Talk:Pi/Archive 11

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Archive 5

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Archive 9

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Featured article status update

Update on progress towards FA: Thanks to all the editors that have recently improved the article. User Jakob.scholbach did a great review (above) and there have also been some good suggestions from user Nageh. The article meets all the formalistic FA requirements (cites, links, illustrations, MOS, etc); and the prose has been reviewed by several editors, so the prose is probably as good as it is going to get. The only remaining tasks I'm aware of are implementing 3 or 4 remaining suggestions from the review, and polishing the "speed of convergence" subsection. After than, perhaps in late May, I'll nominate the article for FA. All other editors are welcome to review and improve the article as they see fit, of course. If anyone out there is a graphics wizard, it would be great if you could create an English version the graph File:Rekordaj alproksimighoj al pi.png. That is a nice graph that should be in this article, but its axis labels are not in English ... all you have to do is translate the labels from Esperanto to English. --Noleander (talk) 18:03, 1 May 2012 (UTC)

I can certainly replace the axis labels easily. Are you sure you don't want to do it yourself so you can decide exactly how you want everything? I'm just going to open it in MS Paint, erase the old labels, and put new ones in with the text tool. Use Flip/Rotate to do the vertical one. It's no trouble, but if you'd rather I did it, let me know your preferences. Should I keep it all black and white, or maybe use blue for the labels and title to add a little color? I could also color the graph plot using the fill tool. Preferred font? Should the labels be bigger than they are now? Should I leave off the title, since it'll have a caption on the page? Lots of little decisions like these. Tell me what you prefer, and I'll just use my own judgment on the rest.

I don't know Esperanto, but I presume the title says "Record approximations of pi", and the x-axis label says "year". I would guess the y-axis label says "decimal position", but that doesn't make sense. Tell me the exact wording you want, including how it's capitalized. --Joseph Lindenberg (talk) 18:04, 2 May 2012 (UTC)

Thanks for volunteeering:

Colors: a simple black-on-white would be best. WP sort of has a policy to avoid relying on colors, due to color-blind readers.
Axes: The vertical axis should be "Number of digits" and the horiz axis "Year".
Scale: the vertical axis has to be logarithmic. Horiz axis should probably keep the "breaks" so the graph is not flat for centuries.
Year axis: the labels on the vertical axis are too hard to read (to get the number of zeros); suggest use scientific notation e.g. 10¹² etc
Font: use Arial or Helvetica.
File format: Ideally, the picture should be in SVG vector format, not a pixel format like GIF/PNG/TIFF. That way, future editors can edit the file, and tweak individual graphic elements (for example, as new records are set, future editors could add new points onto the end of the graph). I've used InkScape in the past to create SVG pictures: InkScape is free, mature, and works on Mac or PC. To get to SVG Format would entail re-drawing the picture from scratch.
Data: Another reason to re-draw the picture from scratch is because we don't know what source the original picture creator used: their data may be suspect. the WP:V policy applies to data in graphs as well: we must be able to identify a source. I'd suggest the data points from Chronology of computation of π are the best data to use. The Arndt book has a great table (in an appendix) summarizing the num digits over time, and it is consistent with the Chronology of computation of π data, so I'd just use the latter as a starting point.
Newest data: it would be great if you could extend the old graph to include the newest data through 2011 (as shown in Chronology of computation of π)

Thanks! --Noleander (talk) 18:17, 2 May 2012 (UTC)

I realize SVG is preferable, but I don't know anything about working with vector graphics. I assumed we were just talking about replacing the labels on the existing graph. I was surprised you were seeking a volunteer to do something so simple. (And wondering how in the world it could be that you didn't know how to use MS Paint.) Maybe we should continue to look for another volunteer. Sorry I misunderstood. (By the way, on the color issue, three other graphs in the article do use blue for the actual plot line. So you might want to consider doing that for consistency.) --Joseph Lindenberg (talk) 18:51, 2 May 2012 (UTC)

No problem. At first I thought just replacing the labels would be okay, but the more I think about it, it probably needs to be redrawn from scratch. Or, the graph could be left out of the article ... I don't think its absence is a bar to FA status. Thanks for considering it anyway. --Noleander (talk) 18:54, 2 May 2012 (UTC)

I posted a request at Wikipedia:Graphic_Lab/Illustration_workshop#Pi_graph:_convert_from_PNG_to_SVG to see if anyone there could help. Not sure how active that group is, though. --Noleander (talk) 19:05, 2 May 2012 (UTC)

User Nageh drew a great illustration of the hunt for digits, :And it is in vector format, so it can be easily updated in the future. Great job! --Noleander (talk) 16:22, 3 May 2012 (UTC)

FA nomination initiated

This article has been nominated for FA status at Wikipedia:Featured article candidates/Pi/archive1. If anyone would like to review the article, please do so there. --Noleander (talk) 02:31, 15 May 2012 (UTC)

"Correct title" template?

I removed the {{Correct title}} template from the top of the article, which read:

The correct title of this article is

π

. It appears incorrectly here because of technical restrictions

First, I think that is super ugly to put such a notice at the top of a high-quality article. Second, many, many articles & books about $π$ use "pi" in their titles, and $π$ in their body - this article is following suit. Third, I don't think there is consensus that "pi" as a title is "wrong" or "incorrect": "pi" is a valid alternative to $π$ within a title. The "technical restrictions" are just one factor that causes "pi" to be a valid title. Thoughts? --Noleander (talk) 16:14, 3 May 2012 (UTC)

I agree, it should not be there unless the title is seriously wrong and confusing (like the old title for C Plus Plus). Some editors think that hatnotes are some kind of an interactive game where you scour the encyclopedia for any possible use for them, even if they contribute nothing and resolve no confusion. The threshold for ugly notices should be very high, since a professionally edited work contains exactly none. —Designate (talk) 23:35, 17 May 2012 (UTC)

More than that, the claim is just false. There are no technical restrictions in play. If we wanted the title to be π we could make it be that; the question has been debated and the decision made. (I don't know whether we could get it to display this incongruous-looking

π

thingie, which I dislike for other reasons, but I think we could.) --Trovatore (talk) 23:41, 17 May 2012 (UTC)

irrational number

The link to irrational in the section irrationality and transcendence section points to the wrong article. It should be irrational. (ie irrational_number)128.97.68.15 (talk) 19:45, 18 May 2012 (UTC)

Thanks for reporting that. I've fixed it. --Noleander (talk) 19:50, 18 May 2012 (UTC)

Featured article

The article was promoted to FA status today. Thanks to all who helped, particularly those that helped with the Peer Reviews! --Noleander (talk) 18:04, 4 June 2012 (UTC)

