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Shouldn't Stirling's formula contain the asympotically-equals sign (~) instead of the aprroixmatly equals sign. The form is a much more precise statement. I don't know how to edit this in. Dmn
Of particular interest to me is this: if we live in a non Euclidian universe, does that alter the value of pi? Is it possible that a non euclidian universe would render pi a distance dependedt function? Just musing, really.
-- Pi is usually defined as the ratio of a circle's circumference to its diameter in Euclidean geometry. So if the universe was not Euclidean, this ratio would be different, but it would not be called pi.
I took a college geometry class that began with taxi geometry, where the distance between any 2 points is the sum of the vertical distance and the horizontal distance. (You could not move diagonally.) the first assignment was to calculate the value of pi, defined as the ratio of the circumfence of a circle to the diameter. A circle was defined as the locus of points that all had the same distance in taxi geometry from the center point. Pi was 4.
I define Pi as a function of the distance metric in a metric space: Pi equals half the arc length of the curve created by the locus of points of distance 1 from a given point. In a hexagonal world such as that used in many turn-based video games, Pi == 3. In a geometry with distance metric d((x1, y1), (x2, y2)) == (abs(x2 - x1) + abs(y2 - y1)) such as city blocks, Pi == 4. Of course, the familiar Euclidean distance metric provides a value of Pi just a bit more than 355/113, and nearly all digital signal processing takes place in Euclidean geometry.
In geometries that don't preserve lengths of translated lines (such as the geometry of curved spacetime), "distance 1" is meaningless, and Pi depends on the location and the radius.
That is not the standard definition however: Pi is a well defined real number, and it has nothing to do with geometry. It is always 3.14.. no matter what. Mathematical constants don't depend on physical contingencies. If our world is not Euclidean, then there will be some circles of diameter one whose circumference is different from Pi. --AxelBoldt
Geometry was a purely axiomatic mathematic until Cartesian thought entered. You can't claim that these equations are Euclidean, Euclid wouldn't have recognized them.
Concerning this section, I just was thinking about adding a comment after all the volume/area formulae on the Pi page, kind of "all these formulae are in fact a consequence of the second one, as all of them give the volume of solid of revolution (by the formula \pi x \integral...)". I hesitate, because I know that the "pi" page is really a most public place (and thus should be considered almost "locked" for edits, in some sense).
Any comments? — MFH: Talk 00:03, 11 May 2005 (UTC)
I am inclined to question the inclusion of the physics formulae. Surely the appearance of pi in these is simply a quirk of the definition of the physical constants such as Plank's constant and the gravitational constant. The significance of a physical constant tends to be recognised early in the development of the theory in which it features. When different derivations are made from the theory sometimes a factor of pi will appear in a formula, and sometimes not, for detailed mathematical reasons (eg the inversion of a fourier transform).
Also I believe the mnemonic linked to Isaac Asimov was coined by James Jeans -- Alan Peakall 12:00 Nov 29, 2002 (UTC)
In a long ago and fruitless sojourn into the land of entry-level statistics, I seem to remember that statisticians use a wholly different pi that stands for some variable or another. The statistical use probably doesn't deserve a whole article, but there should be a mention that the same Greek letter is used in statistics too, if anybody knows exactly what it stands for. Tokerboy 23:03 Dec 7, 2002 (UTC)
See pi (letter) for various usages of the Greek letter in different fields. SCCarlson
I understand that pi is infinitely long when expressed as a number. I also understand that it never repeats. I have also heard that all possible finite sequences of numbers are contained within it. I can see that the first two statements don't imply the latter, ie
is a counter example. However, I have heard this asserted on a (mostly) serious radio program. Any thoughts?
MrJones 10:54, 19 Oct 2003 (UTC)
Recently there has been a post to Usenet, under the name of Simon Plouffe, which states that he (Plouffe) discovered the formula given in the Bailey-Borwein-Plouffe paper, and that Bailey in particular arrived on the scene after that formula was already discovered. (I forget at the moment what he said about Borwein.) See: "The story behind a formula of Pi", sci.math, Jun 23, 2003 by simon.plouffe@sympatico.ca, also "Sur l'histoire entourant la d écouverte d'une formule de Pi.", fr.sci.maths, 2003-06-24, by plouffe@math.uqam.ca.
Taking this account at face value, it seems that crediting the discovery to Bailey primarily -- "David H. Bailey, together with Peter Borwein and Simon Plouffe, discovered a new formula..." -- is unjustified. I wonder if one could get a comment directly from Plouffe via email. Hmm, comments from Bailey and Borwein would also be interesting.
The Bailey, Borwein, & Plouffe paper itself does not clarify the discovery of the formula. It just says "we" discovered it. A later paper by Borwein (a summary of pi computing history) says "it was discovered". I've been unable to find anything by Bailey or Borwein which states a direct attribution for the discovery of the formula.
