Talk:Pi/Archive 4

message: Why isn't Archimedes mentioned anywhere in the article aside from the introduction? —The preceding unsigned comment was added by 140.247.28.35 (talk • contribs) 22:41, 3 May 2006  (UTC)
:Good point. I have added a note about an approximation by Archimedes in the "History" section. -- Meni Rosenfeld (talk) 12:07, 4 May 2006 (UTC)
thread_title: Archimedes

message: The property of pi that it can be specified to any number of digits using a series that can be specified in less than 15 digits is far more important than a lot of approximations or discussion about how many digits have been calculated. For one thing, it connects back to how pi was derived (geometrically) in the first place; and to how pi shows up in nature and science in a lot of different--sometimes surprising ways--in mathematics. Here is a suggested explanation (which fits remarkably well in just about any section (approximations, definition, properties, or even trivia--I just don't want to see it left out, especially when so much else is left in that is far less important). It also serves as a good lead-in to historical approximations since there are really two kinds, each with their own histories (finite and infinite precision):
Even though pi is irrational and transcendental, approximations to any arbitrary degree of precision can be created from simple-to-write infinite series. Such series can be used as a definition of the "exact" value of pi, because the value of the infinite series approaches (cyclically) the exact value of pi. The way it is used (usually by computers) is to calculate the value to enough iterations so that the first n digits become stable. One of the earliest and most common of such series is the following: pi = 4/1 - 4/3 + 4/5 - 4/7 + .... 
Many further improvements to the above mentioned "historical" approximations were done with the help of computers. A historical account on numerical and formulaic approximations of pi is given in history of numerical approximations of pi.
—Preceding unsigned comment added by 70.162.103.106 (talk • contribs) 2006-05-24 01:43:03
:There are many problems with this addition (which I intend to remove from the article again as soon as I can safely do under 3RR, unless somebody beats me to it):
:# It is not a particular property of pi that it can be approximated by "simple" series expansions. That is true for many interesting trancendental numbers.
:# The very fact that many digits have been calculated also in itself implies that there are definite ways to calculuate arbitrary amounts of digits.
:# The article already does mention the Leibniz series (1/1-1/3+1/5-1/7+...) in the appropriate section.
:# Leibniz' series is by far not the most common method of approximating pi -- it converges too extremely slowly to be of any interest to practical calculation. Much better series for doing this are known. In particular, the claim that this series is usually used in computer approximations of pi is just false. See Leibniz formula for pi: it takes billions of terms just to get 10 correct decimals.
:# For the same reason, the series is horribly badly suited to serve as a definition of pi -- about the only thing one can do with the definition is to prove it equivalent to one of the other existing useful definitions, and work from the latter no matter whether one wants to find applications or digits of pi.
:# There is no such thing as an "infinite-precision approximation".
:# The fact that pi shows up all over analysis is not particularly connected to the Leibniz series. A better candidate for the fundamental connection is the fact that the arc-length parameterization of the unit circle in Euclidean geometry happens to satisfy a particularly simple differential equation. (This can ultimately be used to explain why the Leibniz series works, rather than vice versa).
: Henning Makholm 11:02, 24 May 2006 (UTC)
thread_title:  Infinite series more important than approximations 

message: I decided to give the link instead of breaking the horizontal scroll, so here it is. It was a site made for the sole purpose of showing off pi to 1000000 places, and the author has an alternate site, so I don't think this is bandwidth theft... Random the Scrambled 12:15, 29 May 2006 (UTC)
thread_title:  Pi to 1000000 decimal places 

message: I've made some progress on a rewrite of this article. Contributions welcome; beware of unfinished sentences, etc. Fredrik Johansson 22:24, 29 May 2006 (UTC)
replies: text: I cleaned up the definition section and separated out the numerical value discussion. I took out the claim that advanced textbooks define pi in terms of trig functions. They generally do no such thing. I would be inclined to break up the numerical value into groups of five digits as is done in the e article (not adding any digits), any objections?--agr 14:21, 30 May 2006 (UTC)
replies: text: You haven't edited my proposed rewrite; did you post this comment in the wrong section? Fredrik Johansson 16:39, 30 May 2006 (UTC)
replies: text: I guess I did. --agr 16:51, 30 May 2006 (UTC)
thread_title:  Rewrite 

