions that their values of Pi could be unique. What would it mean if Pi<1, or Pi=1, or Pi=Infinity? What would it mean if Pi were not a constant? What would it mean if Pi could change its sign? —Preceding unsigned comment added by 76.11.118.129 ( talk) 03:41, 21 February 2010 (UTC)
While this is historically the correct way, and quite possibly the way the article should go, it is also dangerous, because it gives the layman the wrong impression. It is much more fruitful to consider pi an abstract constant (possibly defined through exp(i*pi)=-1), which happens to also give a certain relationship in a circle.
I would advice that, at a minimum, the introduction stresses that the "traditional" definition is a historical left-over and ultimately only a secondary characterization of pi. 188.100.196.8 ( talk) 00:26, 7 January 2010 (UTC)
I don't know why my edit to this page was removed. I have never seen the removal of constructive information from a talk page before. I relevantly submit that a useful definition for pi is as the only root of the sin function between 1 and 4, where sin is defined by its power series. The existence of such a root is guaranteed by the intermediate value theorem. This is the method by which pi is defined in at least two well known math volumes I'm familiar with (Principles of Mathematical Analysis by W. Rudin; Functions of One Complex Variable by Conway). —Preceding unsigned comment added by 75.140.4.134 ( talk) 07:20, 17 August 2010 (UTC)
Manually collapsing WP:OR |
---|
The following discussion has been closed. Please do not modify it. |
Polygons inscribed in a circleA simplest way to calculate pi is to observe polygons (polygons from three sides, to polygons increasing by multiple of two) inscribed in a circle and watch the height and the base of the sides of the polygons and use the theorem of Pythagoras to find the degree of the angles. The more sides there are in the polygons and the less the degree of the angle of the triangles. Since the angles start with 60 degree and diminish by multiple of two and the sides increase by multiple of two we have an equation: Sin (60/2^x) * 2^x *3=pi Angles of triangles of polygons.
…… Twentythreethousand ( talk) 20:57, 11 January 2010 (UTC) Twentythreethousand ( talk) 00:25, 15 January 2010 (UTC) you can check what it looks like on a graph with radians and degrees and the graph is a constant on pi and on 180. you can make a graph with this equation. Twentythreethousand ( talk) 00:06, 22 January 2010 (UTC) Twentythreethousand ( talk) 19:30, 31 January 2010 (UTC) Twentythreethousand ( talk) 01:13, 2 February 2010 (UTC) 1degree,0.1degree,0.001degree,0.0001degree, Twentythreethousand ( talk) 16:24, 12 February 2010 (UTC)
dear Arthur Rubin you said you know,but your equation is not even in the article and what I have stated in this discussion group is not hard trigonometry and not even hard integral calculus If the calculator machine allowed an irrational number without any increase or a decrease of the number which is a straight line and a measure of a distance that require only two or three digits,what's the use of calculating pi to the billions of digits. Twentythreethousand ( talk) 18:09, 13 February 2010 (UTC)
one other thing Plato the republic and criticism the major statement by Charles Kaplan about the creator and the imitator there was a movie called Coming to America that was made relating to the book.For the last generation.I am not the creator of math.We all live in a circle. —Preceding unsigned comment added by Twentythreethousand ( talk • contribs) 18:39, 14 February 2010 (UTC) New Interesting FormulaI suggest adding formulas 1.1 and 2.13 from http://iamned.com/math/infiniteseries.pdf to the main article They are interesting —Preceding unsigned comment added by 71.139.200.147 ( talk) 06:14, 17 January 2010 (UTC)
Extremely Accurate Approximation
—Preceding unsigned comment added by 67.161.40.148 ( talk) 05:44, 19 January 2010 (UTC)
The often quoted ramanujan approximation uses 13 digits to get 10 places: http://mathworld.wolfram.com/images/equations/PiApproximations/Inline49.gif there's a bunch of them here: http://mathworld.wolfram.com/PiApproximations.html The only really good one is http://mathworld.wolfram.com/images/equations/PiApproximations/Inline77.gif but it's a coincidence due to the continued fraction expansion of pi^4
@RDBury From the work I;ve done those approximations are either coincidences or in the case of Ramanujan derived using elliptic integrals. All expressions that don't involve logarithms are constructable, but obtaining the approximation probably done though trial and error via a computer without an underlying theory. As for computation, you wouldn't use a pi approximation, but a pi formula. —Preceding unsigned comment added by 67.161.40.148 ( talk) 16:25, 20 January 2010 (UTC) |
The text currently says that Einstein was the first to suggest that rivers have a tendency towards an ever more loopy path because the slightest curve will lead to faster currents on the outer side, which in turn will result in more erosion and a sharper bend. He may well have been the first to discover the connection with pi but I cannot believe he was the first to explain the process, even though the cited source claims this. Martin Hogbin ( talk) 18:44, 30 January 2010 (UTC)
Strangely enough π is also used in economics to represent profit. l santry ( talk) 16:11, 4 February 2010 (UTC)
The ploufe formulas need to go. You wouldn't use them to actually compute pi. They don't seem to fit in with the overall flow of the article. —Preceding unsigned comment added by 67.161.40.148 ( talk) 05:38, 17 February 2010 (UTC)
Furthermore, the physicist using 39 digits to draw a circle of known universe is highly ambiguous, fully unsourced, and seems to be one of those 78% of all statistics that are made up. —Preceding unsigned comment added by 71.180.59.107 ( talk) 05:15, 24 March 2010 (UTC)
I think adding a chapter named "computing pi" addressing historical and computational aspect of this number would have a stand in this article. As it's been a difficult topic for a long time in history. Also I noticed that it's been already addressed in other articles like,