I have read that it is possible to get an approximation of pi by dropping toothpicks on a floor. Specifically, drop toothpicks on a grid of squares with the squares' sides equal to the length of the toothpicks. Count the times a toothpick intersects a square's side. Then pi should equal 2 times the number of toothpicks dropped divided by the number of intersections. Is this true?
The formulas involving pi under the physics section involve costants that are commonly considered to be less fundamental than if you absorbed pi into them. for instance Newton's law of gravitation can be put in the form
which has the interpretation that the field(force over the mass of the object it acts on in this case) per unit area(since the field posesses spherical symmetry) is 4 π GM.
in Einsteins field equation we are dealing with a field density, thus we do not include 4 π r2 and the 4πGM turns up, as the more fundamental constant.
The 2π in the uncertainty principle arises from considering frequency, rather than the arguably more fundamental angular frequency, in the definition of planks constant; h dived by 2pi is used more often than h itself.
64.161.172.140 01:48, 13 Feb 2004 (UTC)
Am I the only person who gets Main Page edits when following the page history link for π ? I think that the ampersand character may be fucking with the dynamic linking... Perhaps the page should be moved back to Pi? Matt gies 01:24, 5 Mar 2004 (UTC)
How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics! How I want a drink, alcoholic of course, after the heavy chapters involving quantum mechanics!
Those two sentences to help remember the decimal sequences to π are attributed by various webpages to one of several individuals: George Polya, Martin Gardner and Issac Asimov. What's the true attribution? - Bevo 22:52, 22 Mar 2004 (UTC)
Please note, "value" usually has a certain connotation in mathematics, and to say that π has a "value" is a bit mathematically misleading. π is defined to be a specific REAL NUMBER (a constant); π is not defined to be a constant function which takes on "values". Furthermore, a constant IS a number, a constant does not "have a value which is a number". I don't mean to be nit-picking a tedious point, but the phrasing "the value of π" sounds awkward and silly to my mathematical ears.
Revolver 17:21, 12 Apr 2004 (UTC)
Let me clarify a bit more, since I realise there are some cases where "value of π" is warranted, but this is for a specific reason. One correct situation in which "value of π" is appropriate is when referring to a numerical approximation or numerical estimate of π, but it should be realised in this case that this is not the same thing as π -- the number π has many different numerical values or approximations:
These are ideas based on estimation, measurements, approximations, and expansions. But when talking about purely mathematical properties of π, e.g. its irrationality or transcendence, it's more correct to simply say "π is irrational" or "π is transcendental", very few people would say "the value of π is irrational or transcendental".
Another case where "value of π" might be appropriate is when you are using the term "π" to refer to the symbol π, and you are assigning a value (number) to this symbol, then in this case, π does have a value, because it's the value represented by the symbol π. For example,
These are the only times I can see how "value of π" is not redundant. Revolver 17:58, 12 Apr 2004 (UTC)
Prove that the value of π is in between 3 and 4, and that all these values are possible.
I move that the section on pi culture be moved to a separate article. This article is already getting a bit cluttered and will undoubtedly have more material added to it in the future. As the focus of this particular article is on pi as a mathematical constant, not various mnemomics or "pi day", this may work better at another article. A similar thing was done at the article trigonometric function when the section on mnemomics for the trig functions became rather lengthy and distracting. (I'm not saying to eliminate the section, maybe briefly mention pi day, mnemomics, etc., then give a link.) Discussion?
Revolver 00:10, 13 Apr 2004 (UTC)
This paragraph is getting weird and weird. The
(...). This also leads to some rather interesting adaptations of popular songs such as "Rock Around the Clock".
and
A random, somewhat strange joke involving pi: | pi aren't square, pi are round! | -Oh, the Irony.
(while the previous version (pi r squared...) made it easier to understand...)
My vote is : vanity, move to WP:BJ... — MFH: Talk 07:20, 14 May 2005 (UTC)
Looking at Ramanujan's eqaution for 1/π given in the article,
it looks like it's possible to simplify the fraction in the infinite sum by removing a k! factor. I think perhaps (4k)! was intended for (4k!). Can anyone confirm or disconfirm this guess? Eric119 01:09, May 28, 2004 (UTC)
Yep, it is (4k)! (looked in the library). Its also already been changed Mrjeff 12:54, 30 Jul 2004 (UTC)
When did the title start displaying as π ? - Bevo 23:26, 5 Jun 2004 (UTC)
That's even worse. Now I see a completely odd, non-Latin, non-Greek character. Rick K 02:01, Jun 6, 2004 (UTC)
Shanks' famous calculation of π is listed twice in the history corresponding to two different years, 1853 and 1874. What's going on there? 4pq1injbok 19:01, 2 Jul 2004 (UTC)
Granted, it has been proven that the literal decimal expansion of Pi never cycles. However, I am wondering if there is a "deeper pattern" in the expansion which does, in fact, cycle. In other words, consider the sequence:
[012 123 234 345 456 567 678 789 8910 91011 101112 111213...]