Excellent. Maybe suggest a Main Page entry for 22 July?—A bit iffy (talk) 19:35, 4 June 2012 (UTC)

Seems reasonable to me. Let's hope the Americans don't feel strongly about it ;-) Sławomir Biały (talk) 19:38, 4 June 2012 (UTC)

Actually, I was thinking of pi day (March 14, 2013) ... US centric as it is. What is the signfificance of 22 July? --Noleander (talk) 19:45, 4 June 2012 (UTC)

I think the idea is that it's 22/7. All these pi-ish days are kind of silly, based on artificial and meaningless interpretations of date notations. How about the anniversary of some significant event related to the number? Admittedly I don't know what event that might be. --Trovatore (talk) 19:48, 4 June 2012 (UTC)

Well, there's really no reason to put it on any kind of special day. But since 22/7 is one coming up, I suggest that one, unless there is one of more significance that someone else suggests. 3/14/2013 seems too far off to me, but if Noleander is ok with that, I don't mind it. Sławomir Biały (talk) 12:53, 5 June 2012 (UTC)

Sure, 22/7 is fine. Nine months is a bit long to wait, and I favor the European/military date convention ... I don't want to do anything to support the 3/14 convention :-) I'll put it on TFAR for 22 July. --Noleander (talk) 13:59, 5 June 2012 (UTC)

It is in the WP:TFAR holding area now. --Noleander (talk) 14:05, 5 June 2012 (UTC)

Well done everyone! Martin Hogbin (talk) 16:08, 7 June 2012 (UTC)

I was unaware that it was expressed as 22/7 in Europe. In that case, I suppose it's fine, but I much prefer 3/14. Mind you, I've never touched the article, so w/e. This is also Sven Manguard 14:22, 8 June 2012 (UTC)

Irrespective of notational preferences, March 14 is certainly the date best known for being pi day, and I think we could get everyone to agree on it if it were coming up soon. But it isn't, and 22 July is. --Trovatore (talk) 18:38, 8 June 2012 (UTC)

"Exploiting" numbers?

Have changed these two instances of "exploited"; not sure numbers should be subjected to exploitation, even if they are inanimate.

"Although infinite series were exploited for π most notably by European mathematicians..." and

"Lambert's proof exploited a continued-fraction representation of the tangent function...."

Have run across this same construction elsewhere recently, so maybe it's not as pejorative in BrE than AmE, where I take the meaning to be something like "searched for a weakness in order to misuse". Not sure what to replace it with. engaged? employed? riffed off of? improvised? elaborated? refactored? Maybe someone who understands what is happening to these numbers can suggest something more descriptive, so to be more informative for the international reader, or revert. Neotarf (talk) 14:39, 12 June 2012 (UTC)

In mathematics, "exploited" just means "used", but perhaps with a suggestion of "used in a particularly unusual or interesting way". Gandalf61 (talk) 15:31, 12 June 2012 (UTC)

The alternatives for exploited that were used, "elaborated on" and "engaged", respectively, are both manifestly inferior alternatives. It's not even clear what "Infinites series were elaborated on for π" in supposed to mean! Sławomir Biały (talk) 15:54, 12 June 2012 (UTC)

No argument. "Exploit" is a perfectly good English word whose meaning is precise. As such it is there to be exploited. After all, mathematics is not for the pure-hearted and those of upright morals, it's for evil people only. --Matt Westwood 21:14, 12 June 2012 (UTC)

I do not think there is any English-variety issue here. Exploit is a word with multiple nuances depending on context. Exploiting people is almost always bad (but then, so is using people), but exploiting, say, a regularity or a symmetry, is perfectly normal and even praiseworthy. --Trovatore (talk) 19:41, 12 June 2012 (UTC)

volume vs diameter?

Lambiam: Regarding the number of digits sufficient for computing universe's volume etc: Can you supply the quote from Arndt on that? I no longer have the book, but I my notes say "diameter" not "volume". Thanks. --Noleander (talk) 14:47, 12 June 2012 (UTC)

I included the quote in this edit. --Lambiam 23:17, 12 June 2012 (UTC)

Too many examples in "rate of convergence" section.

An editor just added a 3rd example to the "rate of convergence" section. I removed it, because it clouds the point that the section is making. That section is intended to be a concise explanation of why mathematicians kept searching for better series. It illustrates the point by comparing to simple series. Providing a 3rd example in that section would do nothing other than confuse readers. There are scores, perhaps hundreds, of series that could be listed in that section. But we have an entire article for that purpose: List of formulae involving π. --Noleander (talk) 05:40, 15 June 2012 (UTC)

I also removed a simplification of Nilakantha's series. Again, the point of that section is focused: show two simple series, compare them, and show the reader how one converges faster than the other. Presenting alternative versions is just confusing things for lay readers. --Noleander (talk) 05:50, 15 June 2012 (UTC)

how about the lexarithm in ancient greek

each lettre is a number so that¦ Α=1, Β=2, Γ=3, Δ=4, Ε=5, F=6, S΄= 6, Ζ=7, Η=8, Θ=9, Ι=10, Κ=20, Λ=30, Μ=40, Ν=50, Ξ=60, Ο=70, Π=80, Q=90, Ρ=100, Σ=200, Τ=300 Υ=400, Φ=500, Χ=600, Ψ=700, Ω=800, ΣΑΜΠΙ=900

given this each word is an adittion of numbers numer. given this: ΜΗΚΟΣ (length) = 40+8+20+70+200 = 338 ΠΕΡΙΦΕΡΕΙΑΣ (circumference) =80+5+100+10+500+5+100+5+10+1+200 = 1016 ΚΥΚΛΟΥ (circle) = 20+400+20+30+70+400 = 940 and finally

ΔΙΑΜΕΤΡΟΣ (diameter) = 4+10+1+40+5+300+100+70+200 = 730

so the tlngth of the circumferance of a cirle or (if you prefer) ratio of a circle's circumference = ΜΗΚΟΣ ΠΕΡΙΦΕΡΕΙΑΣ ΚΥΚΛΟΥ = 338+1016+940 = 2294 and diameter = ΔΙΑΜΕΤΡΟΣ = 730

SO

ratio of a circle's circumference / diameter = pi

= ΜΗΚΟΣ ΠΕΡΙΦΕΡΕΙΑΣ ΚΥΚΛΟΥ / ΔΙΑΜΕΤΡΟΣ = Π

= 2294 / 730 = 3.14...

quite funny isn't it? funniest part is the the same applies for the golden ratio Φ and that it was first pointed out by the pythagorean school of thought. — Preceding unsigned comment added by 85.75.67.238 (talk) 18:25, 24 June 2012 (UTC)

