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I have no horse in this race, but my watchlist is showing this content being added and removed back and forth a lot today. Discussions via edit summary obviously aren't going to cut it, so I wanted to start a discussion and see if we can figure out some consensus on the material, one way or another. The edit summaries don't really explain the objection to the material, would one of the editors involved in adding or removing the content mind explaining why it should be added/removed? There's a lot of editing back and forth so try as I might it's hard to make sense of what the issue is exactly. - Aoidh ( talk) 06:18, 5 May 2016 (UTC)
This is just tit-for-tat disruptive editing. Takahiro4 added a template, which was against any known (to me) use of such templates. It was placed in such a way as to break the flow of text in the article and, furthermore, was unnecessary as we already Wikilink to the concept. I reverted the edit, and explained as much. Takahiro reverted back, with a cryptic, non-explaining edit summary. I reverted again, and told Takahiro to explain on the talk page why he thought this was a good idea. Instead of doing that, he proceeded to remove large well-sourced sections of text from the article (that I had recently written). He reverted this two more times [1], [2]. His massive removal was reverted by three different editors. This is clearly a case of one editor acting disruptively. I suggest that the solution is not page protection, but just blocking the obviously disruptive editor. I note that Takahiro4 was the one who requested page protection, after he was over 3RR. That also seems like a disruptive abuse of process, and the kind of thing that protecting admins should look at before they decide to protect a page that is undergoing active revision ( WP:TROUT might be relevant). I have pinged the protecting admin, but if I don't here back, I will raise the issue at ANI. Sławomir Biały ( talk) 09:35, 5 May 2016 (UTC)
Another reference (which I just added to
area of a disk) that should be added to the discussion of the isoperimetric inequality here is: Isaac Chavel (2001), Isoperimetric inequalities, Cambridge University Press (especially the introduction). There are clear statements there about the isoperimetric functional and its minimizer. Also it shows in great depth how isoperimetry is related to Sobolev inequalities, so is a good secondary source for that entire paragraph.
Sławomir
Biały
11:29, 5 May 2016 (UTC)
Also you always say it isn't me."I am not involved at this edit."That is not possible.And david is involving with my discussion,unsuitable.And just other patrollers are automatically responded.Unfortunately your judge is not correct.But I thought about fourier.I think fourier transform is not good,but I feel fourier series are strong connected with pi.Because Fourier transform is just expressed using e^πi by euler's equation,clearly fourier series are connected with pi.I hope this suggestion. See you later.-- Takahiro4 ( talk) 05:54, 6 May 2016 (UTC)
A lot of new material has been added under the heading "Fourier series and modular forms". I don't believe most of this is directly relevant to pi. At most, there should be a brief mention of these topics, with links to the main articles. -- Macrakis ( talk) 17:39, 7 May 2016 (UTC)
Fourier series and modular forms
The constant π appears naturally in Fourier series.
In harmonic analysis, periodic functions are often regarded as functions on the circle group T. The Fourier decomposition shows that a complex-valued function f on T can be written as an infinite linear superposition of complex exponentials , each of which involves π. The complex exponentials, in turn, can be characterized by their transformation properties under T: they constitute a character of T, that is, a function from T to the group of unit modulus complex numbers, that is also a group homomorphism. Using the Haar measure on the circle group, the constant π is half the magnitude of the Radon–Nikodym derivative of this character. The other characters have derivatives whose magnitudes are positive integral multiples of 2π. [1] As a result, the constant π is the unique number such that the circle group, equipped with its Haar measure, is Pontrjagin dual to the lattice of integral multiples of 2π. This is a version of the one-dimensional Poisson summation formula.
Modular forms satisfy an invariance property under the modular group (or its various subgroups), a lattice in the group . Like the complex exponentials of Fourier series, modular forms are characterized by their transformation properties. They also involve π, once again because of the Stone–von Neumann theorem.
- ^ Nicolas Bourbaki (1979), Fonctions d'une variable réelle, Springer, §II.3.
That's pretty good, but I think the article should at least include the form of the Fourier series, to show where π appears. Also, the text above does not connect Fourier series with periodic functions on the circle. Finally, there is no mention at all of the Jacobi theta function. Also, I really disagree that there should be no expository material here. There is plenty of expository material about other aspects of π throughout the article. It should be kept to a minimum, but it cannot be eliminated entirely. Sławomir Biały ( talk) 11:23, 8 May 2016 (UTC)
It looks like Ozob did I nice job of clarifying the intended logic of things. I have streamlined it a bit more, in a way to clarify the sense in which π is essential to Fourier analysis, at the slight expense of leaving out some of the more familiar formulae of the subject, since these apparently distract from the main point. Sławomir Biały ( talk) 20:42, 8 May 2016 (UTC)
I have concerns about the following statement in the article:
Monte Carlo methods for approximating π are very slow compared to other methods, and are never used to approximate π when speed or accuracy is desired. [1]
It is referenced to Arndt and Haenel (2006) and Posamentier and Lehmann (2004), neither of which is very awe inspiring as a reliable source for mathematical claims like this. Moreover, the assessment of Arndt and Haenel is that Monty Carlo methods converge slowly. This is clearly not even true, since every conventional method already is a Monty Carlo method (with a fairly boring probability distribution). Sławomir Biały ( talk) 13:15, 13 May 2016 (UTC)
References
Typically isn't randomness an additional input to an algorithm that can be used for accelerating it? Compare with primality testing, where the fastest algorithms are the probabilistic algorithms. This is the reason Monte Carlo methods are used in the first place. Knuth defines a Monte Carlo method as "Any method that uses random numbers (possibly not producing a correct answer)." This distinguishes "method" from "algorithm" I guess. Anyway, it's trivial to construct a Monte Carlo method (in fact an "algorithm") that is at least as fast as conventional methods: just toss a coin to decide which of two reasonably fast algorithms to use. This does not use randomness in a very essential way that actually accelerates the convergence, but it also certainly doesn't hurt either.
On a related matter, we know that pi can be felt in spectra of random processes like Johnson noise. Is there any practical implementation of this? I'd be curious to know if there is an estimate of the marginal cost, in bits of entropy, to produce a digit of pi. It seems from the random walk example that convergence is very slow. I did another simulation, with comparable performance, that used Brownian local time.
Sławomir
Biały
12:42, 18 May 2016 (UTC)
In the lead section we find:
"The digits appear to be randomly distributed; however, to date, no proof of this has been discovered."
This is highly suspicious information. It is known that pi is infinite and never repeating. Someone needs to clarify this, as it will confuse the reader. EeeveeeFrost ( talk) 01:26, 11 July 2016 (UTC)
@ Sławomir Biały: Sure, I understand. Just let me ask you something: Don't you think that the sentence might confuse the average reader? Because when I read it for the first time, I understood that there is a possibility that pi is not just infinitely many numbers that are (or appear to be) random; and that made me feel confused at first. We know that pi is calculated using an infinite sum π/4 = 1 - 1/3 + 1/5 - 1/7..... and that obviously leads to non repeating and "random looking" numbers.
Anyway, if you don't think that the sentence might be misleading, then I'll just give up and leave the way it is. EeeveeeFrost ( talk) 15:58, 11 July 2016 (UTC)
I'm not certain I agree that 1-random is "the" default meaning of random here, but I'll accept that it might be in some circles. I've clarified the language in a way that hopefully settles that objection. Sławomir Biały ( talk) 23:04, 11 July 2016 (UTC)
There used to be an HTML comment at the top of the article saying "Please note that Wikipedia is not the place to store millions of digits of pi." Somebody removed it. Why?? Georgia guy ( talk) 23:19, 11 July 2016 (UTC)
The current text on spigot algorithms says that no such algorithm is known for decimal digits of pi.
Yet there's this article 'A Spigot Algorithm for the Digits of Pi', by Stanley Rabinowitz and Stan Wagon, to be found here: http://www.mathpropress.com/stan/bibliography/spigot.pdf that says how to do it.
Is this research discredited or should we alter the text on spigot algorithms? Dr. Crash ( talk) 15:15, 10 October 2016 (UTC)
The article states: For example, one may compute directly the arc length of the top half of the unit circle given in Cartesian coordinates by x2 + y2 = 1, as the integral:
But at the same time, in abuse of notation it is explained: A related abuse of notation occurs when integrals like are written as , as if were a term multiplied into the integral's argument.