Spaces are included above to make the pattern obvious. Without the spaces you would have:
[012123234345456567678789891091011101112111213...]
The digit-sequence above will not cycle. However, there is an obvious "pattern" in the sequence that repeats over and over, and I am wondering if there might be such a repeating pattern in Pi's decimal expansion (perhaps not such a short and simple one, but a pattern nevertheless). Or perhaps, the sequence of Pi is more or less just...random!
Anyway, has the issue I am discussing above been investigated for this wonderful irrational number ?? Thankyou...Mike Keith (lynne_mike@alltel.net)
The first two historical values for pi given are both in bold, and so were (presumably) both world records. However, the first one is actually closer to pi than the second. What's going on there?
I don't understand the recent suppression of
|mid 6th century BC|| 1 Kings 7:23||3
by Rossnixon, with "explanation"
Bible ref would be internal, not external circumference of the vessel
The text is: [1]
23 He 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 [p] to measure around it.
As far as I understand, this clearly means: circumference = diameter × 3. Although this is certainly not a candidate for a world record, it might be noteworthy, allows people to discover on-line details of the bible, and besides this, there are other more urgent things ("random joke"...) to delete on this page, imho. — MFH: Talk 12:02, 14 May 2005 (UTC)
the book i'm looking at (Chaos Theory, Peitgen Juergens Saupe) says that Lindemann proved pi transcendental in 1885, not 1882.
The definition of a constructible real number is a number which lies in a field gotten by taken a finite sequence of quadratic extensions of the rationals, i.e. it's an x such that there are m1, m2, ..., mi, such that x is in Q[sqrt(m1), sqrt(m2), ..., sqrt(mi)]. (Sometimes the definition is taken to be geometric, but it's not much to show that this definition is equivalent.) Every constructible number is then "expressible as a finite number of integers, fractions, and square roots", (in fact, this is a defining property), so every constructible number is "expressible as a finite number of integers, fractions, and nth roots", and all of these numbers are algebraic. However, not all algebraic numbers can be expressed this way, (Galois theory). So, constructible ==> "exp. in finite # of int., frac., nth roots" ==> algebraic, but none of these implications is reversible. Revolver 08:48, 7 Oct 2004 (UTC)
The reason it [π] occurs so often in physics is simply because it's convenient in many physical models.
While the original Greek letter for pi was phonetically equivalent to the English letter p, it has now evolved to be pronounced like the word pie in most circles.
Surely this should be up near the beginning of the article, not in the properties section. Furthermore, it is very poorly phrased: what it means to say is something like "Although in Greek the name of the letter π is/was pronounced something like the name of the english letter p, the standard English pronunciation is identical to pie." Furthermore, I'm not entirely sure that the Greek pronunciation is all that relevant to this article. I would make these changes myself, but frankly I'm having trouble coming up with a phrasing that isn't totally clunky and awkward. Someone else want to take care of this please? -- 68.78.77.224 04:29, 22 Nov 2004 (UTC) Iustinus
I read somewhere that in modern Greek, what we call π is called something else, but I can't for the life of me remember what it was. Does anyone else know, perchance? Gus 04:31, 2005 Jan 3 (UTC)
Maybe something like "number of the circle" in Greek (like the German de:Kreiszahl), or you may think of "perifereia" (=" periphery"), that's where (the initial) π comes from. (could be mentioned in the introduction...) — MFH: Talk 00:21, 11 May 2005 (UTC)
Someone today just switched the digits of pi to a breakup of 3 digits each rather than the former 5 ie.
I think this second format is harder to read (personally I can't stand it), any input? Additionally the code is messed up with s NitrogenX (Michael Hines) 05:22, Feb 25, 2005 (UTC)
Maybe I missed something, but why not fix up the crummy Pi title, and move the lot to a proper "π" page?
Roy da Vinci 05:25, 13 Mar 2005 (UTC)
The problem with having a pi symbol as the title is it is automaticly changed to the uppercase pi symbol which looks like Π. as demonstrated here: [2]
This article claims that pi is both an irrational number and at the same time having a finite length of 1.3511 trillion digits. Both of these claims can not be true, since finite length implies pi being a rational number, which can be expressed as a ratio of two integers:
-- Fredrik Orderud 00:44, 9 May 2005 (UTC)
Kanada's claim of finding 1.3511 trillion digits of pi in 2004 was pure fiction, based on a vandalized edition of the Yasumasa Kanada article. I've therefore removed this finding from the "History" of pi in the main article. -- Fredrik Orderud 19:52, 9 May 2005 (UTC)
I don't think that all of the records from 1954 to 1992 were by Wrench and Smith, as the table indicates now.