message: I have reverted a couple of attempts to refine the value in the introduction to 3.141592, and feel I ought to explain my reasons: To avoid confusion, the short value in the introduction should be one that can be interpreted as a truncated approximation as well as a round-to-nearest one. The possible choices are then 3, 3.1, 3.14, 3.14159, 3.14159265, 3.14159265358979 and so forth. Of these, 3 and 3.1 are obviously too imprecise, 3.14 is believed by some to be exact (which mistake we should not encourage), and giving 8 or 14 decimals seem to be excessively many for a short introduction. The only remaining possibility is 3.14159, which I believe should therefore be retained. Henning Makholm 20:03, 1 June 2006 (UTC)
replies: text: I support this. Random the Scrambled 00:12, 13 June 2006 (UTC)
replies: text: 3.141592653589 is the most common form of PI... you are wrong, I am right, and length is better —The preceding unsigned comment was added by 131.247.243.34 (talk) 02:41, 11 December 2006 (UTC)
replies: text: 3.141592653589 may be the most common form of PI, however, when entered by hand, few enter more than six digits realistically. —The preceding unsigned comment was added by 70.73.118.166 (talk) 06:09, 5 February 2007 (UTC)

text: The other (if not the main) reason why 3.14159 is most commonly used is because 7 (the number of syllables you use to say it) is a magic number. ~ Keiji (iNVERTED) (Talk | Contribs) 07:16, 5 February 2007 (UTC)
thread_title:  Digit creep: Why 3.14159 is the right approximation for the introduction 

message: Maybe this article should be π instead, and pi should redirect to it.
:Nice thought, but no. Not all browsers handle special characters well, particularly those used by the visually impared. Also Wikipedia automatically capitalizes the first letter of all articles so you get Π instead (which does redirect here).--agr 22:52, 11 June 2006 (UTC)
replies: text: I think it is a good idea. π & ∏ are part of the extended ASCII set and are supported by almost everything. Dread Lord CyberSkull ✎☠ 00:22, 19 August 2006 (UTC)
replies: text: But Π is never this number.  Very bad idea.  Gene Nygaard 23:03, 6 October 2006 (UTC)
replies: text: The template  allows ∏ to be displayed as π. It has been used in π (film). Just64helpin 17:39, 18 January 2007 (UTC)
thread_title:  move to π? 

message: The approximation 355/113 (3.1415929…) is the best one that may be expressed with a three-digit numerator and denominator.
In fact it's better that that, the next smallest denominator that gives a better approximation isn't till 52163/16604! 195.7.54.2 10:33, 20 June 2006 (UTC)
thread_title:  Fractional approximation 

message: http://en.wikipedia.org/w/index.php?title=Pi&diff=prev&oldid=59749599
Why was that deleted? I found this quote:
:"A value of π to 40 digits would be more than enough to compute the circumference of the Milky Way galaxy to an error less than the size of a proton."
From this paper. I dare propose that this isn't even trivia; people (such as myself) see that scientists have calculated it out to billions of digits and assume that much accuracy is necessary or important. Where shall we put that quote back in? --DevastatorIIC 03:19, 22 June 2006 (UTC)
replies: text: Certainly the misconception that we calculate millions of digits of π so that we can do more precise calculations with it needs to be addressed.  The point is that no practical problem ever needs more than a handful, and more digits are either for number-theoretic reasons or for testing computers.  That was the point of the removed text, and I thought it was a good one. -lethe talk [ +] 03:41, 22 June 2006 (UTC)

text: I have certainly seen similar statements in other (print) encyclopedias, and think that it gives a good sense of how remote from practical considerations these very precise values of π really are. Happy to see it go back in. Madmath789 04:23, 22 June 2006 (UTC)

text: I have attempted to add a rewording that addresses this to the Numerical value section. Not completely satisfied with the result; in order to make the wording flow better I had to move the "sufficient for engineering and science" sentence from its prominent place at the beginning of a paragraph. Edit away if you have a better solution to that. Henning Makholm 14:44, 23 June 2006 (UTC)
thread_title:  Trivia deleted 

message: How many animations that show a circle perimeter straightening do we need (or want)? While animations in general are annoying I can see some presentational value in one here, but why two animations of basically the same idea? We should decide on one and let the other go. FWIW I think that overall :Image:Diameter and Pi 1.gif is cleaner and less visually noisy than :Image:Pi-unrolled.gif, but it could be confusing that :Image:Diameter and Pi 1.gif uses dashed circular arcs to denote "this is the straight line whose length is being measured". Henning Makholm 07:40, 25 June 2006 (UTC)
replies: text: I think one animation is useful, but not two. I also dislike the curved arc denoting distance, so I vote Pi-unrolled. Perhaps we could enlist someone to make a better one? Maybe a circle unrolling on a coordinate plane? --DevastatorIIC 20:09, 25 June 2006 (UTC)