Am I missing something? -- bender235 ( talk) 23:06, 19 November 2016 (UTC)
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We need to update the record number of digits, which has increased significantly in November. See http://www.pi2e.ch/ which is linked at your reference 3. The new values are: 22 459 157 718 361 decimal digits 18 651 926 753 033 hexadecimal digits There is an error in saying trillion is 10^13. It is 10^12.
The original text is:
extended the decimal representation of π to, as of 2015, over 13.3 trillion (10^13) digits.[3]
The new text should be"
extended the decimal representation of π to, as of November 2016, over 22.4 trillion (10^12) digits.[3]
A new footnote reference to http://www.pi2e.ch/ might be added, even though it is linked at reference 3.
agb — Preceding unsigned comment added by 143.43.206.244 ( talk) 20:29, 22 December 2016 (UTC)
This looks like it might be some good WP:RS. I don't think I saw everything from it in this in the article, but I didn't look closely. Was trying to figure out how old the concept of PI is (not necessarily its computation -- it is after all a ratio, so you don't have to necessarily calculate to use it (i.e. if you have one circle of diameter d, and circumference c, then you can estimate the circumference of a circle of 2d to be 2c by proportion without ever calculating pi, but understanding that the ratio is fixed). I think our article is incomplete on dealing with the concept of Pi, but I'm no expert in this subject. -- David Tornheim ( talk) 14:56, 27 March 2017 (UTC)
Re this diff.
If my memory is correct, which it may not be, this was added by User:Sławomir Biały. At the time, I really didn't understand what it was supposed to mean, but I figured that was probably because I hadn't thought about it hard enough.
So now that it's come down to a showdown — Sławomir, what did you mean exactly? It sounds interesting. Would be good to have a cite. -- Trovatore ( talk) 08:57, 14 April 2017 (UTC)
The number π appears generally in the mathematical analysis of any periodic phenomenon; it appears therefore in areas .... D.Lazard ( talk) 12:07, 14 April 2017 (UTC)
I do not see anymore why this technical discussion is relevant for this article. After reading this discussion, I oppose to mention eigenvalues in the lead. In fact, most readers ignore what is an eigenvalue, and the link between π and eigenvalues is obscure for most of the others, including two experimented mathematics Wikipedia editors who have participated to this discussion ( Trovatore and myself).
IMO, this discussion should be focused to the sections "Spectral characterization" and "Gaussian integral", which suffer of several issues. Firstly they appear as subsections of "Fundamentals", when they should appear in section "Use". Secondly, they present things from a non-neutral point of view, consisting in presenting eigenvalues as the most fundamental concept to which everything to be linked. This appear already in the title of the first section: Is there really any spectral characterization of π? Does exist any source talking of a "spectral characterization of π"? Thirdly, although the applications presented in these sections are fully relevant for the section "Use", the tentative to present them as specific cases of a general eigenvalue problem is a fundamental error. In fact, eigenvalues are not an object of study by themselves, there are a tool for studying (and classifying) various problems. Thus the fact that π occurs as an eigenvalue is not a property of eigenvalues, but a property of some underlying problem. I agree that this is a rather subtle distinction, but explained why a point of view is not neutral, is rarely easy.
My conclusion is that these sections should be moved, the first one should be renamed, and they should be rewritten for much less focusing on eigenvalues. D.Lazard ( talk) 11:14, 15 April 2017 (UTC)
It is said that is not algebraic, but by using Taylor series,the inverse trigonometric function for Sine you can obtain. It's not mentioned in the article or is it new?
199.119.233.200 ( talk) 12:12, 22 May 2017 (UTC)
I hope the following example will clarify the problem,and they are all angles in term of cos and sin.
For Lengths of a=x where x,y,z are the lengths of the sides of the triangle in terms of a,b,c.
For Lengths of b=y
For Lengths of c=z
199.119.233.150 ( talk) 18:52, 22 May 2017 (UTC)
Can you add a topic on the digits of π The first 141 digits of π(not including the first 3) is: 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172 Mug1wara ( talk) 08:05, 2 June 2017 (UTC)
The section Pi#Cauchy distribution and potential theory says
Am I correct in assuming that this should have a "dx" at the end? Loraof ( talk) 16:39, 2 July 2017 (UTC)
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At the beginning of the article, after the name of pi and the equivalent greek letter π, it would be useful to mention, as an addition, that "this letter is the initial of the greek word περιφέρεια, which stands for periphery, and that this was first introduced by Leonhard Euler in the 17th century". I don't think any reference or documentation is needed here - it is straightforward. Thanks. 37.6.21.2 ( talk) 23:16, 10 August 2017 (UTC)
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2001:E68:540D:9DDD:99E:F815:EBCB:D24D ( talk) 12:49, 21 August 2017 (UTC)
There is currently a discussion at
Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. The thread is
Pi page. --
Shirt58 (
talk)
08:16, 17 September 2017 (UTC)
It has always bothered me that the definition of pi does not state that it is defined using the common metric. In other metric spaces the value of pi defined as the ratio of the circumference of a circle to its radius will vary. For instance, in the metric space used to measure distance in a city with regularly spaced orthogonal streets, the value of pi is 2*sqrt(2). If the coordinates are shifted by 45 degrees the metric becomes d = max(|x1-x2|,|y1-y2|) and we get a rational value for pi of 4. PetersRet ( talk) 16:50, 2 August 2017 (UTC)
That is true, but look at the first paragraph of the article in which it says pi is the ratio of the circumference to the radius. I was merely pointing out that this is not true in all metric spaces. PetersRet ( talk) 18:21, 2 August 2017 (UTC)
I'd also like to see more than 6 significant digits in the lead!! (Which states that the ancients knew it to 7.) I'm also slightly uncomfortable with the claim that it can't be exactly expressed as a fraction. It can be exactly expressed, as well as exactly defined, as a recurring fraction (which is not a ratio of two whole numbers). A minor point. 98.21.70.161 ( talk) 18:26, 24 October 2017 (UTC)
¶ Not quite related to this, but a few years ago on some other place on the internet (I have forgotten where), I was whining about the precision of calculations made with a value of pi that only went to ten decimal spaces, and someone responded that (and I probably have misremembered the exact details) that the value to ten decimal places was sufficient to calculate the volume of the entire galaxy to within a cubic inch, or something like that. Whatever the demonstration of the accuracy of a relatively short value of pi might be, I would be very appreciative if someone knowledgeable would add the appropriate statement and citation to the article. Sussmanbern ( talk) 17:37, 6 November 2017 (UTC)
"Digits" of pi has to include all digits, including the leading three. Thus the current article text:
"Decimal: The first 50 decimal digits are 3.14159265358979323846264338327950288419716939937510..."
"Hexadecimal: The base 16 approximation to 20 digits is 3.243F6A8885A308D31319..."
need to be changed to either
"Decimal: The first 51 decimal digits are 3.14159265358979323846264338327950288419716939937510..."
"Hexadecimal: The base 16 approximation to 21 digits is 3.243F6A8885A308D31319..."
"Decimal: The first 50 decimal digits to the right of the decimal point are 3.14159265358979323846264338327950288419716939937510..."
"Hexadecimal: The base 16 approximation to 20 digits to the right of the decimal point is 3.243F6A8885A308D31319..."