A History of Pi by Petr Beckmann, page 197, lists:
1954-1955 NORC is programmed to computer 3089 digits
1957 Pegasus computer (London) computes 7480 places
1959 IBM 704 (Paris) computes 16,167 decimal places
1961 Shanks and Wrench improve computer program for pi, use IBM 7090 (NEw York) t compute 100,000 decimal places
1966 IBM 7030 (Paris) computes 250,000 decimal places
1967 CDC 6600 (Paris) computes 500,000 decimal places
I don't want to change the table (so I don't mess it up again), so I would appreciate it if someone made these changes to the table. -- Bubba73 00:50, 31 May 2005 (UTC)
I have heard of a way to compute pi given enough random numbers. I think it was called the "Monte Carlo Value for Pi." Is there a formula one has to plug the random numbers into to get this pi value? I found " http://www.random.org/stats/", which gives the monte carlo pi value for random numbers on their page in real time, and " http://www.fourmilab.ch/random/", which briefly explains it,
"For very large streams (this approximation converges very slowly), the value will approach the correct value of Pi if the sequence is close to random. A 32768 byte file created by radioactive decay yielded:
Monte Carlo value for Pi is 3.139648438 (error 0.06 percent)."
but I want to know an algorithm or a formula to be able to compute pi with the numbers from A Million Random Digits with 100,000 Normal Deviates. If anybody could help me out, I would be really grateful. Thanks, DC
#include <cstdio> #include <cstdlib> #include <ctime> int main() { int i=0, j; const int n=100000000; long double x, y; srand(time(0)); for (j=n; j--;) { x=(2*(long double)rand())/RAND_MAX-1; y=(2*(long double)rand())/RAND_MAX-1; if (x*x+y*y<=1) i++; } printf("Using %d random points, I got that pi is about %.100Lg.\n", n, ((long double)4)*i/n); return 0; }
Using 100000000 random points, I got that pi is about 3.14186652000000000008010647700729123243945650756359100341796875.
#include <stdio.h> #include <stdlib.h> #include <time.h> main(int argc, char **argv){ int n,j,i=0; float x,y,r=RAND_MAX,r2=r*r; if( argc<2 || (n=atoi( argv[1] ))<1 ) n=10000000; printf("Using %d random points...\n", n); srandom(time(0)); for (j=n; j--;) { x=random(); y=random(); if ( x*x+y*y <= r2 ) i++; } printf("I got that pi is about %19f.\n", i*4.0/n); }
(~/C) time ./rand-pi 99999999 Using 99999999 random points... I got that pi is about 3.141776671417766842. 5.970u 0.010s 0:05.99 99.8% 0+0k 0+0io 88pf+0w
— MFH: Talk 14:17, 24 Jun 2005 (UTC)
Is is true, or only inaccurate folklore, that at some point maybe 100 years ago, a U.S. state legislated that pi was equal to three? Was there a bill that never got passed? Or is the whole story nonsense? If the story has some truth, does it rate a mention in this article? Dmharvey File:User dmharvey sig.png Talk 14:58, 6 Jun 2005 (UTC)
Sukh, the 70 digits were correct, it would have been enough to click on the link to the (sequence A000796 in the OEIS) link, in order to verify it! (If even the editors don't use the links to sources...) — MFH: Talk 12:57, 24 Jun 2005 (UTC)
Mike Rosoft placed a request to change the name from Π to Pi on 28 June 2005.
Could we prune the approximations a little? Especially the one that uses 18 digits to approximate the first 17 digits of Pi isn't exactly amazing. -- W( t) 30 June 2005 23:20 (UTC)
355/113 should be kept. It's not just "cute", it's a continued fraction approximation. What this means is that you're getting a much better approximation than you'd expect to get with a denominator as small as 113. With such a small denominator, you'd only really expect to get two or three digits after the decimal point; here you're actually getting six. Such an approximation doesn't really "compress" anything (after all you still need to specify the numerator), but it's still interesting. Dmharvey File:User dmharvey sig.png Talk 1 July 2005 13:06 (UTC)
A while back, I created redirects from common approximations (3.14, 3.141, etc). Someone has deleted them. Why? -- Celestianpower talk 12:40, 12 July 2005 (UTC)
Has anyone ever held a contest on how many digits of pi one can memorize. I teach high school math and we had a pi day contest on march 14 and we had a student memorize 318 digits of pi. Anyone know what the record is?
The official world record is 42,195 places.