I do think it's funny, and pretty cool if applicable! It might even give a clue that the Greeks knew Pi at some very early point, and used it as the basis for making up some or all of these Greek words! But first: Where did you discover that each of those Greek words means what you indicated they mean? I used Google Translate (iffy at times), and it said: ΜΗΚΟΣ (length)—Google Translate agrees. ΠΕΡΙΦΕΡΕΙΑΣ (circumference)—Google Translate says "region". ΚΥΚΛΟΥ (circle)—Google Translate says "value". And finally, ΔΙΑΜΕΤΡΟΣ (diameter)—Google Translate agrees. I checked all the Greek-letter-for-number portions you included, and checked all the calculations you listed just above this for Pi, and they appear to be CORRECT. :) The full final calculation to complete decimal points came to 3.14246575342466, but at least the first 3 digits are right, which is intriguing! QUESTIONS: What Greeks used these words in the way you did above, all? When is the earliest place in time that these Greek words are they found used to mean this, for Mathematics? SOURCES? Links? Thanks! (Btw, I didn't look into or check the "Golden Ratio" part.) Misty MH (talk) 05:53, 25 June 2012 (UTC)

I hope you don't mind: I turned your contribution into its own section, I think, lol. Misty MH (talk) 05:57, 25 June 2012 (UTC)

Yep! It worked. :) Misty MH (talk) 05:59, 25 June 2012 (UTC)

To Google translate, "Greek" means "Modern Greek", but the Pythagoreans would have used Ancient Greek, in which περιφέρεια did mean "circumference". (The form περιφέρειας is the genitive: "of the circumference".) However, to include material in Wikipedia, we need be able to cite it to a reliable source, something that is lacking here. --Lambiam 21:17, 28 June 2012 (UTC)

What did people call Pi throughout history?

The article states in the first/intro section that "It has been represented by the Greek letter "π" since the mid-18th century." Okay, if that is true, and implies it might not have been used before that, then: What did people call Pi throughout history? Was it called that but they simply spelled it out rather than using the single letter for it? For those interested in studying this throughout history, the answer to this would seem pretty important. What it was called or referred to in various cultures seems important to the research and study of this topic, so that people can actually find the topic in old or ancient texts. Wondering if the depth of this question might warrant a separate article. In any case, I myself would like to know here what it was called! References? Thanks! Misty MH (talk) 05:34, 25 June 2012 (UTC)

Yes, if you find that someone had a name for it before then, that would be interesting. Dicklyon (talk) 06:09, 25 June 2012 (UTC)

In Japanese, for example (I guess Chinese the same), "pi" is "called" enshuuritsu (円周率) which is literally circle-circumference-ratio. Because of the particular feature of Chinese word-construction it's possible to get a description into a single word. The curious thing is that in English in particular we simply have no normal word for it.

Imaginatorium (talk) 12:49, 25 June 2012 (UTC)

@Misty: My recollection from reading the sources was there there was (at least in the Western world) no uniform term. Every mathematician used their own personal notation for pi, and for many other constants and operations. And, some did not use circum/diameter ratio at all. --Noleander (talk) 14:07, 25 June 2012 (UTC)

Thanks all. It would be cool to see what the ancients did use! Misty MH (talk) 04:48, 28 June 2012 (UTC)

Bible material?

Misty: Could you provide some quotes from the secondary sources that support the Bible material you want to include? Then we can look at the material and see what would be the best way to represent it in the article. Thanks. --Noleander (talk) 14:04, 25 June 2012 (UTC)

The article itself referred to the Bible already. When I tried to add a verse below for context, you deleted my edit! Reverting it makes it look like those Bible passages say the value of Pi is three, when it clearly does not. I explained this not only in my reasons for the changes (twice) but on your Talk page. Are you trying to DELIBERATELY misrepresent the Bible? because there is no justification for reverting a clear correction of fact. This isn't a POV or Personal Research issue. It's a misrepresentation issue. And such a correction doesn't require secondary sources or citations. Please change it back, and if you like, reword it to fit your idea of encyclopedic style (mentioned in your reversion); I don't care how it's worded stylistically, as long as it's accurate and not misleading. Thanks. Misty MH (talk) 22:59, 25 June 2012 (UTC)

Note also that secondary sources were mentioned already in a note (which I mentioned on your Talk page before your second reversion), where the note says "Suggestions that the pool had a hexagonal shape or an outward curving rim have been offered to explain the disparity. See Borwein, Jonathan M.; Bailey, David H. (2008), Mathematics by Experiment: Plausible Reasoning in the 21st century (revised 2nd ed.), A. K. Peters, ISBN 978-1-56881-442-1, pp. 103, 136, 137." (This note was there before I recently edited the article.) However, the wording in the article itself needed correcting, which I did, and which you undid, twice, and without discussion. Misty MH (talk) 23:06, 25 June 2012 (UTC) Edit Misty MH (talk) 23:12, 25 June 2012 (UTC) Edit Misty MH (talk) 23:13, 25 June 2012 (UTC) Edit: Typo correction only. Misty MH (talk) 00:59, 26 June 2012 (UTC)

The issue is that the cited source (which is "Pi-Unleashed" by Arndt and Haenel) supports the article as presently worded. The same cited source mentions various attempts to portray the value offered in the Bible in a more favorable light, including the hypothesis that the pool was hexagonal (which dates to the 19th century), but it clearly doesn't attach much significance to these attempts. Sławomir Biały (talk) 23:21, 25 June 2012 (UTC)

Agreed; it does say that, for I checked a ©2000 version of the book Pi-Unleashed, by Jörg Arndt and Christoph Haenel, in the chapter called Antiquity (between 13.4 and 13.6). It is clear that the author (and possibly other people mentioned) did not bother to check the Bible itself. For just a few verses later, 1 Kings 7:26 says that it was "a handbreadth thick; and its brim was shaped like the brim of a cup, like a lily blossom" (NKJV, also in 2 Chronicles 4:5). However, no mention of this is made in the passage by the author. This makes the Pi article clearly in error about what the Bible actually says. If someone wants to fix it in a way that's acceptable, please do. I comment more below. Misty MH (talk) 01:53, 26 June 2012 (UTC)

MistyMH: I have no objection to including more material about pi in the Bible, but it is best if the the material comes from some secondary source about pi. If you have a source that discusses pi in the Bible, go ahead and post some quotes from that source here in the Talk page, and we can go from there. We could maybe add another sentence, but not too much or it starts to get a bit out of proportion (that is, pi in the Bible is just not that important, so the article cannot devote too much space to it, per WP:UNDUE). --Noleander (talk) 01:07, 26 June 2012 (UTC)