—DIV (
120.17.34.237 (
talk)
13:29, 19 October 2017 (UTC))
According to scientific rules, numbers are divided into groups of 3 digits to ease readability. ("Following the 9th CGPM (1948, Resolution 7) and the 22nd CGPM (2003, Resolution 10), for numbers with many digits the digits may be divided into groups of three by a thin space, in order to facilitate reading." https://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf 5.3.4). I will therefore change the groups of 5 into groups of 3. 2A03:2260:A:B:29EC:BFAD:2CF3:8941 ( talk) 17:12, 17 November 2017 (UTC) Okay, I cannot edit right know, because the article is protected... 2A03:2260:A:B:29EC:BFAD:2CF3:8941 ( talk) 17:15, 17 November 2017 (UTC)
"The practice of grouping digits in this way is a matter of choice; it is not always followed in certain specialized applications such as...". -- Deacon Vorbis ( talk) 17:52, 17 November 2017 (UTC)
something like is not right, is right 165.255.71.229 ( talk) 09:01, 7 December 2017 (UTC)
Hi there, it seems to me that many users might come to this page looking for the first few digits of the decimal expansion of pi. To find these it is necessary to scroll to the sixth section, where they aren't particularly well sign-posted. Would it make sense to have more than the current 5 decimal places in the first paragraph? 82.150.96.2 ( talk) 10:01, 4 January 2018 (UTC)
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100,000 digits of pi (again)
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3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 89122 79381 83011 94912 98336 73362 44065 66430 86021 39494 63952 24737 19070 21798 60943 70277 05392 17176 29317 67523 84674 81846 76694 05132 00056 81271 45263 56082 77857 71342 75778 96091 73637 17872 14684 40901 22495 34301 46549 58537 10507 92279 68925 89235 42019 95611 21290 21960 86403 44181 59813 62977 47713 09960 51870 72113 49999 99837 29780 49951 05973 17328 16096 31859 50244 59455 34690 83026 42522 30825 33446 85035 26193 11881 71010 00313 78387 52886 58753 32083 81420 61717 76691 47303 59825 34904 28755 46873 11595 62863 88235 37875 93751 95778 18577 80532 17122 68066 13001 92787 66111 95909 21642 01989 38095 25720 10654 85863 27886 59361 53381 82796 82303 01952 03530 18529 68995 77362 25994 13891 24972 17752 83479 13151 55748 57242 45415 06959 50829 53311 68617 27855 88907 50983 81754 63746 49393 19255 06040 09277 01671 13900 98488 24012 85836 16035 63707 66010 47101 81942 95559 61989 46767 83744 94482 55379 77472 68471 04047 53464 62080 46684 25906 94912 93313 67702 89891 52104 75216 20569 66024 05803 81501 93511 25338 24300 35587 64024 74964 73263 91419 92726 04269 92279 67823 54781 63600 93417 21641 21992 45863 15030 28618 29745 55706 74983 85054 94588 58692 69956 90927 21079 75093 02955 32116 53449 87202 75596 02364 80665 49911 98818 34797 75356 63698 07426 54252 78625 51818 41757 46728 90977 77279 38000 81647 06001 61452 49192 17321 72147 72350 14144 19735 68548 16136 11573 52552 13347 57418 49468 43852 33239 07394 14333 45477 62416 86251 89835 69485 56209 92192 22184 27255 02542 56887 67179 04946 01653 46680 49886 27232 79178 60857 84383 82796 79766 81454 10095 38837 86360 95068 00642 25125 20511 73929 84896 08412 84886 26945 60424 19652 85022 21066 11863 06744 27862 20391 94945 04712 37137 86960 95636 43719 17287 46776 46575 73962 41389 08658 32645 99581 33904 78027 59009 94657 64078 95126 94683 98352 59570 98258 22620 52248 94077 26719 47826 84826 01476 99090 26401 36394 43745 53050 68203 49625 24517 49399 65143 14298 09190 65925 09372 21696 46151 57098 58387 41059 78859 59772 97549 89301 61753 92846 81382 68683 86894 27741 55991 85592 52459 53959 43104 99725 24680 84598 72736 44695 84865 38367 36222 62609 91246 08051 24388 43904 51244 13654 97627 80797 71569 14359 97700 12961 60894 41694 86855 58484 06353 42207 22258 28488 64815 84560 28506 01684 27394 52267 46767 88952 52138 52254 99546 66727 82398 64565 96116 35488 62305 77456 49803 55936 34568 17432 41125 15076 06947 94510 96596 09402 52288 79710 89314 56691 36867 22874 89405 60101 50330 86179 28680 92087 47609 17824 93858 90097 14909 67598 52613 65549 78189 31297 84821 68299 89487 22658 80485 75640 14270 47755 51323 79641 45152 37462 34364 54285 84447 95265 86782 10511 41354 73573 95231 13427 16610 21359 69536 23144 29524 84937 18711 01457 65403 59027 99344 03742 00731 05785 39062 19838 74478 08478 48968 33214 45713 86875 19435 06430 21845 31910 48481 00537 06146 80674 91927 81911 97939 95206 14196 63428 75444 06437 45123 71819 21799 98391 01591 95618 14675 14269 12397 48940 90718 64942 31961 56794 52080 95146 55022 52316 03881 93014 20937 62137 85595 66389 37787 08303 90697 92077 34672 21825 62599 66150 14215 03068 03844 77345 49202 60541 46659 25201 49744 28507 32518 66600 21324 34088 19071 04863 31734 64965 14539 05796 26856 10055 08106 65879 69981 63574 73638 40525 71459 10289 70641 40110 97120 62804 39039 75951 56771 57700 42033 78699 36007 23055 87631 76359 42187 31251 47120 53292 81918 26186 12586 73215 79198 41484 88291 64470 60957 52706 95722 09175 67116 72291 09816 90915 28017 35067 12748 58322 28718 35209 35396 57251 21083 57915 13698 82091 44421 00675 10334 67110 31412 67111 36990 86585 16398 31501 97016 51511 68517 14376 57618 35155 65088 49099 89859 98238 73455 28331 63550 76479 18535 89322 61854 89632 13293 30898 57064 20467 52590 70915 48141 65498 59461 63718 02709 81994 30992 44889 57571 28289 05923 23326 09729 97120 84433 57326 54893 82391 19325 97463 66730 58360 41428 13883 03203 82490 37589 85243 74417 02913 27656 18093 77344 40307 07469 21120 19130 20330 38019 76211 01100 44929 32151 60842 44485 96376 69838 95228 68478 31235 52658 21314 49576 85726 24334 41893 03968 64262 43410 77322 69780 28073 18915 44110 10446 82325 27162 01052 65227 21116 60396 66557 30925 47110 55785 37634 66820 65310 98965 26918 62056 47693 12570 58635 66201 85581 00729 36065 98764 86117 91045 33488 50346 11365 76867 53249 44166 80396 26579 78771 85560 84552 96541 26654 08530 61434 44318 58676 97514 56614 06800 70023 78776 59134 40171 27494 70420 56223 05389 94561 31407 11270 00407 85473 32699 39081 45466 46458 80797 27082 66830 63432 85878 56983 05235 80893 30657 57406 79545 71637 75254 20211 49557 61581 40025 01262 28594 13021 64715 50979 25923 09907 96547 37612 55176 56751 35751 78296 66454 77917 45011 29961 48903 04639 94713 29621 07340 43751 89573 59614 58901 93897 13111 79042 97828 56475 03203 19869 15140 28708 08599 04801 09412 14722 13179 47647 77262 24142 54854 54033 21571 85306 14228 81375 85043 06332 17518 29798 66223 71721 59160 77166 92547 48738 98665 49494 50114 65406 28433 66393 79003 97692 65672 14638 53067 36096 57120 91807 63832 71664 16274 88880 07869 25602 90228 47210 40317 21186 08204 19000 42296 61711 96377 92133 75751 14959 50156 60496 31862 94726 54736 42523 08177 03675 15906 73502 35072 83540 56704 03867 43513 62222 47715 89150 49530 98444 89333 09634 08780 76932 59939 78054 19341 44737 74418 42631 29860 80998 88687 41326 04721 56951 62396 58645 73021 63159 81931 95167 35381 29741 67729 47867 24229 24654 36680 09806 76928 23828 06899 64004 82435 40370 14163 14965 89794 09243 23789 69070 69779 42236 25082 21688 95738 37986 23001 59377 64716 51228 93578 60158 81617 55782 97352 33446 04281 51262 72037 34314 65319 77774 16031 99066 55418 76397 92933 44195 21541 34189 94854 44734 56738 31624 99341 91318 14809 27777 10386 38773 43177 20754 56545 32207 77092 12019 05166 09628 04909 26360 19759 88281 61332 31666 36528 61932 66863 36062 73567 63035 44776 28035 04507 77235 54710 58595 48702 79081 43562 40145 17180 62464 36267 94561 27531 81340 78330 33625 42327 83944 97538 24372 05835 31147 71199 26063 81334 67768 79695 97030 98339 13077 10987 04085 91337 46414 42822 77263 46594 70474 58784 77872 01927 71528 07317 67907 70715 72134 44730 60570 07334 92436 93113 83504 93163 12840 42512 19256 51798 06941 13528 01314 70130 47816 43788 51852 90928 54520 11658 39341 96562 13491 43415 95625 86586 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34072 39610 36854 06643 19395 09790 19069 96395 52453 00545 05806 85501 95673 02292 19139 33918 56803 44903 98205 95510 02263 53536 19204 19947 45538 59381 02343 95544 95977 83779 02374 21617 27111 72364 34354 39478 22181 85286 24085 14006 66044 33258 88569 86705 43154 70696 57474 58550 33232 33421 07301 54594 05165 53790 68662 73337 99585 11562 57843 22988 27372 31989 87571 41595 78111 96358 33005 94087 30681 21602 87649 62867 44604 77464 91599 50549 73742 56269 01049 03778 19868 35938 14657 41268 04925 64879 85561 45372 34786 73303 90468 83834 36346 55379 49864 19270 56387 29317 48723 32083 76011 23029 91136 79386 27089 43879 93620 16295 15413 37142 48928 30722 01269 01475 46684 76535 76164 77379 46752 00490 75715 55278 19653 62132 39264 06160 13635 81559 07422 02020 31872 77605 27721 90055 61484 25551 87925 30343 51398 44253 22341 57623 36106 42506 39049 75008 65627 10953 59194 65897 51413 10348 22769 30624 74353 63256 91607 81547 81811 52843 66795 70611 08615 33150 44521 27473 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69998 92256 95968 81592 05600 10165 52563 7567 ... |
107.194.6.189 ( talk) 02:38, 17 February 2018 (UTC)
In the Approximate value section, would someone change "approximation" to "truncation" in several places? These are not the value of pi rounded to the specified number of places, but the value of pi truncated to the specified number of places. Please consider also adding "3.8Ti0l" as an alternate sexagesimal representation. 64.132.59.226 ( talk) 19:25, 14 February 2018 (UTC)
Actually, should we have 50 places in the fractional part for each representation? These truncations would be:
64.132.59.226 ( talk) 19:32, 14 February 2018 (UTC)
The animation use the circle's diameter (and not the the radius) and finishes by labeling the full rotation of the circle as being pi and (not 2 times pi) — Preceding unsigned comment added by NicolasLefebvre54 ( talk • contribs) 04:06, 20 March 2018 (UTC)
The article states that: differential calculus typically precedes integral calculus in the university curriculum, so it is desirable to have a definition of π that does not rely on the latter. One such definition, due to Richard Baltzer, and popularized by Edmund Landau, is the following: π is twice the smallest positive number at which the cosine function equals 0.