Bubba73 29 June 2005 02:56 (UTC)
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 1 | Archive 2 | Archive 3 | Archive 4 | Archive 5 |
Shouldn't Stirling's formula contain the asympotically-equals sign (~) instead of the aprroixmatly equals sign. The form is a much more precise statement. I don't know how to edit this in. Dmn
Of particular interest to me is this: if we live in a non Euclidian universe, does that alter the value of pi? Is it possible that a non euclidian universe would render pi a distance dependedt function? Just musing, really.
-- Pi is usually defined as the ratio of a circle's circumference to its diameter in Euclidean geometry. So if the universe was not Euclidean, this ratio would be different, but it would not be called pi.
I took a college geometry class that began with taxi geometry, where the distance between any 2 points is the sum of the vertical distance and the horizontal distance. (You could not move diagonally.) the first assignment was to calculate the value of pi, defined as the ratio of the circumfence of a circle to the diameter. A circle was defined as the locus of points that all had the same distance in taxi geometry from the center point. Pi was 4.
I define Pi as a function of the distance metric in a metric space: Pi equals half the arc length of the curve created by the locus of points of distance 1 from a given point. In a hexagonal world such as that used in many turn-based video games, Pi == 3. In a geometry with distance metric d((x1, y1), (x2, y2)) == (abs(x2 - x1) + abs(y2 - y1)) such as city blocks, Pi == 4. Of course, the familiar Euclidean distance metric provides a value of Pi just a bit more than 355/113, and nearly all digital signal processing takes place in Euclidean geometry.
In geometries that don't preserve lengths of translated lines (such as the geometry of curved spacetime), "distance 1" is meaningless, and Pi depends on the location and the radius.
That is not the standard definition however: Pi is a well defined real number, and it has nothing to do with geometry. It is always 3.14.. no matter what. Mathematical constants don't depend on physical contingencies. If our world is not Euclidean, then there will be some circles of diameter one whose circumference is different from Pi. --AxelBoldt
Geometry was a purely axiomatic mathematic until Cartesian thought entered. You can't claim that these equations are Euclidean, Euclid wouldn't have recognized them.
Concerning this section, I just was thinking about adding a comment after all the volume/area formulae on the Pi page, kind of "all these formulae are in fact a consequence of the second one, as all of them give the volume of solid of revolution (by the formula \pi x \integral...)". I hesitate, because I know that the "pi" page is really a most public place (and thus should be considered almost "locked" for edits, in some sense).
Any comments? — MFH: Talk 00:03, 11 May 2005 (UTC)
I am inclined to question the inclusion of the physics formulae. Surely the appearance of pi in these is simply a quirk of the definition of the physical constants such as Plank's constant and the gravitational constant. The significance of a physical constant tends to be recognised early in the development of the theory in which it features. When different derivations are made from the theory sometimes a factor of pi will appear in a formula, and sometimes not, for detailed mathematical reasons (eg the inversion of a fourier transform).
Also I believe the mnemonic linked to Isaac Asimov was coined by James Jeans -- Alan Peakall 12:00 Nov 29, 2002 (UTC)
In a long ago and fruitless sojourn into the land of entry-level statistics, I seem to remember that statisticians use a wholly different pi that stands for some variable or another. The statistical use probably doesn't deserve a whole article, but there should be a mention that the same Greek letter is used in statistics too, if anybody knows exactly what it stands for. Tokerboy 23:03 Dec 7, 2002 (UTC)
See pi (letter) for various usages of the Greek letter in different fields. SCCarlson
I understand that pi is infinitely long when expressed as a number. I also understand that it never repeats. I have also heard that all possible finite sequences of numbers are contained within it. I can see that the first two statements don't imply the latter, ie
is a counter example. However, I have heard this asserted on a (mostly) serious radio program. Any thoughts?
MrJones 10:54, 19 Oct 2003 (UTC)
Recently there has been a post to Usenet, under the name of Simon Plouffe, which states that he (Plouffe) discovered the formula given in the Bailey-Borwein-Plouffe paper, and that Bailey in particular arrived on the scene after that formula was already discovered. (I forget at the moment what he said about Borwein.) See: "The story behind a formula of Pi", sci.math, Jun 23, 2003 by simon.plouffe@sympatico.ca, also "Sur l'histoire entourant la d écouverte d'une formule de Pi.", fr.sci.maths, 2003-06-24, by plouffe@math.uqam.ca.
Taking this account at face value, it seems that crediting the discovery to Bailey primarily -- "David H. Bailey, together with Peter Borwein and Simon Plouffe, discovered a new formula..." -- is unjustified. I wonder if one could get a comment directly from Plouffe via email. Hmm, comments from Bailey and Borwein would also be interesting.
The Bailey, Borwein, & Plouffe paper itself does not clarify the discovery of the formula. It just says "we" discovered it. A later paper by Borwein (a summary of pi computing history) says "it was discovered". I've been unable to find anything by Bailey or Borwein which states a direct attribution for the discovery of the formula.