Agreed, though I have no interest in adding more material from the Bible, only correcting what it currently says about the Bible. Do I REALLY need a source to justify an obvious correction?? See my comment just above. Misty MH (talk) 01:53, 26 June 2012 (UTC)

Yeah, sources are needed because this is a matter of interpretation of an ancient text. Therefore, editors are really not permitted to select verses to illustrate a point: the secondary sources have to select the verses. Look at it this way: if that "lily blossom" verse is important in relation to pi, there will be a source about pi that quotes it in that regard. If you cannot find such a source, then it is probably best to leave the article alone. --Noleander (talk) 02:03, 26 June 2012 (UTC)

I've moved the external links to the reference, as they should not be in the article body. And are there any better links for them? Looking at e.g. the Kings one it redirects to [1] which has three lines of text with headings, surrounded by twelve adverts/commercial links. Surely there is a Bible source which isn't so ad-laden; these would be removed if they were just external links, not refs, because of the advertising.--JohnBlackburne^words_deeds 23:18, 25 June 2012 (UTC)

Interesting idea, though now maybe almost no one will bother to check the accuracy of the statement in the article, which is simply and plainly wrong. See 1 Kings 7:26 and 2 Chronicles 4:5. (IGNORE what follows there, which is another topic anyway, as a literal rendering of the Hebrew may indicate "thousands" rather than "two thousand".) Misty MH (talk) 01:53, 26 June 2012 (UTC)

Someone edited it. Thanks. Misty MH (talk) 20:28, 27 June 2012 (UTC)

Important: The passages in 1 Kings 7 and 2 Chronicles 4 do not indicate Pi, because the diameter measurement isn't stated anywhere. This also means that Pi cannot be derived from the passages. Crucial passages 1 Kings 7:26 and 2 Chronicles 4:5 are not directly referred to in the notes or article, I think. These contextual-verses indicate that the shape of the rim was like a cup's brim, curved outward; while vss. 23 and 2 (respectively) say the stated distance was from brim to brim (wider than the diameter) NOT from side to side (the actual diameter). Therefore, the passages in 1 Kings 7 and 2 Chronicles 4 do NOT indicate Pi because the diameter measurement isn't stated. And therefore the article, as worded, is wrong on this point. Misty MH (talk) 20:28, 27 June 2012 (UTC)

I have to ask this, but what relevance does an ancient collection of bronze-age fairy stories have to an article about a mathematical concept? Might as well discuss J.R.R.Tolkien's ents in the entry on trees. --Matt Westwood 13:06, 5 July 2012 (UTC)

I would not quite put it the same way, but I also feel that the discussion of the Bible is a bit out of place. Nowhere does it actually discuss the value of Pi as it was known at the time. The only conclusions drawn from it are by pure exegesis. It seems much more likely that the priests of Solomon's temple had made much more accurate measurements than those now reported in the Bible. I would suggest either that some more authoritative source be found, or than the discussion of the Bible be removed. Sławomir Biały (talk) 15:05, 5 July 2012 (UTC)

Several authoritative secondary sources on pi discuss the bible's text in relation to pi. They all use it as an example of how the ratio of circumference-to-diameter was perceived in ancient times. Since secondary sources devoted to pi discuss it in relation to pi, it is appropriate for the article. Now, if the secondary sources did not discuss it, of course it would be WP:OR or WP:SYNTH for an editor to include the material. --Noleander (talk) 15:25, 5 July 2012 (UTC)

I really don't think I would consider any of the sources presented to be authorities on the history of mathematics, nor (as far as I can tell) do they provide references to such sources. Sławomir Biały (talk) 15:38, 5 July 2012 (UTC)

Hmm. They seem like pretty good sources to me. What makes you think they are not reliable for the history of pi? --Noleander (talk)

Usually one expects scholastic sources for the history of mathematics, not pop science sources. There are textbooks and journals on the subject. Arndt & Haenel seem to lack any credible literature review on the subject of pi in ancient Judaism. At a minimum, one would expect this. Instead, they refer disparagingly to all other literature on the subject, and the only item they bother to reference is just so they can make it a target of their ridicule. This is not what one expects from a serious, scholarly work. Sławomir Biały (talk) 17:04, 5 July 2012 (UTC)

Just about every source on the history of pi (including Beckman, Schepler, Posamentier, and Arndt) mention the Bible's circumference/diameter material. Of course those sources are more than sufficient, so I must be missing your point. --Noleander (talk) 18:14, 5 July 2012 (UTC)

I'm much more satisfied with the Schepler source. Schepler says that it is likely that the Hebrews had adopted the value of 3 from the Semites. Furthermore, the value of three is stated very unambiguously in the Talmud. Sławomir Biały (talk) 19:41, 5 July 2012 (UTC)

The point is that religion of any kind has no relevance to modern society, as nobody with a modicum of intelligence can possibly take it seriously. It's interesting from a sociological perspective, and vital to get an overview in a study of history, but in the context of mathematics and science has absolutely no place at all. --Matt Westwood 19:32, 5 July 2012 (UTC)

Tut tut, verifiability not truth ;-) The bit about the Bible wouldn't have much weight but I think a little extra about it probably is justified. Pi is a mathematical constant but that does not justify excluding non-mathematical material about it. Dmcq (talk) 18:13, 6 July 2012 (UTC)

Matt Westwood's comments do not appear to be aimed at improving this article but rather at attacking ideas and people he disapproves of. Wikipedia is not a forum for him to engage in attacking other editors and their beliefs. Probably he is deliberately trolling. 212.118.224.148 (talk) 13:04, 7 July 2012 (UTC)

This seems to be an old chestnut and was written about back in the day. I have added the following, citing The Scientific & the Divine.

“

Rabbi Nehemiah explained the discrepancy as being due to the thickness of the vessel. His early work of geometry, Mishnat ha-Middot, was written around 150 AD and takes the value of

π

to be three and one seventh.

”

Andrew Davidson (talk) 09:04, 22 July 2012 (UTC)

Pi repeats?

Hagar Dronbecker, an amateur mathematician, has apparently discovered that Pi does repeat, at the hyper-thousandth level.

Before going further, I'll be the first to admit that not a single one of the sources I've found is what I would consider reliable. If I were to submit my doctoral thesis on the sources I've thus far found, I've no doubt that I'd be (quite literally) laughed off campus! But perhaps it might be prudent to add to the article that it's possible that Pi might indeed repeat?

Just a thought. And yes, it's 00:38hrs here, and my brain is indeed tired.