I have looked into one of the citations "Walter Rudin - Principle of Mathematical Analysis" (p 182-183), and found out that the existence of such constant is proved using an integral. Is there another proof that doesn't uses integral calculus at all? Otherwise this statement seems to be false. — Preceding unsigned comment added by 109.67.101.82 ( talk) 08:53, 23 March 2018 (UTC)
Question; Why does this keep getting deleted for "unsourced"? It is clearly stated that this is engraved in stone at the Washington Park MAX station (Portland, Oregon). I took that picture. What else would make it "sourced"?
As for "trivial", a wrong value engraved in stone at a very public location is "trivial"??? Then, what about the one right above it about Knuth's silly version numbers? Would you delete that as well? Williampfeifer ( talk) 21:24, 14 April 2018 (UTC)
The article should not contain a lengthy decimal representation of a number that isn't π. In fact, the added text
3.1415926535 821480865144 288109757245 870066330572 703698336733 620005681271 420199561150 244594555982 534904897932
has more digits of non-π than the article has of the digits of π itself! Sławomir Biały ( talk) 22:33, 14 April 2018 (UTC)
Would this count as a reliable source?:
https://blog.plover.com/math/wrong-pi.html
I agree, a simple mistake is trivial. What makes it non-trivial is that it's engraved in stone in a very public place, for about 20 years now, and isn't been fixed. (Yes, the city knows about it; there was an article in the Oregonian newspaper about it back then, but I can't figure out how to access old articles on that paper)
I'm aware that someone could not see that picture. That is why I added the numbers as text. However, this text addition itself is being objected to. So I'm caught between a rock and a hard place.
Williampfeifer (
talk)
01:44, 15 April 2018 (UTC)
How about something like this:
At the
Washington Park MAX station (Portland, Oregon) are granite plaques honoring various attributes of Oregon. One plaque, intending to honor the science sector, supposedly bears the engraved value of pi. However, the digits are incorrect, beginning at the 12th place after the decimal
[1]. Instead of 3.14159265358979323846..., it shows 3.1415926535821480865144..., and so on. In fact, the digits, as engraved on the plaque are pi's digits 1 to 10, followed by digits 101 to 110, then the digits 201 to 210 and so on.
Williampfeifer (
talk)
02:55, 15 April 2018 (UTC)
It's pure trivia. HiLo48 ( talk) 03:33, 15 April 2018 (UTC)
Fact is
My opinion is
Sorry, Williampfeifer. Purgy ( talk) 07:54, 15 April 2018 (UTC)
References
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No formula was derived to calculate pi in 21st century until 2017. In 2017 a young Indian Mathematician Karthikeya Gounder alias Karthik(18 years old) had derived a new formula to calculate the value of pi upto infinite digits in the paper " π-The Transcendental Number"[1]. In that paper,Pi is expressed in a new way rather than a series converging to the exact value. It relates the mathematical constant pi with Trignometric tan.
References 1.Karthikeya Gounder: π-The Transcendental Number
MAT-KOL(BanjaLuka) ISSN:0354-6969(p),ISSN:1986-5228(o)
Vol.XXIII(1)(2017),61-66 DOI:10.7251/MK1701061G
Paper link: http://www.imvibl.org/dmbl/meso/mat_kol_23_1_2017/mat_kol_23_1_2017_61_66.pdf
Additional reference 1. http://www.academia.edu/32137897/Karthikeya_Gounder_π-THE_TRANSCENDENTAL_NUMBER_MAT-KOL_XXIII_1_2017_61-66 Karthikeyagounderr ( talk) 05:08, 29 April 2018 (UTC)
There is a new type of calculus in Regular rule published in 2018 by Amir Forsati. its proof is written on that page too.
Please not that the in the tangent is 180 degrees.
proof confirmation by StackExchange geeks. — Preceding unsigned comment added by Pw2iur ( talk • contribs) 18:31, 10 April 2018 (UTC)
Does anybody think it would be appropriate to include a section with pi written out to 1,000 decimal places? DangleSnipeCelly ( talk) 20:43, 4 May 2018 (UTC)DangleSnipeCelly1
OK. Thank you. DangleSnipeCelly ( talk) 23:48, 4 May 2018 (UTC)DangleSnipeCelly1
![]() | 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. |
Archive 10 | ← | Archive 13 | Archive 14 | Archive 15 | Archive 16 | Archive 17 |
I have no horse in this race, but my watchlist is showing this content being added and removed back and forth a lot today. Discussions via edit summary obviously aren't going to cut it, so I wanted to start a discussion and see if we can figure out some consensus on the material, one way or another. The edit summaries don't really explain the objection to the material, would one of the editors involved in adding or removing the content mind explaining why it should be added/removed? There's a lot of editing back and forth so try as I might it's hard to make sense of what the issue is exactly. - Aoidh ( talk) 06:18, 5 May 2016 (UTC)
This is just tit-for-tat disruptive editing. Takahiro4 added a template, which was against any known (to me) use of such templates. It was placed in such a way as to break the flow of text in the article and, furthermore, was unnecessary as we already Wikilink to the concept. I reverted the edit, and explained as much. Takahiro reverted back, with a cryptic, non-explaining edit summary. I reverted again, and told Takahiro to explain on the talk page why he thought this was a good idea. Instead of doing that, he proceeded to remove large well-sourced sections of text from the article (that I had recently written). He reverted this two more times [1], [2]. His massive removal was reverted by three different editors. This is clearly a case of one editor acting disruptively. I suggest that the solution is not page protection, but just blocking the obviously disruptive editor. I note that Takahiro4 was the one who requested page protection, after he was over 3RR. That also seems like a disruptive abuse of process, and the kind of thing that protecting admins should look at before they decide to protect a page that is undergoing active revision ( WP:TROUT might be relevant). I have pinged the protecting admin, but if I don't here back, I will raise the issue at ANI. Sławomir Biały ( talk) 09:35, 5 May 2016 (UTC)
Another reference (which I just added to
area of a disk) that should be added to the discussion of the isoperimetric inequality here is: Isaac Chavel (2001), Isoperimetric inequalities, Cambridge University Press (especially the introduction). There are clear statements there about the isoperimetric functional and its minimizer. Also it shows in great depth how isoperimetry is related to Sobolev inequalities, so is a good secondary source for that entire paragraph.