I have read that it is possible to get an approximation of pi by dropping toothpicks on a floor. Specifically, drop toothpicks on a grid of squares with the squares' sides equal to the length of the toothpicks. Count the times a toothpick intersects a square's side. Then pi should equal 2 times the number of toothpicks dropped divided by the number of intersections. Is this true?
The formulas involving pi under the physics section involve costants that are commonly considered to be less fundamental than if you absorbed pi into them. for instance Newton's law of gravitation can be put in the form
which has the interpretation that the field(force over the mass of the object it acts on in this case) per unit area(since the field posesses spherical symmetry) is 4 π GM.
in Einsteins field equation we are dealing with a field density, thus we do not include 4 π r2 and the 4πGM turns up, as the more fundamental constant.
The 2π in the uncertainty principle arises from considering frequency, rather than the arguably more fundamental angular frequency, in the definition of planks constant; h dived by 2pi is used more often than h itself.
64.161.172.140 01:48, 13 Feb 2004 (UTC)
Am I the only person who gets Main Page edits when following the page history link for π ? I think that the ampersand character may be fucking with the dynamic linking... Perhaps the page should be moved back to Pi? Matt gies 01:24, 5 Mar 2004 (UTC)
How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics! How I want a drink, alcoholic of course, after the heavy chapters involving quantum mechanics!
Those two sentences to help remember the decimal sequences to π are attributed by various webpages to one of several individuals: George Polya, Martin Gardner and Issac Asimov. What's the true attribution? - Bevo 22:52, 22 Mar 2004 (UTC)
Please note, "value" usually has a certain connotation in mathematics, and to say that π has a "value" is a bit mathematically misleading. π is defined to be a specific REAL NUMBER (a constant); π is not defined to be a constant function which takes on "values". Furthermore, a constant IS a number, a constant does not "have a value which is a number". I don't mean to be nit-picking a tedious point, but the phrasing "the value of π" sounds awkward and silly to my mathematical ears.
Revolver 17:21, 12 Apr 2004 (UTC)
Let me clarify a bit more, since I realise there are some cases where "value of π" is warranted, but this is for a specific reason. One correct situation in which "value of π" is appropriate is when referring to a numerical approximation or numerical estimate of π, but it should be realised in this case that this is not the same thing as π -- the number π has many different numerical values or approximations:
These are ideas based on estimation, measurements, approximations, and expansions. But when talking about purely mathematical properties of π, e.g. its irrationality or transcendence, it's more correct to simply say "π is irrational" or "π is transcendental", very few people would say "the value of π is irrational or transcendental".
Another case where "value of π" might be appropriate is when you are using the term "π" to refer to the symbol π, and you are assigning a value (number) to this symbol, then in this case, π does have a value, because it's the value represented by the symbol π. For example,
These are the only times I can see how "value of π" is not redundant. Revolver 17:58, 12 Apr 2004 (UTC)
Prove that the value of π is in between 3 and 4, and that all these values are possible.
I move that the section on pi culture be moved to a separate article. This article is already getting a bit cluttered and will undoubtedly have more material added to it in the future. As the focus of this particular article is on pi as a mathematical constant, not various mnemomics or "pi day", this may work better at another article. A similar thing was done at the article trigonometric function when the section on mnemomics for the trig functions became rather lengthy and distracting. (I'm not saying to eliminate the section, maybe briefly mention pi day, mnemomics, etc., then give a link.) Discussion?
Revolver 00:10, 13 Apr 2004 (UTC)
This paragraph is getting weird and weird. The
(...). This also leads to some rather interesting adaptations of popular songs such as "Rock Around the Clock".
and
A random, somewhat strange joke involving pi: | pi aren't square, pi are round! | -Oh, the Irony.
(while the previous version (pi r squared...) made it easier to understand...)
My vote is : vanity, move to WP:BJ... — MFH: Talk 07:20, 14 May 2005 (UTC)
Looking at Ramanujan's eqaution for 1/π given in the article,
it looks like it's possible to simplify the fraction in the infinite sum by removing a k! factor. I think perhaps (4k)! was intended for (4k!). Can anyone confirm or disconfirm this guess? Eric119 01:09, May 28, 2004 (UTC)
Yep, it is (4k)! (looked in the library). Its also already been changed Mrjeff 12:54, 30 Jul 2004 (UTC)
When did the title start displaying as π ? - Bevo 23:26, 5 Jun 2004 (UTC)
That's even worse. Now I see a completely odd, non-Latin, non-Greek character. Rick K 02:01, Jun 6, 2004 (UTC)
Shanks' famous calculation of π is listed twice in the history corresponding to two different years, 1853 and 1874. What's going on there? 4pq1injbok 19:01, 2 Jul 2004 (UTC)
Granted, it has been proven that the literal decimal expansion of Pi never cycles. However, I am wondering if there is a "deeper pattern" in the expansion which does, in fact, cycle. In other words, consider the sequence:
[012 123 234 345 456 567 678 789 8910 91011 101112 111213...]