Happy Trails! --Dr. Entropy (talk) 04:38, 22 July 2012 (UTC)

Thanks for the suggestion, but the article needs to limit itself to mainstream conclusions. See WP:FRINGE. --Noleander (talk) 05:02, 22 July 2012 (UTC)

In case there's any doubt, the non-repeatability of pi is one of those things that mathematicians are certain about, see Proof that π is irrational, and per Irrational number it easily follows that pi does not repeat. Johnuniq (talk) 07:47, 22 July 2012 (UTC)

Hiya, Johnuniq! Thank you for the proof article; it brought back memories and made my brain hurt more. Thanks again. :) Happy Trails! --Dr. Entropy (talk) 22:40, 22 July 2012 (UTC)

π memorization records

The chart in the article doesn't seem to match the information in the text at all. Kaldari (talk) 08:10, 22 July 2012 (UTC)

Thanks for pointing that out. I've removed the chart, to be on the safe side. The chart doesnt have, for example, the 67K record. The data in the chart may actually be pretty accurate, but I don't see a source for the data points, so it is probably not worth the risk. --Noleander (talk) 15:09, 22 July 2012 (UTC)

Digits "appear to be random"?

Why not more positive and say that the digits are random? Isn't indexing the digits of pi a acceptable way of returning truly random numbers? Thanks. JMOprof (talk) 15:12, 22 July 2012 (UTC)

No proof has yet been found that the digits are random (or "normal"). The digits appear to be random/normal, but without a proof, the article cannot say the digits are random. --Noleander (talk) 15:17, 22 July 2012 (UTC)

The digits really aren't random- for example, the first digit after the decimal point is always "1". The word random isn't technically appropriate in this context, which is why it says the digits "appear to be random". The proper technical statement, as Noleander says, is that pi is a normal number, which is almost universally believed but hasn't been proved. Staecker (talk) 15:27, 22 July 2012 (UTC)

Thanks. I now get it. As written, it seems to wait for "a shoe to drop" as in "appear to be random, but are not, as shown by Noleander and Staecker in 2012..." ☺ May I suggest "appear to be random, but haven't been proved so"? Well deserved featured article. JMOprof (talk) 17:51, 22 July 2012 (UTC)

The wording in the article was the result of quite a bit of discussion. Much of it revolving around the fact that "random" should be avoided in this context, because it does not apply to sequences (such as the digits of pi) which have a deterministic algorithm for generation. Thus, the emphasis is on tests like the test for normality. --Noleander (talk) 18:12, 22 July 2012 (UTC)

Lesson for me. The wording differs between the Wikipedia home page and the article. I've no comments about the article. ☺ thanks. JMOprof (talk) 18:16, 22 July 2012 (UTC)

Pyramid material - need quotes from sources.

Dave Light: could you please post some quotes from sources here about the pyramid material you want to add to the article? The sources I've seen indicate that such material is fringe science, so it needs to be vetted carefully. We may have to start a discussion at WP:RS, but lets see the quotes from the sources first. Thanks. --Noleander (talk) 15:02, 22 July 2012 (UTC)

Well, I'm at the 3RR limit for reverting this Fringe info ... if any other editors want to help out, please pitch in. --Noleander (talk) 15:16, 22 July 2012 (UTC)

Removed it again and repaired the formatting. It's not just a dubious addition but disagrees with the sourced information that's already there. It really needs discussing here.--JohnBlackburne^words_deeds 16:01, 22 July 2012 (UTC)

Hi Noleander. I am not sure what your sources are or who you have been talking to, but the sources that are referenced on this matter, supporting the correct information, are Professors Flinders Petrie, Professor Verner, Professor I E S Edwards. There is a misconception in some circles that this issue is fringe. It is not fringe. The surveys and documents are quite clear on this matter. I have studied this subject in detail for 10 years, published a book and a paper, and spoken at several conferences on this matter. Professors Petrie, Verner and Edwards were the acknowledged authorities on this matter, and their conclusions are still supported today. The publications by Rossi was refuted in my own publication and Lego had already refuted her argument in 1991. I don't want to enter into an edit war, but it is a requirement that Wikipedia reflects the authoritative sources and facts. — Preceding unsigned comment added by Dave Light (talk • contribs) 16:17, 22 July 2012 (UTC)

Here are some quotes to support the facts:

1/Possibly the greatest authority on the pyramids of Egypt was Egyptologist Professor I.E.S Edwards, author of ‘The Pyramids of Egypt’ and of whom Dr Mark Lehner, author of ‘The Complete Pyramids’, referred to as ‘the great pyramid authority’, (Lehner 1997: 34). Edwards wrote: “The normal angle of incline was about 52° - a slope which, in the Pyramid of Meidum and in the Great Pyramid, would have resulted if the height had been made to correspond with the radius of a circle the circumference of which was equal to the perimeter of the Pyramid at ground level. The northern stone Pyramid at Dashur, with its gradient of 43°35’, provides the only striking exception to this rule” (Edwards 1979: 269).

2/Possibly the other greatest pyramid authority of the second half of the 20th century was Egyptologist Professor Miroslav Verner, author of ‘The Pyramids, their Archaeology and History”. He wrote: "…the ancient Egyptians' constructions are the best evidence of their mathematical capabilities. Let us take for instance, the Great Pyramid in Giza. If we imagine a circle whose radius is the height of the pyramid, then the circumference is identical with the base of the pyramid. This could be achieved only if the wall had the correct angle, and everything had to be calculated in advance. We can conclude that although the ancient Egyptians may have never precisely defined the value of pi, in practice they used it.” (Verner 2001: 70).

3/ To further support this, see also page 454 where Verner writes “Today, Egyptologists rightly ask whether Archimedes, to whom the discovery of Pi is attributed, might have become acquainted with that principle during his stay in Egypt.”

4/Egyptologist Dr Bojana Mojsov, in her recent book about the Egyptian funerary god "Osiris", wrote about pyramids and Old Kingdom architecture saying: (2005: 26): "The architects seem have been aware of the mathematical properties now represented by the letter "Pi". Possibly obtained from practical experience, this knowledge had a profound influence on their ability to design and build complex structures." (Mojsov 2005).

5/The greatest pyramid authority of the late 19th century and the first half of the 20th century was undoubtedly Flinders Petrie, and was author of ‘The Pyramids and Temples of Gizeh” and the survey of the Meidum pyramid. He was the first accurate surveyor of Giza and the excavator and surveyor of the Pyramid of Meidum, he concluded, after many years in the field in Egypt: "but these relations of areas and of circular ratio are so systematic that we should grant that they were in the builder’s design" (Petrie 1940: 30). Earlier in the chapter quoted above, he wrote more specifically, that: “We conclude therefore that the approximation of 7 to 22 as the ratio of diameter to circumference was recognised” (Petrie 1940: 27).