text: To be fair, the animations total only 56.5 KB. The page itself is 40 KB long. I just think they're distracting and of moderate usefulness. --DevastatorIIC 01:08, 27 June 2006 (UTC)
replies: text:  I have now removed :Image:Diameter and Pi 1.gif from the article. Henning Makholm 21:16, 27 October 2006 (UTC)
thread_title:  Animations 

message: In the section on number theory, should it be mentioned that the average number of ways to write a number as the sum of two perfect squares comes from the fact that a circle of radius r is defined as the set of all points (x,y) such that x2+y2 = r2, or is this somewhat beyond the scope of the section? -- He Who Is[ Talk ] 17:24, 10 July 2006 (UTC)
thread_title:  Number Theory 

message: I fear that many of our math-related articles scare away non-mathematicians by using advanced math jargon too early in the article, so that the reader never gets to the later parts he can still understand.  I've reorded the sections a bit to put most of the accessible information at the top.
I also added a section giving an example of how to approximate pi using only elementary algebra.  Then I noticed that the german article seems to have several sections which discuss related ideas.  Perhaps some german-speaker can help integrate them. Lunkwill 05:17, 13 July 2006 (UTC)
thread_title:  Intuitive explanation of calculating pi 

message: "The German mathematician Ludolph van Ceulen in 1615 computed the first 32 decimal places of π. He was so proud of this accomplishment that he had them inscribed on his tombstone."
In his page, it says he died in 1610. How is it possible he computed the first 32 decimals of pi 5 years after he died?
:The things people will do for calculating π :)
:Seriously, I've looked up the matter, and I have found conflicting references regarding the time of his computation - my more or less trusted source only says that 35 digits (not 32, btw) was as far as he got by his death in 1610. I've changed the sentence accordingly. -- Meni Rosenfeld (talk) 07:00, 23 July 2006 (UTC)
thread_title:  Problem with Ludolph finding first 32 decimals in 1615 

message: The Good article nomination for  has failed
:I am failing the nomination of the article for a number of reasons.
# The page could be a lot more accessible to readers with a limited mathematical background, especially since there are many more technical articles on specific aspects of pi. The page seems to have been hijacked by mathematicians: things like pi mnemonics (which mathematicians rightly consider unimportant) should appear much earlier and there should be more content on the history of mankind's fascination with pi. 
# A number of sections are disorganized and look like an accumulation of information tidbits. For instance the early approximations section needs a rewrite and is too long given that there is a separate article for that history. The formulae section is also pretty bad in that respect: there is no unity in the material presented nor is there any serious effort to motivate the presence of these formulas.
# There is still a Trivia section which is evidence that the page is still being built. Of course there is not much edit-warring but the page is still very actively edited.
Pascal.Tesson 08:15, 23 July 2006 (UTC)
replies: text: PS: I just noticed the to-do list on top of this talk page. The criticism there is very well put. I would add this: the history section seems to focus only on the practical matter of calculating pi which is not only a very narrow view of the subject but a particularly hard one to appreciate for the layman. Pascal.Tesson 08:23, 23 July 2006 (UTC)

text: Actually I also find mnemonics not so important but I feel they should be mentioned (if only in passing) earlier than they are currently. In any case, I am very impressed by User:Fredrik/Pi which I think has the right spirit. Why not go live with it?Pascal.Tesson 11:26, 23 July 2006 (UTC)
replies: text: Thanks, but I think the empty sections need some content first... Fredrik Johansson 22:57, 19 August 2006 (UTC)
thread_title:  [[Wikipedia:Good articles|Good Article]] [[Wikipedia:Good articles/Nominations|nomination]] has failed 

message: I have discovered the best ratio of π accuracy to characters for an approximation.
As an example:
22/7 requires 4 characters and equals 3.142857142857142857..., which is correct to 3 significant figures or 0.75 per character.
355/113 requires 7 characters and equals 3.141592920353982300..., which is correct to 7 significant figures  or one per character.
So the best is ³√31, which requires 4 characters and equals 3.141380652391393004..., which is correct to 4 significant figures or one per character as well. But it beats 355/113 because it has the virtue of brevity and memorability.
I challenge anyone to find a better one.
User:Gee Eight 5 August 2006 20.03 UTC
:3 requires 1 character and is correct to 1 significant digit. And it clearly beats your cube root in terms of brevity and memorability. -- EJ 20:11, 5 August 2006 (UTC)
replies: text: Anyway, π also requires 1 character, and it is correct to infinitely many significant digits. -- EJ 20:24, 5 August 2006 (UTC)
replies: text: I know what you're trying to convey, but I believe we are to assume he meant a finite composition of elementary operations on integers. 74.132.209.231 20:54, 16 August 2006 (UTC)
replies: text: What's wrong with thinking of 355/113 as 113\355, which is quite memorable? — Arthur Rubin |  (talk) 17:45, 21 August 2006 (UTC)