Spaces are included above to make the pattern obvious. Without the spaces you would have:
[012123234345456567678789891091011101112111213...]
The digit-sequence above will not cycle. However, there is an obvious "pattern" in the sequence that repeats over and over, and I am wondering if there might be such a repeating pattern in Pi's decimal expansion (perhaps not such a short and simple one, but a pattern nevertheless). Or perhaps, the sequence of Pi is more or less just...random!
Anyway, has the issue I am discussing above been investigated for this wonderful irrational number ?? Thankyou...Mike Keith (lynne_mike@alltel.net)
The first two historical values for pi given are both in bold, and so were (presumably) both world records. However, the first one is actually closer to pi than the second. What's going on there?
I don't understand the recent suppression of
|mid 6th century BC|| 1 Kings 7:23||3
by Rossnixon, with "explanation"
Bible ref would be internal, not external circumference of the vessel
The text is: [1]
23 He 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 [p] to measure around it.
As far as I understand, this clearly means: circumference = diameter × 3. Although this is certainly not a candidate for a world record, it might be noteworthy, allows people to discover on-line details of the bible, and besides this, there are other more urgent things ("random joke"...) to delete on this page, imho. — MFH: Talk 12:02, 14 May 2005 (UTC)
the book i'm looking at (Chaos Theory, Peitgen Juergens Saupe) says that Lindemann proved pi transcendental in 1885, not 1882.
The definition of a constructible real number is a number which lies in a field gotten by taken a finite sequence of quadratic extensions of the rationals, i.e. it's an x such that there are m1, m2, ..., mi, such that x is in Q[sqrt(m1), sqrt(m2), ..., sqrt(mi)]. (Sometimes the definition is taken to be geometric, but it's not much to show that this definition is equivalent.) Every constructible number is then "expressible as a finite number of integers, fractions, and square roots", (in fact, this is a defining property), so every constructible number is "expressible as a finite number of integers, fractions, and nth roots", and all of these numbers are algebraic. However, not all algebraic numbers can be expressed this way, (Galois theory). So, constructible ==> "exp. in finite # of int., frac., nth roots" ==> algebraic, but none of these implications is reversible. Revolver 08:48, 7 Oct 2004 (UTC)
The reason it [π] occurs so often in physics is simply because it's convenient in many physical models.
While the original Greek letter for pi was phonetically equivalent to the English letter p, it has now evolved to be pronounced like the word pie in most circles.
Surely this should be up near the beginning of the article, not in the properties section. Furthermore, it is very poorly phrased: what it means to say is something like "Although in Greek the name of the letter π is/was pronounced something like the name of the english letter p, the standard English pronunciation is identical to pie." Furthermore, I'm not entirely sure that the Greek pronunciation is all that relevant to this article. I would make these changes myself, but frankly I'm having trouble coming up with a phrasing that isn't totally clunky and awkward. Someone else want to take care of this please? -- 68.78.77.224 04:29, 22 Nov 2004 (UTC) Iustinus
I read somewhere that in modern Greek, what we call π is called something else, but I can't for the life of me remember what it was. Does anyone else know, perchance? Gus 04:31, 2005 Jan 3 (UTC)
Maybe something like "number of the circle" in Greek (like the German de:Kreiszahl), or you may think of "perifereia" (=" periphery"), that's where (the initial) π comes from. (could be mentioned in the introduction...) — MFH: Talk 00:21, 11 May 2005 (UTC)
Someone today just switched the digits of pi to a breakup of 3 digits each rather than the former 5 ie.
I think this second format is harder to read (personally I can't stand it), any input? Additionally the code is messed up with s NitrogenX (Michael Hines) 05:22, Feb 25, 2005 (UTC)
Maybe I missed something, but why not fix up the crummy Pi title, and move the lot to a proper "π" page?
Roy da Vinci 05:25, 13 Mar 2005 (UTC)
The problem with having a pi symbol as the title is it is automaticly changed to the uppercase pi symbol which looks like Π. as demonstrated here: [2]
This article claims that pi is both an irrational number and at the same time having a finite length of 1.3511 trillion digits. Both of these claims can not be true, since finite length implies pi being a rational number, which can be expressed as a ratio of two integers:
-- Fredrik Orderud 00:44, 9 May 2005 (UTC)
Kanada's claim of finding 1.3511 trillion digits of pi in 2004 was pure fiction, based on a vandalized edition of the Yasumasa Kanada article. I've therefore removed this finding from the "History" of pi in the main article. -- Fredrik Orderud 19:52, 9 May 2005 (UTC)
I don't think that all of the records from 1954 to 1992 were by Wrench and Smith, as the table indicates now.