6/ W M Flinders Petrie - The Pyramids and Temples of Gizeh - 2nd edition 1885 republished in a new and revised edition, 1990. Summary of probable theories Page 94 – The’ King’s’ Chamber: "The king’s chamber walls are determined by the same π proportions which rules the exterior of the Pyramid; the circuit of the side of the chamber being equal to a circle described by its width as a radius; and further, the length of the side of the chamber is equal to diameter of its circuit."

7/ W M Flinders Petrie, Nature Journal 1925 wrote: “The bases of some of the other pyramids are also known from my surveys. That of king Snefru and Meydum immediately preceded the Great Pyramid, and was planned on a similar system of measures. Both have the proportions resulting from the height being the radius of a circle equal to the circuit of the base, the angles found being: By Pi theory: 51*51’14”.3 Khufu’s pyramid 51* 50’ 40” +/- 1’5” Sneferu’s pyramid 51* 52’ +/-2” ? The dimensions found are: Khufu’s, height 7, circuit 44, x 40 cubits. Sneferu’s, “ 7, “ 44, x 25 cubits. The modulus of design, being thus 40 or 25 cubits shows the deliberate intention to embody the proportions of 7 : 22.”

References: (not alphabetical)

Legon,, J.A.R. ' 1979 The Plan of the Giza Pyramids', Archaeological Reports of the Archaeology Society of Staten Island, Vol.10 No.1. New Yor.

Edwards, I. E. S.

 1979 The Pyramids of Egypt. Middlesex: Penguin.

Lehner, M.

 1997 The Complete Pyramids. London: Thames & Hudson Ltd

Petrie, W. M. F.

 1883 	The Pyramids and Temples of Gizeh. London: Field & Tuer.

Petrie, W.M.F 1892 Medum. London. Field and Tuer Petrie, W.M.F 1925 Surveys of the Great Pyramid, Nature Journal. Pp942-943 Verner, M.

 2003 The Pyramids: Their Archaeology and History. London: Atlantic Books.

Cole, J.H.

 1925. Determination of the Exact Size and Orientation of the Great Pyramid of Giza.
                  Cairo: Government Press. Survey of Egypt paper no. 39.

Clarke, S. and R. Engelbach 1991 Ancient Egyptian Construction and Architecture Dover Publications.

Edwards, I. E. S. 1979 The Pyramids of Egypt. Middlesex: Penguin.

Lehner, M. 1997 The Complete Pyramids. London: Thames & Hudson Ltd

Mojsov, B. 2005 Osiris. London: Blackwell Publishing.

Petrie, W. M. F. 1940 Wisdom of the Egyptians. London: British School of Archaeology in Egypt and B. Quaritch Ltd.

Verner, M. 2003 The Pyramids: Their Archaeology and History. London: Atlantic Books. — Preceding unsigned comment added by Dave Light (talk • contribs)

These citations are all from Egyptologists, and not mathematicians. The quote given by Verner gives this away when he uses the word "identical" whereas in reality it is only approximate.

As such I believe the existing paragraph on the pyramids is probably adequate, but no more weight should be given it than currently, as Egyptology has even less relevance to mathematics than numerology does. --Matt Westwood 16:27, 22 July 2012 (UTC)

Dave Light: this section in question is discussing the history of the concept, not the mathematics. This is historical fact. In fact the correspondence is extremely close. The question here is not Verner's use of the english language, it is the Egyptian's abilities, which are well attested. Flinders Petrie was an expert surveyor. He was well trained in mathematical principles.

Okay, so we see that there are several pyramid experts that assert that the size may have been motivated by the number pi. The problem is that (1) there is no evidence that the egyptians knew about pi; and (2) people that study pyramids tend to be very enthusiastic about finding meaning where there is none. Numerology is filled with examples that look persuasive, but are just conincidental. But, in the spirit of compromise, how about this change:

The Great Pyramid at Giza, constructed circa 2589–2566 BC, was built with a perimeter of approximately 1760 cubits and a height of 280 cubits; the ratio 1760/280 ≈ 6.2857 is about equal to 2π ≈ 6.2832. Some ~~pyramidologists~~ Egyptologists conclude that the pyramid builders had knowledge of π and deliberately designed the pyramid to incorporate the proportions of a circle. ~~Most~~ Other historians dispute that ancient Egyptians had a concept of π and state that the correspondence is merely coincidental.

I still maintain that the pi assertion is fringe, but unless the sources are shown to be not reliable, I have no objection to changing the wording. --Noleander (talk) 17:49, 22 July 2012 (UTC)

He's been blocked for 24 hours, so he won't be replying here today. Dougweller (talk) 18:24, 22 July 2012 (UTC)

Comment: The proposed change in wording seems reasonable to me. "Most historians" is in fact an unreferenced assertion because no specific data on the proportion of Egyptologists who agree with the position is provided in the accompanying references in the article. Clearly though "other historians" is entirely justifiable in light of the existing references. --Mike Agricola (talk) 00:34, 23 July 2012 (UTC)

The current wording "Most historians dispute that ancient Egyptians had a concept of π ..." is absurd as it is immediately contradicted by the following paragraph, "The earliest written approximations of π are found in Egypt ...". The book The Shape of the Great Pyramid seems to be a good source for this issue as it provides a comprehensive review of the literature and various theories. It provides a good account of the pi-theory in chapter 9 and says "...of all the theories concerning the shape of the Great Pyramid, it is the pi-theory which is the best known." I shall try a different wording to this effect. Andrew Davidson (talk) 11:42, 23 July 2012 (UTC)

Andrew: The book you cite explicitly rejects the theory that pi was used in the pyramid design (pp 165-166). --Noleander (talk) 13:38, 23 July 2012 (UTC)

Andrew: Could you please revert your change, since you are using the source to represent a statement which implies to the reader the opposite of what the source is stating? Thanks. --Noleander (talk) 13:48, 23 July 2012 (UTC)

I was looking at that on Google books earlier today - I also found this:[2]" Herz-Fischler describes fifteen such proposals for the design plan of the Great Pyramid, all of which highlight correlations in dimensional details that Egyptologists regard as unimportant. This shows an important aspect of archaeology and science, that the selection of data is influenced by the theories that one already believes. And sometimes this can degrade the objectivity of the process, if selecting evidence is self-serving. But in this case, Herz-Fischler uses an independent means of evaluating the relevance of these data. He provides a statistical analysis of the proposed correlations and shows that none of the fifteen stands out as being more significant than any of the others (ibid.: 29)." (from Archaeological Fantasies: How Pseudoarchaeology Misrepresents the Past and Misleads the Public ). Dougweller (talk) 13:35, 23 July 2012 (UTC)

I added this sentence: Skeptics maintain that the suggested relationship to $π$ is merely a coincidence, because the pyramid is missing its outer layer of stones, and thus the shape cannot be accurately analyzed - citing a book by Michael Shermer. --Noleander (talk) 13:48, 23 July 2012 (UTC)

Euler buckling formula error?