text: For a ratio better than 1, take the decimal expansion and round it just before the Feynman point. Fredrik Johansson 18:03, 21 August 2006 (UTC)
thread_title:  Best approximation ever 

message: The article shows as of August 19, 2006:
::In 1997, David H. Bailey, Peter Borwein and Simon Plouffe published a paper (Bailey, 1997) on a new formula for π as an infinite series:
::(fomula here...)
::This formula permits one to fairly readily compute the kth binary or hexadecimal digit of π, without having to compute the preceding k − 1 digits. Bailey's website contains the derivation as well as implementations in various programming languages. The PiHex project computed 64-bits around the quadrillionth bit of π (which turns out to be 0).
Comment: Better said "digit" not "bit, especially since it is not specified if the digit is binary or hexadecimal.  And ah, who cares what the digit is, zero or one, or zero through 15 (hex)?  Would someone care to edit this please? —The preceding unsigned comment was added by 65.96.106.226 (talk • contribs) .
:I don't understand. What is misleading and better said how? Fredrik Johansson 20:44, 19 August 2006 (UTC)
replies: text: Well, it doesn't really matter. If it's binary, do it four times, and you've got a hex digit. If it's hex, you've got four bits, and if you like you can throw away three of them. But I haven't read the passage in the article; could be it could stand clarification. --Trovatore 02:04, 24 August 2006 (UTC)
replies: text: The problem was that it is allegedly unclear whether the text refers to the quadrillionth binary digit or hexadecimal digit (difinitely not the same thing). But it is clear - this page clearly mentions the quadrillionth binary digit. And if we have already mentioned that the bit was computed, we might as well state what it is. This sentence should probably remain as it is. -- Meni Rosenfeld (talk) 09:25, 24 August 2006 (UTC)
replies: text: That quote would settle it for me: 'clearly mentions the quadrillionth binary digit'  I'll look at the source. If it says digit, then digit is what it should say.Yellowdesk 07:09, 6 September 2006 (UTC)

text: Surely you know that "bit" stands for "binary digit"? -- Meni Rosenfeld (talk) 08:35, 6 September 2006 (UTC)
thread_title:  Misleading digits and bits 

message: This revert sure could have used an edit summary, but is still legitimate. This section's purpose is to demonstrate that π can be calculated with a naive method, and only one example is required for that. Numerous "real" methods of calculating π are discussed later in the article. -- Meni Rosenfeld (talk) 18:53, 25 August 2006 (UTC)
replies: text: I have no objections to that. I unreverted primarily in an attempt to show the anonymous contributor that getting well-meant additions removed completely without explanation and argument is not what one should expect from Wikipedia in general.  If things can be kept civil, I wouldn't mind getting rid of the secion completely. It is too complex compared to the precision one gets. If we want to describe a conceptually simple but computationally stupid way to approximate pi, why not just add the side lengths of a fine polygonal approximation to a circle (not necessarily a regular one, just e.g. one where the numerically smaller of each corner's coordinates is rational)? Henning Makholm 12:58, 28 August 2006 (UTC)
thread_title:  [[User:Heliac|Heliac]]'s revert 

message: Paul August has added (diff) images of mathematicians to the "Formulae" section. I do not think these images really belong in this article. Any thoughts? -- Meni Rosenfeld (talk) 09:55, 28 August 2006 (UTC)
replies: text: I agree. They are not relevant as illustations of the topic of the article, and the article is long enough without them. (Yes, I know some people use browser windows small enough that the images occupy space that would otherwise be vacant, but that is not a universal thruth). Henning Makholm 12:46, 28 August 2006 (UTC)
thread_title:  Images? 