A History of Pi by Petr Beckmann, page 197, lists:
1954-1955 NORC is programmed to computer 3089 digits
1957 Pegasus computer (London) computes 7480 places
1959 IBM 704 (Paris) computes 16,167 decimal places
1961 Shanks and Wrench improve computer program for pi, use IBM 7090 (NEw York) t compute 100,000 decimal places
1966 IBM 7030 (Paris) computes 250,000 decimal places
1967 CDC 6600 (Paris) computes 500,000 decimal places
I don't want to change the table (so I don't mess it up again), so I would appreciate it if someone made these changes to the table. -- Bubba73 00:50, 31 May 2005 (UTC)
I have heard of a way to compute pi given enough random numbers. I think it was called the "Monte Carlo Value for Pi." Is there a formula one has to plug the random numbers into to get this pi value? I found " http://www.random.org/stats/", which gives the monte carlo pi value for random numbers on their page in real time, and " http://www.fourmilab.ch/random/", which briefly explains it,
"For very large streams (this approximation converges very slowly), the value will approach the correct value of Pi if the sequence is close to random. A 32768 byte file created by radioactive decay yielded:
Monte Carlo value for Pi is 3.139648438 (error 0.06 percent)."
but I want to know an algorithm or a formula to be able to compute pi with the numbers from A Million Random Digits with 100,000 Normal Deviates. If anybody could help me out, I would be really grateful. Thanks, DC
#include <cstdio> #include <cstdlib> #include <ctime> int main() { int i=0, j; const int n=100000000; long double x, y; srand(time(0)); for (j=n; j--;) { x=(2*(long double)rand())/RAND_MAX-1; y=(2*(long double)rand())/RAND_MAX-1; if (x*x+y*y<=1) i++; } printf("Using %d random points, I got that pi is about %.100Lg.\n", n, ((long double)4)*i/n); return 0; }
Using 100000000 random points, I got that pi is about 3.14186652000000000008010647700729123243945650756359100341796875.
#include <stdio.h> #include <stdlib.h> #include <time.h> main(int argc, char **argv){ int n,j,i=0; float x,y,r=RAND_MAX,r2=r*r; if( argc<2 || (n=atoi( argv[1] ))<1 ) n=10000000; printf("Using %d random points...\n", n); srandom(time(0)); for (j=n; j--;) { x=random(); y=random(); if ( x*x+y*y <= r2 ) i++; } printf("I got that pi is about %19f.\n", i*4.0/n); }
(~/C) time ./rand-pi 99999999 Using 99999999 random points... I got that pi is about 3.141776671417766842. 5.970u 0.010s 0:05.99 99.8% 0+0k 0+0io 88pf+0w
— MFH: Talk 14:17, 24 Jun 2005 (UTC)
Is is true, or only inaccurate folklore, that at some point maybe 100 years ago, a U.S. state legislated that pi was equal to three? Was there a bill that never got passed? Or is the whole story nonsense? If the story has some truth, does it rate a mention in this article? Dmharvey File:User dmharvey sig.png Talk 14:58, 6 Jun 2005 (UTC)
Sukh, the 70 digits were correct, it would have been enough to click on the link to the (sequence A000796 in the OEIS) link, in order to verify it! (If even the editors don't use the links to sources...) — MFH: Talk 12:57, 24 Jun 2005 (UTC)
Mike Rosoft placed a request to change the name from Π to Pi on 28 June 2005.
Could we prune the approximations a little? Especially the one that uses 18 digits to approximate the first 17 digits of Pi isn't exactly amazing. -- W( t) 30 June 2005 23:20 (UTC)
355/113 should be kept. It's not just "cute", it's a continued fraction approximation. What this means is that you're getting a much better approximation than you'd expect to get with a denominator as small as 113. With such a small denominator, you'd only really expect to get two or three digits after the decimal point; here you're actually getting six. Such an approximation doesn't really "compress" anything (after all you still need to specify the numerator), but it's still interesting. Dmharvey File:User dmharvey sig.png Talk 1 July 2005 13:06 (UTC)
A while back, I created redirects from common approximations (3.14, 3.141, etc). Someone has deleted them. Why? -- Celestianpower talk 12:40, 12 July 2005 (UTC)
Has anyone ever held a contest on how many digits of pi one can memorize. I teach high school math and we had a pi day contest on march 14 and we had a student memorize 318 digits of pi. Anyone know what the record is?
The official world record is 42,195 places.
Bubba73 29 June 2005 02:56 (UTC)