The quoted formula defines the variable "L", but uses the variable "s".

I believe that the variable "s" should be replaced with "k L", where L is defined as in the current text and k is a variable determined by the nature of the end connections of the column... At least that's what I gather from the Wikipedia "Buckling" entry... NitPicker769 (talk) 02:25, 23 July 2012 (UTC)

Thanks for finding that. It has been fixed. --Noleander (talk) 15:18, 23 July 2012 (UTC)

Pi

Have just read all the way through the article, and now my head hurts. I am going for a lie down! WillE (talk) 11:30, 25 July 2012 (UTC)

Dr who reference

In 'midnight', the Dr does not recite pi to 30 places, rather its square root http://www.youtube.com/watch?v=QWboRfYGhpI — Preceding unsigned comment added by 101.165.24.192 (talk) 16:48, 15 August 2012 (UTC)

Inconsistency.

Why should there not be a section on the inconsistency of defining pi by the ratio of the circumference by the diameter? I mean a circle is defined by the radius, the radians are defined by the radius, a sphere is defined by its radius, .... Why is pi the only mathematically defined notion related to a circle not defined by the radius? Yes, I know that the diameter is two times the radius. But that does not explain the question. So, there needs to be a section which explains why pi is only half 6.283185307179.... No where in this article mentions this, why? — Preceding unsigned comment added by Reddwarf2956 (talk • contribs) 06:18, 17 August 2012 (UTC)

Oh no let's not start this lame old argument again. --Matt Westwood 18:17, 17 August 2012 (UTC)

Oh great, a lame answer. Reddwarf2956 (talk) 04:48, 19 August 2012 (UTC)

Sorry, but it's a mega-lame question which has been done to death on the discusson on Tau. Let's all puke in synchrony. --Matt Westwood 05:22, 19 August 2012 (UTC)

If you are going to reply, please make it a mathematical reason why pi should not have a section dealing with the inconsistency of its definition. Reddwarf2956 (talk) 12:00, 19 August 2012 (UTC)

Wikipedia is only here to represent what the consensus "out there" is. Perhaps English would be better off with a more funetik speling sistm. But that does not mean we write all of articles that way. Currently the article's coverage of tau is commensurate (quite generous, even) with the attention it has received, wouldn't you say? Leonxlin (talk) 16:14, 19 August 2012 (UTC)

Repeat, if you are going to reply with an argument against the suggested section, please make it a mathematical reason why pi should not have a section dealing with the inconsistency of its definition. Until then, the request stands. Also note, that without this section, pi is in violation of WP:DUE in that there is no minority viewpoint in which "controversies regarding aspects of the minority view should be clearly identified and explained". Reddwarf2956 (talk) 19:38, 19 August 2012 (UTC)

In my opinion this article gives due weight to the "τ" constant already, inside the "in popular culture" section. Once we begin to see mainstream textbooks use τ instead of π the article will need to be changed, but at the moment the due weight for τ is very low, and certainly does not extend to an entire section. — Carl (CBM · talk) 21:02, 19 August 2012 (UTC)

We are easily giving more than WP:DUE weight to tau in this article. I have never seen a reliable scientific source use the constant τ for 2π. Sławomir Biały (talk) 23:49, 19 August 2012 (UTC)

We are still dealing with opinions here. I keep saying pi has a "inconsistency of its definition" I have not brought up tau, but it is a mathematical constant which has not been formally named. You call it tau, so I will too. I have seen that constant tau is used in programming as names like twopi, two_pi, TWOPI, TWO_PI, ... for example MATHEMATICA: 2Pi, FORTRAN: http://naif.jpl.nasa.gov/pub/naif/toolkit_docs/FORTRAN/spicelib/twopi.html . Or, as here a way numbering software versions: https://en.wikipedia.org/wiki/Pugs#Version_numbering . It is at the OEIS as A058291, and A019692. A simple search on Google will find many, many more examples of the constant tau by other names and used as 6.2831853.... And, tau is mathematically consistent. Yet here on Wikipedia, there is a pious bias against tau or anything that looks like tau in value. Every where I look for the constant there is no references back to tau, two pi, or even 6.2831853. They all redirect back to pi or do not exist. The above commentators reference tau and know what it is and what its value is, yet you expect me to talk about it as if it was numerology, sorry if any number here is consider numerology that is pi because as a Wikipedia topic it has the lack of consistency. And, this Wikipedia topic "pi" does not reference any of these references above or any of many other places that I did not state. In fact there is the act of hijacking 2pi and saying that it, pi, in a lot of places http://en.wikipedia.org/wiki/List_of_formulae_involving_%CF%80 . But, that does not change the problem pi has as stated here earlier, it is inconsistent in that it does not use radius for consistency sake. And, no one wants to agree that tau is not the issue here, it is the unnecessary bias against tau because it is mathematically a better constant to deal with things like pi. Just look at how both pi and tau is used in spherical coordinates. On the x and y axes the use of the maximum value is tau. The maximum angle from the positive z axis is pi. Yet here you insist on C/d and ignore the facts. Just do a search for the number of times an even and odd multiples of pi are used in the period of functions, or just in functions here http://en.wikipedia.org/wiki/List_of_formulae_involving_%CF%80 .

Now pi is not the first mathematically inconsistent thing. Just look at when 1 was called prime and 2 was called not prime. http://planetmath.org/HistoryOfPrimeNumbers.html

So, do you want to continue or do you want to fix this issue that tau, while not formal, is a mathematical constant more fundamental than pi. Put it in another way, when you see the "Equation of a Circle" stated with diameters in a text book, then I will except pi as mathematically consistent until then pi needs to explain itself in this encyclopedia as to why it is inconsistent. Yes, I know this means using tau as a more fundamental constant, as in tau radians make a circle. But, it helps, not hurts, the writing to be understood by the readers. And, to say that tau does not need its own space to express all of the uses of 6.2831853... is a lie.