Sławomir
Biały
11:29, 5 May 2016 (UTC)
Also you always say it isn't me."I am not involved at this edit."That is not possible.And david is involving with my discussion,unsuitable.And just other patrollers are automatically responded.Unfortunately your judge is not correct.But I thought about fourier.I think fourier transform is not good,but I feel fourier series are strong connected with pi.Because Fourier transform is just expressed using e^πi by euler's equation,clearly fourier series are connected with pi.I hope this suggestion. See you later.-- Takahiro4 ( talk) 05:54, 6 May 2016 (UTC)
A lot of new material has been added under the heading "Fourier series and modular forms". I don't believe most of this is directly relevant to pi. At most, there should be a brief mention of these topics, with links to the main articles. -- Macrakis ( talk) 17:39, 7 May 2016 (UTC)
Fourier series and modular forms
The constant π appears naturally in Fourier series.
In harmonic analysis, periodic functions are often regarded as functions on the circle group T. The Fourier decomposition shows that a complex-valued function f on T can be written as an infinite linear superposition of complex exponentials , each of which involves π. The complex exponentials, in turn, can be characterized by their transformation properties under T: they constitute a character of T, that is, a function from T to the group of unit modulus complex numbers, that is also a group homomorphism. Using the Haar measure on the circle group, the constant π is half the magnitude of the Radon–Nikodym derivative of this character. The other characters have derivatives whose magnitudes are positive integral multiples of 2π. [1] As a result, the constant π is the unique number such that the circle group, equipped with its Haar measure, is Pontrjagin dual to the lattice of integral multiples of 2π. This is a version of the one-dimensional Poisson summation formula.
Modular forms satisfy an invariance property under the modular group (or its various subgroups), a lattice in the group . Like the complex exponentials of Fourier series, modular forms are characterized by their transformation properties. They also involve π, once again because of the Stone–von Neumann theorem.
- ^ Nicolas Bourbaki (1979), Fonctions d'une variable réelle, Springer, §II.3.
That's pretty good, but I think the article should at least include the form of the Fourier series, to show where π appears. Also, the text above does not connect Fourier series with periodic functions on the circle. Finally, there is no mention at all of the Jacobi theta function. Also, I really disagree that there should be no expository material here. There is plenty of expository material about other aspects of π throughout the article. It should be kept to a minimum, but it cannot be eliminated entirely. Sławomir Biały ( talk) 11:23, 8 May 2016 (UTC)
It looks like Ozob did I nice job of clarifying the intended logic of things. I have streamlined it a bit more, in a way to clarify the sense in which π is essential to Fourier analysis, at the slight expense of leaving out some of the more familiar formulae of the subject, since these apparently distract from the main point. Sławomir Biały ( talk) 20:42, 8 May 2016 (UTC)
I have concerns about the following statement in the article:
Monte Carlo methods for approximating π are very slow compared to other methods, and are never used to approximate π when speed or accuracy is desired. [1]
It is referenced to Arndt and Haenel (2006) and Posamentier and Lehmann (2004), neither of which is very awe inspiring as a reliable source for mathematical claims like this. Moreover, the assessment of Arndt and Haenel is that Monty Carlo methods converge slowly. This is clearly not even true, since every conventional method already is a Monty Carlo method (with a fairly boring probability distribution). Sławomir Biały ( talk) 13:15, 13 May 2016 (UTC)
References
Typically isn't randomness an additional input to an algorithm that can be used for accelerating it? Compare with primality testing, where the fastest algorithms are the probabilistic algorithms. This is the reason Monte Carlo methods are used in the first place. Knuth defines a Monte Carlo method as "Any method that uses random numbers (possibly not producing a correct answer)." This distinguishes "method" from "algorithm" I guess. Anyway, it's trivial to construct a Monte Carlo method (in fact an "algorithm") that is at least as fast as conventional methods: just toss a coin to decide which of two reasonably fast algorithms to use. This does not use randomness in a very essential way that actually accelerates the convergence, but it also certainly doesn't hurt either.
On a related matter, we know that pi can be felt in spectra of random processes like Johnson noise. Is there any practical implementation of this? I'd be curious to know if there is an estimate of the marginal cost, in bits of entropy, to produce a digit of pi. It seems from the random walk example that convergence is very slow. I did another simulation, with comparable performance, that used Brownian local time.
Sławomir
Biały
12:42, 18 May 2016 (UTC)
In the lead section we find:
"The digits appear to be randomly distributed; however, to date, no proof of this has been discovered."
This is highly suspicious information. It is known that pi is infinite and never repeating. Someone needs to clarify this, as it will confuse the reader. EeeveeeFrost ( talk) 01:26, 11 July 2016 (UTC)
@ Sławomir Biały: Sure, I understand. Just let me ask you something: Don't you think that the sentence might confuse the average reader? Because when I read it for the first time, I understood that there is a possibility that pi is not just infinitely many numbers that are (or appear to be) random; and that made me feel confused at first. We know that pi is calculated using an infinite sum π/4 = 1 - 1/3 + 1/5 - 1/7..... and that obviously leads to non repeating and "random looking" numbers.
Anyway, if you don't think that the sentence might be misleading, then I'll just give up and leave the way it is. EeeveeeFrost ( talk) 15:58, 11 July 2016 (UTC)
I'm not certain I agree that 1-random is "the" default meaning of random here, but I'll accept that it might be in some circles. I've clarified the language in a way that hopefully settles that objection. Sławomir Biały ( talk) 23:04, 11 July 2016 (UTC)
There used to be an HTML comment at the top of the article saying "Please note that Wikipedia is not the place to store millions of digits of pi." Somebody removed it. Why?? Georgia guy ( talk) 23:19, 11 July 2016 (UTC)
The current text on spigot algorithms says that no such algorithm is known for decimal digits of pi.
Yet there's this article 'A Spigot Algorithm for the Digits of Pi', by Stanley Rabinowitz and Stan Wagon, to be found here: http://www.mathpropress.com/stan/bibliography/spigot.pdf that says how to do it.
Is this research discredited or should we alter the text on spigot algorithms? Dr. Crash ( talk) 15:15, 10 October 2016 (UTC)
The article states: For example, one may compute directly the arc length of the top half of the unit circle given in Cartesian coordinates by x2 + y2 = 1, as the integral:
But at the same time, in abuse of notation it is explained: A related abuse of notation occurs when integrals like are written as , as if were a term multiplied into the integral's argument.
Am I missing something? -- bender235 ( talk) 23:06, 19 November 2016 (UTC)
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We need to update the record number of digits, which has increased significantly in November. See http://www.pi2e.ch/ which is linked at your reference 3. The new values are: 22 459 157 718 361 decimal digits 18 651 926 753 033 hexadecimal digits There is an error in saying trillion is 10^13. It is 10^12.
The original text is:
extended the decimal representation of π to, as of 2015, over 13.3 trillion (10^13) digits.[3]
The new text should be"
extended the decimal representation of π to, as of November 2016, over 22.4 trillion (10^12) digits.[3]
A new footnote reference to http://www.pi2e.ch/ might be added, even though it is linked at reference 3.
agb — Preceding unsigned comment added by 143.43.206.244 ( talk) 20:29, 22 December 2016 (UTC)
This looks like it might be some good WP:RS. I don't think I saw everything from it in this in the article, but I didn't look closely. Was trying to figure out how old the concept of PI is (not necessarily its computation -- it is after all a ratio, so you don't have to necessarily calculate to use it (i.e. if you have one circle of diameter d, and circumference c, then you can estimate the circumference of a circle of 2d to be 2c by proportion without ever calculating pi, but understanding that the ratio is fixed). I think our article is incomplete on dealing with the concept of Pi, but I'm no expert in this subject. -- David Tornheim ( talk) 14:56, 27 March 2017 (UTC)
Re this diff.
If my memory is correct, which it may not be, this was added by User:Sławomir Biały. At the time, I really didn't understand what it was supposed to mean, but I figured that was probably because I hadn't thought about it hard enough.
So now that it's come down to a showdown — Sławomir, what did you mean exactly? It sounds interesting. Would be good to have a cite. -- Trovatore ( talk) 08:57, 14 April 2017 (UTC)
The number π appears generally in the mathematical analysis of any periodic phenomenon; it appears therefore in areas .... D.Lazard ( talk) 12:07, 14 April 2017 (UTC)
I do not see anymore why this technical discussion is relevant for this article. After reading this discussion, I oppose to mention eigenvalues in the lead. In fact, most readers ignore what is an eigenvalue, and the link between π and eigenvalues is obscure for most of the others, including two experimented mathematics Wikipedia editors who have participated to this discussion ( Trovatore and myself).