message: How the heck can anyone remember pi to over 80'000 decimals without looking it up? How can anyone remember pi to more than 20 or 30 decimals, for that matter? JIP | Talk 18:48, 30 August 2006 (UTC)
replies: text: There are people with good memory, or more importantly, a memory which is good for this kind of thing - the amount of information in 80,000 digits of pi is negligible compared to what the human brain can contain, but most people's memory isn't suited for this accurate memorization digit by digit. I guess an average person has memorized more than a dozen phone numbers - memorizing a hundred digits of pi is just as easy. I personally know 80 digits or so from memorizing them a while back - which is, of course, very little, but still more than your stated 20-30. -- Meni Rosenfeld (talk) 10:56, 31 August 2006 (UTC)

text: I find it easiest to split the digits into "words" of 3-7 digits and choosing the splitting points to emphasize patterns. For example, I've memorized the beginning of π as 3.1415926 - 535 - 8 - 979 - 323 - 8 - 46264 - 3383...; note how all groups after the first are symmetrical except for the appearance of a few 8's. I'm fairly certain the average (young) person could learn at least several hundred digits of π this way, given some time and sufficient determination. Fredrik Johansson 11:25, 31 August 2006 (UTC)
replies: text: I've memorised 33 decimal places, the first 28 just roll off the tongue as one word, the last 5 are split into a seperate word. Even more interestingly is that I can't seem to forget it. —The preceding unsigned comment was added by 213.48.15.234 (talk) 13:08, 20 February 2007 (UTC)
thread_title:  Memorising pi approximations? 

message: === Workshop ===
There has been some criticism of this work -- unfortunately, somewhat diffuse. I'm astonished to see it was even nominated as a Featured Picture Candidate but it follows that if it can be improved to this standard, I should make the effort. I've solicited additional comments but more are needed. I'm sure all understand it's quite a job to rework every frame of an animation and that, having done the job 4 times already, I'd like very much to be sure the 5th version is the last. 
I call your attention to the Specs section. It's much more useful to me if editors simply edit these specs to suit themselves, rather than making long, detailed text comments. Don't worry about overwriting other editor's specs; I will take all history into account. Let's do this in true wiki-fashion. John Reid 14:01, 2 September 2006 (UTC)
replies: text: Workshop closed. John Reid 21:32, 15 October 2006 (UTC)
thread_title:  Pi-unrolled 

message: There has been some criticism of this work -- unfortunately, somewhat diffuse. I'm astonished to see it was even nominated as a Featured Picture Candidate but it follows that if it can be improved to this standard, I should make the effort. I've solicited additional comments but more are needed. I'm sure all understand it's quite a job to rework every frame of an animation and that, having done the job 4 times already, I'd like very much to be sure the 5th version is the last. 
I call your attention to the Specs section. It's much more useful to me if editors simply edit these specs to suit themselves, rather than making long, detailed text comments. Don't worry about overwriting other editor's specs; I will take all history into account. Let's do this in true wiki-fashion. John Reid 14:01, 2 September 2006 (UTC)
replies: text: Workshop closed. John Reid 21:32, 15 October 2006 (UTC)
thread_title:  Workshop 

message: The (6th) version uploaded distinctly as :Image:Pi-unrolled-720.gif has been promoted to FP. Note that a thumb caching bug means that all efforts to manually purge old versions seem to fail. Please, in the article, leave the "720" code for a couple weeks. John Reid 21:32, 15 October 2006 (UTC)
thread_title:  FP version 

message: I think this might be the worst looking lead section in Wikipedia. Fredrik Johansson 19:29, 7 September 2006 (UTC)
replies: text: I'm afraid I have to agree that the bit that I see when I look at the top of the page is pretty hideous aesthetically, and it could do with a bit of attention from someone who knows a bit about page layout. On another matter, I rather like the section on the Serbian version which has a nice section on the historical progress of calculations of the decimal expansion of Pi - anyone think something similar might be nice for our version? Madmath789 19:48, 7 September 2006 (UTC)
replies: text: Once the unfinished sections in User:Fredrik/Pi get fixed (other editors are welcome to help out), I think we will have a much nicer version ready. Fredrik Johansson 20:00, 7 September 2006 (UTC)
replies: text: If this version can be tweaked so that the animation must lie  next to the TOC (in some browsers the TOC overlays the animation), it might do; dab header on top, followed by text and image of π; followed by TOC and animation. Septentrionalis 17:00, 8 September 2006 (UTC)
replies: text: You know, I don't like the animations at all. At least not at the top of the page. Also, I put {TOCright} on there, but got reverted in the flurry of vandalisms/reversions. I think it makes the page look much nicer. (My version). --DevastatorIIC 09:49, 21 September 2006 (UTC)
replies: text:  When I created the animation, I added it to the article way down in Trivia. John Reid 17:55, 24 September 2006 (UTC)
thread_title:  Aesthetics 