Computation of π
In one of his numerical approximations of π, he correctly computed 2π to 9 sexagesimal digits.[9] This approximation of 2π is equivalent to 16 decimal places of accuracy.[10] This was far more accurate than the estimates earlier given in Greek mathematics (3 decimal places by Archimedes), Chinese mathematics (7 decimal places by Zu Chongzhi) or Indian mathematics (11 decimal places by Madhava of Sangamagrama). The accuracy of al-Kashi's estimate was not surpassed until Ludolph van Ceulen computed 20 decimal places of π nearly 200 years later.[1] in the Kashi's article. Repsieximo ( talk) 19:45, 14 March 2010 (UTC)
why not writing something about pi's pronounciation ? (i am french, we pronounce it like pea) —Preceding unsigned comment added by 77.200.68.70 ( talk • contribs) 17:29, March 14, 2010
It's pronounced like the Greek letter pi. Only pronunciation in the OED is /paɪ/. — kwami ( talk) 16:10, 30 January 2011 (UTC)
{{ editsemiprotected}}
There is a minor error in the section titled "Decimal Representation", third paragraph, first sentence. It says, "Because π is an irrational number, its decimal representation does not repeat, and therefore does not terminate." This does not make sense because repeating and terminating are mutually exclusive concepts. A number must either repeat or terminate. It must do one or the other and it cannot do both. I would suggest rewriting this to say "Because π is an irrational number, its decimal representation does not terminate, and therefore repeats indefinitely."—Preceding unsigned comment added by Fkento ( talk • contribs) 14:15, 15 March 2010 (UTC)
Yes, you are correct. I realized my mistake a few hours later but not soon enough to delete the comment. You can remove the edit request if you so desire. Thanks Fkento ( talk) 18:45, 15 March 2010 (UTC)
A bunch of stuff has been deleted uncessarily from he pi discussion pages—Preceding unsigned comment added by 67.161.40.148 ( talk • contribs)
{{tn| The value of PI was first calculated by an Indian mathematician Budhayan, and he explained the concept of what is known as the Pythagorean Theorem. He discovered this in the 6th century, which was long before the European mathematicians.
Amitsinghsodha ( talk) 05:03, 26 March 2010 (UTC)
Not done
{{tn| Please remove repetitive information from the following consecutive sentences:
Robert Pollard ( talk) 17:50, 5 May 2010 (UTC)
In the section "Numerical approximations", it reads:
But 103933/33102 is NOT the next good approximation, because:
Thus, 52163/16604 is closer to than 355/113. Since both the numerator and denominator of this are smaller than 103933/33102, the latter cannot be the next good fraction.
If what "good" means here is the number of correct decimal places, then compare:
Again, there is a fraction, namely 86953/27678, which is correct to more decimal places than 355/113, but has numerator and denominator both smaller than 103993/33102. So, again, this latter fraction cannot be the next good fraction.
The explanation in the Wiki page reads:
That's the culprit. Continued fraction is not the sole method of finding fractions close to . The "better" fractions that I give above were found using Stern-Brocot tree.
219.79.176.121 ( talk) 15:36, 21 April 2010 (UTC)
On average, the number of significant places of the "best" approximation will be close to the sum of the digits of the numerator and the denominator of the approximating fraction. This can be understood as reasonable by thinking of throwing darts so they "stick" in a line 1 unit long. If there are 10000 darts then the average distance between pairs of darts is going to be 1/10000. Likewise when you think of the number of choices of possible fractions using arbitrary numerators and denominators, the estimate is simply the product of the numerator times the denominator, thus giving us a rough estimate of what to expect. This works very well except we now have the problem that 355/113 is more accurate than we would usually find for the number of digits. This is easily explained by the dart analogy because occasionally the darts will strike considerable closer to each other than what is average, and that is exactly how the 292 comes up. As the digits of Pi seem to be more or less random I'm sure a good probabilistic analysis of the likelihood of the 292 coming up would not be any earth shaking profundity.
What the article calls "Rational Approximations", are derived directly from what the article calls "continuing fraction" (I prefer to think of these as the terms of a continuing fraction, they are a series, not a fraction). In fact, given the terms of a continuing fraction series as far as it has been calculated, along with the residue left over from deriving the terms thus far, we have the complete and "lossless" description of PI because one can be exactly derived from the other in either direction (e.g. they contain exactly equivalent information).
Without proving the rational approximations derived from the continuing fraction series of Pi produce the best approximations of Pi, it is easy to show that it is reasonable that they are. In particular, any candidate fractional approximation of Pi that is not equal in value to any of the approximations of Pi derived from continuing fraction series of Pi, must itself have its own continuing fraction series. That series will be different from the continuing fraction series of Pi and if that series is extended in attempt to approximate Pi, it will fail to do so because it must converge to a different value than Pi. This is because process is reversible and if it approximates Pi it would exactly produce the unique continuing fraction series of Pi, contradicting the condition which said it was not derived from the continuing fraction series of Pi.
Stronger arguments can be made, but this one is more fun.
99.22.92.218 ( talk) 10:35, 30 April 2010 (UTC)
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