IMO, this discussion should be focused to the sections "Spectral characterization" and "Gaussian integral", which suffer of several issues. Firstly they appear as subsections of "Fundamentals", when they should appear in section "Use". Secondly, they present things from a non-neutral point of view, consisting in presenting eigenvalues as the most fundamental concept to which everything to be linked. This appear already in the title of the first section: Is there really any spectral characterization of π? Does exist any source talking of a "spectral characterization of π"? Thirdly, although the applications presented in these sections are fully relevant for the section "Use", the tentative to present them as specific cases of a general eigenvalue problem is a fundamental error. In fact, eigenvalues are not an object of study by themselves, there are a tool for studying (and classifying) various problems. Thus the fact that π occurs as an eigenvalue is not a property of eigenvalues, but a property of some underlying problem. I agree that this is a rather subtle distinction, but explained why a point of view is not neutral, is rarely easy.
My conclusion is that these sections should be moved, the first one should be renamed, and they should be rewritten for much less focusing on eigenvalues. D.Lazard ( talk) 11:14, 15 April 2017 (UTC)
It is said that is not algebraic, but by using Taylor series,the inverse trigonometric function for Sine you can obtain. It's not mentioned in the article or is it new?
199.119.233.200 ( talk) 12:12, 22 May 2017 (UTC)
I hope the following example will clarify the problem,and they are all angles in term of cos and sin.
For Lengths of a=x where x,y,z are the lengths of the sides of the triangle in terms of a,b,c.
For Lengths of b=y
For Lengths of c=z
199.119.233.150 ( talk) 18:52, 22 May 2017 (UTC)
Can you add a topic on the digits of π The first 141 digits of π(not including the first 3) is: 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172 Mug1wara ( talk) 08:05, 2 June 2017 (UTC)
The section Pi#Cauchy distribution and potential theory says
Am I correct in assuming that this should have a "dx" at the end? Loraof ( talk) 16:39, 2 July 2017 (UTC)
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At the beginning of the article, after the name of pi and the equivalent greek letter π, it would be useful to mention, as an addition, that "this letter is the initial of the greek word περιφέρεια, which stands for periphery, and that this was first introduced by Leonhard Euler in the 17th century". I don't think any reference or documentation is needed here - it is straightforward. Thanks. 37.6.21.2 ( talk) 23:16, 10 August 2017 (UTC)
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2001:E68:540D:9DDD:99E:F815:EBCB:D24D ( talk) 12:49, 21 August 2017 (UTC)
There is currently a discussion at
Wikipedia:Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. The thread is
Pi page. --
Shirt58 (
talk)
08:16, 17 September 2017 (UTC)
It has always bothered me that the definition of pi does not state that it is defined using the common metric. In other metric spaces the value of pi defined as the ratio of the circumference of a circle to its radius will vary. For instance, in the metric space used to measure distance in a city with regularly spaced orthogonal streets, the value of pi is 2*sqrt(2). If the coordinates are shifted by 45 degrees the metric becomes d = max(|x1-x2|,|y1-y2|) and we get a rational value for pi of 4. PetersRet ( talk) 16:50, 2 August 2017 (UTC)
That is true, but look at the first paragraph of the article in which it says pi is the ratio of the circumference to the radius. I was merely pointing out that this is not true in all metric spaces. PetersRet ( talk) 18:21, 2 August 2017 (UTC)
I'd also like to see more than 6 significant digits in the lead!! (Which states that the ancients knew it to 7.) I'm also slightly uncomfortable with the claim that it can't be exactly expressed as a fraction. It can be exactly expressed, as well as exactly defined, as a recurring fraction (which is not a ratio of two whole numbers). A minor point. 98.21.70.161 ( talk) 18:26, 24 October 2017 (UTC)
¶ Not quite related to this, but a few years ago on some other place on the internet (I have forgotten where), I was whining about the precision of calculations made with a value of pi that only went to ten decimal spaces, and someone responded that (and I probably have misremembered the exact details) that the value to ten decimal places was sufficient to calculate the volume of the entire galaxy to within a cubic inch, or something like that. Whatever the demonstration of the accuracy of a relatively short value of pi might be, I would be very appreciative if someone knowledgeable would add the appropriate statement and citation to the article. Sussmanbern ( talk) 17:37, 6 November 2017 (UTC)
"Digits" of pi has to include all digits, including the leading three. Thus the current article text:
"Decimal: The first 50 decimal digits are 3.14159265358979323846264338327950288419716939937510..."
"Hexadecimal: The base 16 approximation to 20 digits is 3.243F6A8885A308D31319..."
need to be changed to either
"Decimal: The first 51 decimal digits are 3.14159265358979323846264338327950288419716939937510..."
"Hexadecimal: The base 16 approximation to 21 digits is 3.243F6A8885A308D31319..."
"Decimal: The first 50 decimal digits to the right of the decimal point are 3.14159265358979323846264338327950288419716939937510..."
"Hexadecimal: The base 16 approximation to 20 digits to the right of the decimal point is 3.243F6A8885A308D31319..."
—DIV (
120.17.34.237 (
talk)
13:29, 19 October 2017 (UTC))
According to scientific rules, numbers are divided into groups of 3 digits to ease readability. ("Following the 9th CGPM (1948, Resolution 7) and the 22nd CGPM (2003, Resolution 10), for numbers with many digits the digits may be divided into groups of three by a thin space, in order to facilitate reading." https://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf 5.3.4). I will therefore change the groups of 5 into groups of 3. 2A03:2260:A:B:29EC:BFAD:2CF3:8941 ( talk) 17:12, 17 November 2017 (UTC) Okay, I cannot edit right know, because the article is protected... 2A03:2260:A:B:29EC:BFAD:2CF3:8941 ( talk) 17:15, 17 November 2017 (UTC)
"The practice of grouping digits in this way is a matter of choice; it is not always followed in certain specialized applications such as...". -- Deacon Vorbis ( talk) 17:52, 17 November 2017 (UTC)
something like is not right, is right 165.255.71.229 ( talk) 09:01, 7 December 2017 (UTC)
Hi there, it seems to me that many users might come to this page looking for the first few digits of the decimal expansion of pi. To find these it is necessary to scroll to the sixth section, where they aren't particularly well sign-posted. Would it make sense to have more than the current 5 decimal places in the first paragraph? 82.150.96.2 ( talk) 10:01, 4 January 2018 (UTC)
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100,000 digits of pi (again)