message: *The product of (1 − 1/p2) over the primes, p, is 6/π2.
I'm not sure, but isn't that supposed to say π2/6 ? Kevin Hughes 15:52, 15 October 2006 (UTC)
replies: text: That would be impossible, since all the terms in the product are less than 1. You're confusing it with the product of p2 / (p2-1), which is its reciprocal. -- Meni Rosenfeld (talk) 16:13, 15 October 2006 (UTC)
replies: text: Okay, thanks for the explanation! :-) Kevin Hughes 19:07, 15 October 2006 (UTC)
thread_title:  error? (number theory section) 

message: How is the following supposed to be an approximation of Pi accurate to 9 decimal places?
::(63/25)(17+15\sqrt 5)/(7+15\sqrt5)
I've tried evaluating it as stated and came nowhere near 3.141592653.  Did I make a stupid error, or is this totally bogus?  If bogus, it should be deleted from the article. -- Moondigger 00:35, 20 October 2006 (UTC)
replies: text: Nevermind.  I made a stupid error. -- Moondigger 00:47, 20 October 2006 (UTC)
thread_title:  Incorrect approximation? 

message: As noted before on this page, the Archimedian constant is never denoted with a capital Π, always with a small π.  This was one reason a move of the article name to π was rejected; it was claimed that this would have been capitalised rendering the impossible representation Π.
Against this background, I'm a bit surprised that there have been a number of capital Π's in the article for more than five months.  Am I missing something? JoergenB 01:29, 20 October 2006 (UTC)
thread_title:  Always and only π, never Π. 

message: : I propose that Time Cube Pi be mentioned in this article. Even though it may totally incorrect, you should still mention it because there is a strong association, and particularly as a See Also. -- Zondor 04:11, 23 October 2006 (UTC)
thread_title:  Time Cube Pi 

message: I suggest we add  to this article 204.81.77.4 15:12, 23 October 2006 (UTC)
thread_title: Numbers template

message: It is not irrational. this is proven in its very definition: "The ratio of a circle's circumference to its diameter." The key word is ratio.
It will repeat or terminate somewhere down the line. We just haven't found it yet.Xparasite9 16:02, 27 October 2006 (UTC)
replies: text: No. A rational number is the ratio of two integers. A circle's diamater and circumference can't be both integers (unless you consider the degenerate case of a point, which we don't). Pi has been proven to be irrational. -- Meni Rosenfeld (talk) 16:57, 27 October 2006 (UTC)
thread_title: Pi will either repeat or terminate

message: There you can read that PI can have a limit at 1.3511 trillion digits.
*Watley Review
*Infosatellite
This limit was discovered by Professor Yasumasa Kanada while trying calculate PI up to 1.5 trillion places.
:Have you read this? Mindmatrix 14:45, 14 November 2006 (UTC)
replies: text: The reporter failed to understand what was going on; neither the first time nor the last. Septentrionalis 18:58, 14 November 2006 (UTC)
thread_title:  The ultimate value of PI 

message: Keep the moving Pi image please. It illustrates in an interesting fasion the principlee of Pi. Maunus 15:28, 19 November 2006 (UTC)
replies: text: I don't recall anybody having proposed to remove it recently. Animations are bothersome in general, but I think the consensus is to grudgingly accept that it would be difficult to convey the same information in a static image. Henning Makholm 16:51, 19 November 2006 (UTC)
replies: text:  I am glad.Maunus 17:19, 19 November 2006 (UTC)

text: Animated images are fine, as long as the final frame shows useful information. This for the benefit of users (like me) who disable looping of animated images in our web browsers (e.g., NetScape can be configured to show only one cycle of animation, which leaves the final frame as a static image). — Loadmaster 20:20, 20 December 2006 (UTC)
thread_title: Keep image