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3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196 44288 10975 66593 34461 28475 64823 37867 83165 27120 19091 45648 56692 34603 48610 45432 66482 13393 60726 02491 41273 72458 70066 06315 58817 48815 20920 96282 92540 91715 36436 78925 90360 01133 05305 48820 46652 13841 46951 94151 16094 33057 27036 57595 91953 09218 61173 81932 61179 31051 18548 07446 23799 62749 56735 18857 52724 89122 79381 83011 94912 98336 73362 44065 66430 86021 39494 63952 24737 19070 21798 60943 70277 05392 17176 29317 67523 84674 81846 76694 05132 00056 81271 45263 56082 77857 71342 75778 96091 73637 17872 14684 40901 22495 34301 46549 58537 10507 92279 68925 89235 42019 95611 21290 21960 86403 44181 59813 62977 47713 09960 51870 72113 49999 99837 29780 49951 05973 17328 16096 31859 50244 59455 34690 83026 42522 30825 33446 85035 26193 11881 71010 00313 78387 52886 58753 32083 81420 61717 76691 47303 59825 34904 28755 46873 11595 62863 88235 37875 93751 95778 18577 80532 17122 68066 13001 92787 66111 95909 21642 01989 38095 25720 10654 85863 27886 59361 53381 82796 82303 01952 03530 18529 68995 77362 25994 13891 24972 17752 83479 13151 55748 57242 45415 06959 50829 53311 68617 27855 88907 50983 81754 63746 49393 19255 06040 09277 01671 13900 98488 24012 85836 16035 63707 66010 47101 81942 95559 61989 46767 83744 94482 55379 77472 68471 04047 53464 62080 46684 25906 94912 93313 67702 89891 52104 75216 20569 66024 05803 81501 93511 25338 24300 35587 64024 74964 73263 91419 92726 04269 92279 67823 54781 63600 93417 21641 21992 45863 15030 28618 29745 55706 74983 85054 94588 58692 69956 90927 21079 75093 02955 32116 53449 87202 75596 02364 80665 49911 98818 34797 75356 63698 07426 54252 78625 51818 41757 46728 90977 77279 38000 81647 06001 61452 49192 17321 72147 72350 14144 19735 68548 16136 11573 52552 13347 57418 49468 43852 33239 07394 14333 45477 62416 86251 89835 69485 56209 92192 22184 27255 02542 56887 67179 04946 01653 46680 49886 27232 79178 60857 84383 82796 79766 81454 10095 38837 86360 95068 00642 25125 20511 73929 84896 08412 84886 26945 60424 19652 85022 21066 11863 06744 27862 20391 94945 04712 37137 86960 95636 43719 17287 46776 46575 73962 41389 08658 32645 99581 33904 78027 59009 94657 64078 95126 94683 98352 59570 98258 22620 52248 94077 26719 47826 84826 01476 99090 26401 36394 43745 53050 68203 49625 24517 49399 65143 14298 09190 65925 09372 21696 46151 57098 58387 41059 78859 59772 97549 89301 61753 92846 81382 68683 86894 27741 55991 85592 52459 53959 43104 99725 24680 84598 72736 44695 84865 38367 36222 62609 91246 08051 24388 43904 51244 13654 97627 80797 71569 14359 97700 12961 60894 41694 86855 58484 06353 42207 22258 28488 64815 84560 28506 01684 27394 52267 46767 88952 52138 52254 99546 66727 82398 64565 96116 35488 62305 77456 49803 55936 34568 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31251 47120 53292 81918 26186 12586 73215 79198 41484 88291 64470 60957 52706 95722 09175 67116 72291 09816 90915 28017 35067 12748 58322 28718 35209 35396 57251 21083 57915 13698 82091 44421 00675 10334 67110 31412 67111 36990 86585 16398 31501 97016 51511 68517 14376 57618 35155 65088 49099 89859 98238 73455 28331 63550 76479 18535 89322 61854 89632 13293 30898 57064 20467 52590 70915 48141 65498 59461 63718 02709 81994 30992 44889 57571 28289 05923 23326 09729 97120 84433 57326 54893 82391 19325 97463 66730 58360 41428 13883 03203 82490 37589 85243 74417 02913 27656 18093 77344 40307 07469 21120 19130 20330 38019 76211 01100 44929 32151 60842 44485 96376 69838 95228 68478 31235 52658 21314 49576 85726 24334 41893 03968 64262 43410 77322 69780 28073 18915 44110 10446 82325 27162 01052 65227 21116 60396 66557 30925 47110 55785 37634 66820 65310 98965 26918 62056 47693 12570 58635 66201 85581 00729 36065 98764 86117 91045 33488 50346 11365 76867 53249 44166 80396 26579 78771 85560 84552 96541 26654 08530 61434 44318 58676 97514 56614 06800 70023 78776 59134 40171 27494 70420 56223 05389 94561 31407 11270 00407 85473 32699 39081 45466 46458 80797 27082 66830 63432 85878 56983 05235 80893 30657 57406 79545 71637 75254 20211 49557 61581 40025 01262 28594 13021 64715 50979 25923 09907 96547 37612 55176 56751 35751 78296 66454 77917 45011 29961 48903 04639 94713 29621 07340 43751 89573 59614 58901 93897 13111 79042 97828 56475 03203 19869 15140 28708 08599 04801 09412 14722 13179 47647 77262 24142 54854 54033 21571 85306 14228 81375 85043 06332 17518 29798 66223 71721 59160 77166 92547 48738 98665 49494 50114 65406 28433 66393 79003 97692 65672 14638 53067 36096 57120 91807 63832 71664 16274 88880 07869 25602 90228 47210 40317 21186 08204 19000 42296 61711 96377 92133 75751 14959 50156 60496 31862 94726 54736 42523 08177 03675 15906 73502 35072 83540 56704 03867 43513 62222 47715 89150 49530 98444 89333 09634 08780 76932 59939 78054 19341 44737 74418 42631 29860 80998 88687 41326 04721 56951 62396 58645 73021 63159 81931 95167 35381 29741 67729 47867 24229 24654 36680 09806 76928 23828 06899 64004 82435 40370 14163 14965 89794 09243 23789 69070 69779 42236 25082 21688 95738 37986 23001 59377 64716 51228 93578 60158 81617 55782 97352 33446 04281 51262 72037 34314 65319 77774 16031 99066 55418 76397 92933 44195 21541 34189 94854 44734 56738 31624 99341 91318 14809 27777 10386 38773 43177 20754 56545 32207 77092 12019 05166 09628 04909 26360 19759 88281 61332 31666 36528 61932 66863 36062 73567 63035 44776 28035 04507 77235 54710 58595 48702 79081 43562 40145 17180 62464 36267 94561 27531 81340 78330 33625 42327 83944 97538 24372 05835 31147 71199 26063 81334 67768 79695 97030 98339 13077 10987 04085 91337 46414 42822 77263 46594 70474 58784 77872 01927 71528 07317 67907 70715 72134 44730 60570 07334 92436 93113 83504 93163 12840 42512 19256 51798 06941 13528 01314 70130 47816 43788 51852 90928 54520 11658 39341 96562 13491 43415 95625 86586 55705 52690 49652 09858 03385 07224 26482 93972 85847 83163 05777 75606 88876 44624 82468 57926 03953 52773 48030 48029 00587 60758 25104 74709 16439 61362 67604 49256 27420 42083 20856 61190 62545 43372 13153 59584 50687 72460 29016 18766 79524 06163 42522 57719 54291 62991 93064 55377 99140 37340 43287 52628 88963 99587 94757 29174 64263 57455 25407 90914 51357 11136 94109 11939 32519 10760 20825 20261 87985 31887 70584 29725 91677 81314 96990 09019 21169 71737 27847 68472 68608 49003 37702 42429 16513 00500 51683 23364 35038 95170 29893 92233 45172 20138 12806 96501 17844 08745 19601 21228 59937 16231 30171 14448 46409 03890 64495 44400 61986 90754 85160 26327 50529 83491 87407 86680 88183 38510 22833 45085 04860 82503 93021 33219 71551 84306 35455 00766 82829 49304 13776 55279 39751 75461 39539 84683 39363 83047 46119 96653 85815 38420 56853 38621 86725 23340 28308 71123 28278 92125 07712 62946 32295 63989 89893 58211 67456 27010 21835 64622 01349 67151 88190 97303 81198 00497 34072 39610 36854 06643 19395 09790 19069 96395 52453 00545 05806 85501 95673 02292 19139 33918 56803 44903 98205 95510 02263 53536 19204 19947 45538 59381 02343 95544 95977 83779 02374 21617 27111 72364 34354 39478 22181 85286 24085 14006 66044 33258 88569 86705 43154 70696 57474 58550 33232 33421 07301 54594 05165 53790 68662 73337 99585 11562 57843 22988 27372 31989 87571 41595 78111 96358 33005 94087 30681 21602 87649 62867 44604 77464 91599 50549 73742 56269 01049 03778 19868 35938 14657 41268 04925 64879 85561 45372 34786 73303 90468 83834 36346 55379 49864 19270 56387 29317 48723 32083 76011 23029 91136 79386 27089 43879 93620 16295 15413 37142 48928 30722 01269 01475 46684 76535 76164 77379 46752 00490 75715 55278 19653 62132 39264 06160 13635 81559 07422 02020 31872 77605 27721 90055 61484 25551 87925 30343 51398 44253 22341 57623 36106 42506 39049 75008 65627 10953 59194 65897 51413 10348 22769 30624 74353 63256 91607 81547 81811 52843 66795 70611 08615 33150 44521 27473 92454 49454 23682 88606 13408 41486 37767 00961 20715 12491 40430 27253 86076 48236 34143 34623 51897 57664 52164 13767 96903 14950 19108 57598 44239 19862 91642 19399 49072 36234 64684 41173 94032 65918 40443 78051 33389 45257 42399 50829 65912 28508 55582 15725 03107 12570 12668 30240 29295 25220 11872 67675 62204 15420 51618 41634 84756 51699 98116 14101 00299 60783 86909 29160 30288 40026 91041 40792 88621 50784 24516 70908 70006 99282 12066 04183 71806 53556 72525 32567 53286 12910 42487 76182 58297 65157 95984 70356 22262 93486 00341 58722 98053 49896 50226 29174 87882 