message: I've incorporate the section including his contributions below.  Unless published, it's WP:OR, and cannot be included in the article.  However, they are interesting, if correct.  I'm reverting the article to its previous status.
*General Viète Product:
::By \pi=\left( m\sin \frac{\pi}{m} \right)
            \sec \frac{\pi}{2m}
            \sec \frac{\pi}{4m}
            \sec \frac{\pi}{8m} \cdot \ldots
:Put m=2 gives the Viète Formula
:For m=3 (by Eric Ng, the contributor, or if there are any independent discoverers please cited above),
::\pi=3\cdot
             \frac{2}{\sqrt{2+\sqrt{3}}} \cdot
             \frac{2}{\sqrt{2+\sqrt{2+\sqrt{3}}}} \cdot
             \frac{2}{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}} \cdot \ldots
:For m=5 (by Eric Ng, the contributor, or if there are any independent discoverers please cited above),
::\pi=\frac{5}{\phi} \cdot
            \frac{2}{\sqrt{2+\sqrt{\phi \sqrt{5}}}} \cdot
            \frac{2}{\sqrt{2+\sqrt{2+\sqrt{\phi \sqrt{5}}}}} \cdot
            \frac{2}{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{\phi \sqrt{5}}}}}} \cdot \ldots
::where \phi=\frac{1+\sqrt{5}}{2} the Golden ratio.
*Sine as an Infinite Product:
::By \sin x=x\prod_{n=1}^{\infty} \left( 1-\frac{x^{2}}{n^{2}\pi^{2}} \right)  (See )
:Put x=\frac{\pi}{2} gives the Wallis product
:For x=\frac{\pi}{6} (by Eric Ng, the contributor, or if there are any independent discoverers please be cited),
::\frac{\pi}{3}=
        \prod_{n=1}^{\infty} \left( \frac{36n^{2}}{36n^{2}-1} \right) =
        \frac{6}{5} \cdot \frac{6}{7} \cdot
        \frac{12}{11} \cdot \frac{12}{13} \cdot
        \frac{18}{17} \cdot \frac{18}{19} \cdot
        \frac{24}{23} \cdot \frac{24}{25} \ldots
— Arthur Rubin |  (talk) 15:35, 20 December 2006 (UTC)
thread_title:  [[User:Eric Ng]]'s contributions 

message: In the article, it states that pi and e are not algebraically related.  What about the 'famous five' equation. e^(i*pi) + 1 = 0.
—Preceding unsigned comment added by 69.223.62.238 (talk • contribs) 2006-12-24T21:53:06
: This relation is true, but it does not count as an "algebraic relation". For an algebraic relation you would need to exhibit a polynomial P(x,y) in two variables with integer coefficients and powers, such that P(e,π)=0. (By the way, what the article says is not that e and pi are not algebraically related, but merely that it is unknown whether or not they are. However, the smart money appears to be on "are not"). Henning Makholm 00:37, 25 December 2006 (UTC)
thread_title:  Huh? 

message: I excised the following from the article:
 Dr. Shanks's son Oliver Shanks, also a mathematician, states
 that there is no family connection to William Shanks, and in
 fact, his family's roots are in Central Europe.
This lacks a citation, and, more importantly, it does not seem to be relevant to the article. --JianLi 03:22, 30 December 2006 (UTC)
thread_title:  deleted line 

message: Can I add that Pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998 62803482534211706798214808651328230664709384460955058223172535940812848111745028410 27019385211055596446229489549303819644288109756659334461284756482337867831652712019 09145648566923460348610454326648213393607260249141273724587006606315588174881520920 962829254091715364367892590360011330530548820466521384146951941511609?—The preceding unsigned comment was added by 72.92.84.100 (talk • contribs).
:I don't see a compelling need for so many digits.  There are links to additional digits, if someone were interested.  I would oppose adding more; 50 is enough for any practical purpose.  --TeaDrinker 19:13, 5 January 2007 (UTC)
replies: text: This has been brought up before and it's always been decided that it just adds bloat to the page, especially since there are links to pages with digits. Deathbob 04:35, 14 January 2007 (UTC)
thread_title: Pi

message: Non registered users have not posted non revertible contributions to this article frequently enough for it to be productive to keep them able to post; half of the recent edits (or more) are spam and then reverts. I don't know exactly what is required to lock a page to edits by registered users only but it might be a good idea. I mean, it is funny enough when you are reading an article and midway through refresh and find spam, but it is a waste of the Wiki servers' bandwidth, space, etc. Hazelorb 07:36, 11 January 2007 (UTC)
replies: text: While this idea sounds nice, I don't think the policy supports semi-protection in these circumstances - but you may want to bring this up on WP:AN/I. -- Meni Rosenfeld (talk) 17:24, 11 January 2007 (UTC)
thread_title:  Closing page to non registered users 