02734 20922 22453 39856 26476 69149 05562 84250 39127 57710 28402 79980 66365 82548 89264 88025 45661 01729 67026 64076 55904 29099 45681 50652 65305 37182 94127 03369 31378 51786 09040 70866 71149 65583 43434 76933 85781 71138 64558 73678 12301 45876 87126 60348 91390 95620 09939 36103 10291 61615 28813 84379 09904 23174 73363 94804 57593 14931 40529 76347 57481 19356 70911 01377 51721 00803 15590 24853 09066 92037 67192 20332 29094 33467 68514 22144 77379 39375 17034 43661 99104 03375 11173 54719 18550 46449 02636 55128 16228 82446 25759 16333 03910 72253 83742 18214 08835 08657 39177 15096 82887 47826 56995 99574 49066 17583 44137 52239 70968 34080 05355 98491 75417 38188 39994 46974 86762 65516 58276 58483 58845 31427 75687 90029 09517 02835 29716 34456 21296 40435 23117 60066 51012 41200 65975 58512 76178 58382 92041 97484 42360 80071 93045 76189 32349 22927 96501 98751 87212 72675 07981 25547 09589 04556 35792 12210 33346 69749 92356 30254 94780 24901 14195 21238 28153 09114 07907 38602 51522 74299 58180 72471 62591 66854 51333 12394 80494 70791 19153 26734 30282 44186 04142 63639 54800 04480 02670 49624 82017 92896 47669 75831 83271 31425 17029 69234 88962 76684 40323 26092 75249 60357 99646 92565 04936 81836 09003 23809 29345 95889 70695 36534 94060 34021 66544 37558 90045 63288 22505 45255 64056 44824 65151 87547 11962 18443 96582 53375 43885 69094 11303 15095 26179 37800 29741 20766 51479 39425 90298 96959 46995 56576 12186 56196 73378 62362 56125 21632 08628 69222 10327 48892 18654 36480 22967 80705 76561 51446 32046 92790 68212 07388 37781 42335 62823 60896 32080 68222 46801 22482 61177 18589 63814 09183 90367 36722 20888 32151 37556 00372 79839 40041 52970 02878 30766 70944 47456 01345 56417 25437 09069 79396 12257 14298 94671 54357 84687 88614 44581 23145 93571 98492 25284 71605 04922 12424 70141 21478 05734 55105 00801 90869 96033 02763 47870 81081 75450 11930 71412 23390 86639 38339 52942 57869 05076 43100 63835 19834 38934 15961 31854 34754 64955 69781 03829 30971 64651 43840 70070 73604 11237 35998 43452 25161 05070 27056 23526 60127 64848 30840 76118 30130 52793 20542 74628 65403 60367 45328 65105 70658 74882 25698 15793 67897 66974 22057 50596 83440 86973 50201 41020 67235 85020 07245 22563 26513 41055 92401 90274 21624 84391 40359 98953 53945 90944 07046 91209 14093 87001 26456 00162 37428 80210 92764 57931 06579 22955 24988 72758 46101 26483 69998 92256 95968 81592 05600 10165 52563 7567 ... |
107.194.6.189 ( talk) 02:38, 17 February 2018 (UTC)
In the Approximate value section, would someone change "approximation" to "truncation" in several places? These are not the value of pi rounded to the specified number of places, but the value of pi truncated to the specified number of places. Please consider also adding "3.8Ti0l" as an alternate sexagesimal representation. 64.132.59.226 ( talk) 19:25, 14 February 2018 (UTC)
Actually, should we have 50 places in the fractional part for each representation? These truncations would be:
64.132.59.226 ( talk) 19:32, 14 February 2018 (UTC)
The animation use the circle's diameter (and not the the radius) and finishes by labeling the full rotation of the circle as being pi and (not 2 times pi) — Preceding unsigned comment added by NicolasLefebvre54 ( talk • contribs) 04:06, 20 March 2018 (UTC)
The article states that: differential calculus typically precedes integral calculus in the university curriculum, so it is desirable to have a definition of π that does not rely on the latter. One such definition, due to Richard Baltzer, and popularized by Edmund Landau, is the following: π is twice the smallest positive number at which the cosine function equals 0.
I have looked into one of the citations "Walter Rudin - Principle of Mathematical Analysis" (p 182-183), and found out that the existence of such constant is proved using an integral. Is there another proof that doesn't uses integral calculus at all? Otherwise this statement seems to be false. — Preceding unsigned comment added by 109.67.101.82 ( talk) 08:53, 23 March 2018 (UTC)
Question; Why does this keep getting deleted for "unsourced"? It is clearly stated that this is engraved in stone at the Washington Park MAX station (Portland, Oregon). I took that picture. What else would make it "sourced"?
As for "trivial", a wrong value engraved in stone at a very public location is "trivial"??? Then, what about the one right above it about Knuth's silly version numbers? Would you delete that as well? Williampfeifer ( talk) 21:24, 14 April 2018 (UTC)
The article should not contain a lengthy decimal representation of a number that isn't π. In fact, the added text
3.1415926535 821480865144 288109757245 870066330572 703698336733 620005681271 420199561150 244594555982 534904897932
has more digits of non-π than the article has of the digits of π itself! Sławomir Biały ( talk) 22:33, 14 April 2018 (UTC)
Would this count as a reliable source?:
https://blog.plover.com/math/wrong-pi.html
I agree, a simple mistake is trivial. What makes it non-trivial is that it's engraved in stone in a very public place, for about 20 years now, and isn't been fixed. (Yes, the city knows about it; there was an article in the Oregonian newspaper about it back then, but I can't figure out how to access old articles on that paper)
I'm aware that someone could not see that picture. That is why I added the numbers as text. However, this text addition itself is being objected to. So I'm caught between a rock and a hard place.
Williampfeifer (
talk)
01:44, 15 April 2018 (UTC)
How about something like this:
At the
Washington Park MAX station (Portland, Oregon) are granite plaques honoring various attributes of Oregon. One plaque, intending to honor the science sector, supposedly bears the engraved value of pi. However, the digits are incorrect, beginning at the 12th place after the decimal
[1]. Instead of 3.14159265358979323846..., it shows 3.1415926535821480865144..., and so on. In fact, the digits, as engraved on the plaque are pi's digits 1 to 10, followed by digits 101 to 110, then the digits 201 to 210 and so on.
Williampfeifer (
talk)
02:55, 15 April 2018 (UTC)
It's pure trivia. HiLo48 ( talk) 03:33, 15 April 2018 (UTC)
Fact is
My opinion is
Sorry, Williampfeifer. Purgy ( talk) 07:54, 15 April 2018 (UTC)
References
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No formula was derived to calculate pi in 21st century until 2017. In 2017 a young Indian Mathematician Karthikeya Gounder alias Karthik(18 years old) had derived a new formula to calculate the value of pi upto infinite digits in the paper " π-The Transcendental Number"[1]. In that paper,Pi is expressed in a new way rather than a series converging to the exact value. It relates the mathematical constant pi with Trignometric tan.
References 1.Karthikeya Gounder: π-The Transcendental Number
MAT-KOL(BanjaLuka) ISSN:0354-6969(p),ISSN:1986-5228(o)
Vol.XXIII(1)(2017),61-66 DOI:10.7251/MK1701061G
Paper link: http://www.imvibl.org/dmbl/meso/mat_kol_23_1_2017/mat_kol_23_1_2017_61_66.pdf
Additional reference 1. http://www.academia.edu/32137897/Karthikeya_Gounder_π-THE_TRANSCENDENTAL_NUMBER_MAT-KOL_XXIII_1_2017_61-66 Karthikeyagounderr ( talk) 05:08, 29 April 2018 (UTC)
There is a new type of calculus in Regular rule published in 2018 by Amir Forsati. its proof is written on that page too.
Please not that the in the tangent is 180 degrees.
proof confirmation by StackExchange geeks. — Preceding unsigned comment added by Pw2iur ( talk • contribs) 18:31, 10 April 2018 (UTC)
Does anybody think it would be appropriate to include a section with pi written out to 1,000 decimal places? DangleSnipeCelly ( talk) 20:43, 4 May 2018 (UTC)DangleSnipeCelly1
OK. Thank you. DangleSnipeCelly ( talk) 23:48, 4 May 2018 (UTC)DangleSnipeCelly1