message: Propose moving the formulae and Trivia sections to completely different articles, as they are highly specialized.
As for other edits to this page, I think User:Fredrik/Pi's history section should be incorporated into History of numerical approximations of π which is linked as the main article in 2 sections of this article. I would like to consense a lot of that material into a good blurb and then properly link to that history article. I propose using the other sections of Fredrik's article (especially, "use in math/science" in maybe a slightly briefer form for the blurb section referring to the new formulae page, and the culture blurb exactly as he has intended.)
As for the other sections of this article,
*Maybe relate the sections preceeding History (which will be moved as already planned in the to do list) to lessen the clutter in the TOC, expand said info so it has a right to clutter the TOC, or put properties or any of the other info into the blurb at the top?
*Rewrite both the memorization blurb to be more well rounded and naturality to be less techy
*Open questions as the last section before references/see also
Let me know, I will start making these changes, but I did not want to step on any feet. I did a few minor things already, but these are a little more major. Also, User:Fredrik should feel free to start working in his history section into the appropriate article, and maybe be kind enough to write the blurb for this page?
Hazelorb 04:17, 14 January 2007 (UTC)
replies: text: I was just about to talk about this but i see i've been beat.  Anyway, alot of the formulae section minus things like the physics section would be better housed in Computing Pi. I've been working on it and some peices at the top of the artical have already been moved. Deathbob 04:31, 14 January 2007 (UTC)
replies: text: Awesome glad someone else is helping with this mess. I did not really even know where to start, haha. Hazelorb 04:47, 14 January 2007 (UTC)
replies: text: Added  on specific sections that would be most compatible Deathbob 04:54, 14 January 2007 (UTC)
replies: text: Note that there is already an article list of formulae involving %CF%80. Computing Pi should focus on methods which can actually be used to calculate π efficiently, and IMO should be renamed Methods of computing Pi. -- Meni Rosenfeld (talk) 18:03, 14 January 2007 (UTC)
replies: text:  Well then why are all of those formulas on the main page AND a separate page? It makes no sense. Can we select a few key ones and then link to that formulas page then at least? Hazelorb 21:20, 14 January 2007 (UTC)

text: Yes. But make sure that the key formulae do remain in the main article (as well as the formulae page). -- Meni Rosenfeld (talk) 21:46, 14 January 2007 (UTC)
replies: text:  Which ones do you think we should keep? Right now we have every formula that could possibly involve pi, which is way too many for the main article (of course you know this). I definitely think it has to be few enough that the subheadings are no longer needed. It would be "Key  Formulae" with whichever ones we choose, and the link "main article -- " Also maybe a short explanation (1 sent... 2 sents max) of those ones' immportance/why they are key ones - but the whole explanation could go on the formulae page. Hazelorb 21:52, 14 January 2007 (UTC)

text: The geometry section is a must to stay here, but for the most part that section is HUGE, especially the Analysis part, people just learning about Pi will not understand it, or care about it.  So it think the majority should be split accordingly to the list of formulae involving %CF%80 page and the Computing Pi page. We have a decent link for computing pi higher up the page, the Formulae section needs one if it doesn't already, after we get the layouts of those 2 pages established then see about renaming them then.  Since you have worked on the formulae page you might wish to tag the sections that should be merged completely.  As a side note Software_for_calculating_%CF%80 should probably have cross refs to and from Computing Pi Deathbob 22:32, 14 January 2007 (UTC)

text: "we have every formula that could possibly involve pi..." That's a bit of a stretch. What the article currently contains doesn't come close to scratching the surface. The formulae which I think can be excluded from the main article are (from the analysis section) Viete's, Faster product, Symmetric, Chebychev and Totient. -- Meni Rosenfeld (talk) 18:05, 15 January 2007 (UTC)

text: By the way, there is some discussion of this at Wikipedia talk:WikiProject Mathematics#Computing Pi. -- Meni Rosenfeld (talk) 19:24, 15 January 2007 (UTC)

text: People seem to have stopped talking for the past few days, I wonder if more should be moved over, or what can be done to bring it to thier standards? Deathbob 16:19, 22 January 2007 (UTC)
thread_title:  Separate articles 

message: I see that Hazelorb has moved the pi-unrolled animation to the "Trivia" section, with edit summaries pointing to this talk page. Skimming through a few times, I find no recent discussion of this image -- what have I missed? Had I seen such a proposal, I would have opposed classifying the image as "trivia" -- if it serves any purpose at all in the article, it must be as a first, intuitive, introduction to what the article is about, for readers who are not comfortable with mathematical abstraction. Down in the trivia section I cannot see what purpose it serves. Henning Makholm 01:44, 19 January 2007 (UTC)
replies: text: I see no discussion, justification, or logic in the move. — Arthur Rubin |  (talk) 01:47, 19 January 2007 (UTC)
replies: text: It was an old discussion. I don't really care where it is in the article, except that at the top of the page it scrolls in 800x600 browsers and the past discussion on this page was in opposition of it being there. (not meaning to cause any controversy here, if you REALLY want it at the top of the article you can move it back, just keep in mind the original creator of the image on this talk page said it was originally in trivia, and that it makes the page scroll). Do we really need both images in the top part is the main point. Hazelorb 22:32, 19 January 2007 (UTC)
thread_title:  Pi-unrolled moved to trivia