Reddwarf2956 (talk) 02:28, 20 August 2012 (UTC)

You are spouting the most utter complete and utter blethering claptrap. Nothing you say has any coherence whatsover. --Matt Westwood 05:13, 20 August 2012 (UTC)

There is no need to argue any of these points. In the sense that the scientific world uses the constant π rather than some other constant, there is a bias in favor of π. This doesn't invalidate your opinion that 2π is a more natural choice. But that's irrelevant for an encyclopedia. We just reiterate what reliable sources have to say on a subject. Sławomir Biały (talk) 13:45, 20 August 2012 (UTC)

Irrational and Transcendence

There is a formula for Pi squared divided by 6 being the sum of the inverse squares of the integers. I just wanted to point out that Pi squared divided by 6 is also the surface area for a 4-sphere of diameter 1. 4-sphere being a 5d sphere... if I read the article right Hypersphere. The 4-sphere has a surface area of 8/3 * Pi^2 * R^4. So with R=1/2, we have 8/48 * pi^2 or 1/6 * pi^2. This probably has no real meaning as Pi is going to be involved in circular objects anyway. In fact the 4 formulas for surface and volume of the 3-sphere and 4-sphere would all work with a proper selection of the radius. But the 4-sphere surface area is the simplest. I just thought I would add this in case someone was looking for something tangible to relate to Pi squared. Maybe it has some further meaning that is beyond me, but Im sure someone else would have discovered this relationship and exploited its importance if that was true. I just thought it was interesting that the relationship between the primes and pi squared is also the value of a surface area of a basic object with a length value (diameter) of '1'. Also, vice-versa... a simple n-sphere diameter 1 has a surface area of the sum of the inverse squared integers. — Preceding unsigned comment added by 96.49.55.157 (talk) 01:51, 4 September 2012 (UTC)

π appears in many formula, not least all of the formulae for the sizes of the n-sphere and n-ball in two more dimensions. And as these formula are quite simple it's possible to relate them, to each other or other expressions involving π. But I don't think there's any deeper meaning to this.--JohnBlackburne^words_deeds 01:58, 4 September 2012 (UTC)

pi is too random in a sense — Preceding unsigned comment added by 58.8.105.29 (talk) 03:13, 9 September 2012 (UTC)

"Approximately equal to?"

The article states in the lede: "The constant, sometimes written pi, is approximately equal to 3.14159." That isn't entirely accurate wording. Depending on usage, pi can approximately equal 3.14 or even just 3. Could the sentence be reworded to better reflect this fact? Perhaps something like, "The constant, sometimes written pi, to five decimal places is 3.14159." I'm just really leery of saying pi equals something -- even "approximately," as pi can approximately equal 3 -- given that different uses call for different degrees of accuracy. JayHubie (talk) 02:17, 17 September 2012 (UTC)

Formally you are right: "approximately" has no meaning without defining the accuracy. Nevertheless, it is a common convention that the number of digits defines the accuracy: all the digits (possibly but the last one) are supposed to be exact. Thus I believe that everybody will understand correctly the sentence, namely that the given digits are correct (Note that if one digit less have been given, there would be an ambiguity for the last digit). Thus the sentence follows perfectly the instructions of MOS:MATH which asserts that the lead should contain "an informal introduction to the topic, without rigor, suitable for a general audience". IMO there is nothing to change in this sentence.D.Lazard (talk) 08:25, 17 September 2012 (UTC)

I respectfully disagree. People who've been through elementary math can understand the phrase "to five decimal places." My concern stands, since pi still can be said to be "approximately" equal to 3. The wording is inaccurate. JayHubie (talk) 19:23, 19 September 2012 (UTC)

I agree that the wording seems slightly inappropriate. Perhaps better to say something like: "The value of pi is approximately 3.1415926535..." (but no need to state the number of significant figures). I think your instinct is correct, because "approximately equal" sort of implies two values that just happen to be close, as in (music) "Twelve perfect fifths (1.5^12) is approximately equal to seven octaves (2^7)" (see Pythagorean comma) Imaginatorium (talk) 19:35, 19 September 2012 (UTC)

Phi

In the "about" template at the top of the article, i think you should add a link to the number Phi as well- many people confuse between them.
80.230.2.55 (talk) 17:45, 18 September 2012 (UTC)

Choice of glyph for the Greek letter pi in this article

The number $π$ /paɪ/ is a mathematical constant that is the ratio of a circle's circumference to its diameter. The constant, sometimes written pi, is approximately equal to 3.14159.

Common (not only mathematician, but there it is coined) notation/typografic is $\pi$ or π (a lower Greek letter). Sadly, very uncommon article typograhy is used here. — Preceding unsigned comment added by 2001:638:504:C00E:214:22FF:FE49:D786 (talk • contribs)

You are unhappy with how {{pi}} is rendered on the page? At present it gives

π

. Which of the alternatives you mentioned do you like better? EdJohnston (talk) 17:35, 19 September 2012 (UTC)

Yes, this bugged me too. The normal mathematical symbol for pi is a Greek lowercase letter pi (that's a bizarrely redundant statement actually). Somehow the symbol used here appears as a square shape, like an uppercase Roman numeral 'II' with a bar across the top. I guessed that this was some bizarre property of the font on my computer (or something) combined perhaps with a different Unicode value for "mathematical pi" as opposed to "Genuine Greek pi". If so I submit it is an error, either by font designers or the Unicode lot or both. But I don't know how to find out exactly what the WP *triple-quoted-pi* is supposed to mean.

I grabbed the first mathematical book to hand (Penguin Dictionary of Mathematics) and scanned the first three lines of the definition of 'pi': you can see it here - http://imaginatorium.org/private/pi.jpg You will see that the symbol is a Greek lowercase pi, and this I submit is what WP should show pi as, to conform with standard usage.

Imaginatorium (talk) 18:33, 19 September 2012 (UTC)

I ~~agree;~~ add that

π

looks awful on my setup (Firefox 15.0.1 running under Ubuntu 12.4). The whole project of trying to put serif math into sans-serif running text should just be scrapped, and we should go back to using π inline and

\pi

in displayed text. --Trovatore (talk) 18:45, 19 September 2012 (UTC)

I share the distaste of others with the symbol rendered by {{pi}} and agree with Trovatore that the conventional sans-serif lower-case Greek pi is a better choice for use in running text in this article. EdJohnston (talk) 19:14, 19 September 2012 (UTC)

That is exactly what it should look like; a serif Greek lowercase pi as shown on your scan. {{pi}} uses the HTML entity π; it's not unicode, and it's set in font-family: serif;. If that doesn't show correct on your system, there is a problem with your fonts setup; your default serif font in your browser may be set to something different then the default 'Times'. The reason serif is used is not for aestethic reasons; it is used because math formulae and symbols are illegible and indiscernable (think I vs. l vs. 1) in sans-serif. It is more important to be able to see what is actually represented on screen then care about aestethics. (btw: the triple quote is the wiki markup equivalent of <b>...</b>; it simply makes

π

bold: $π$ .) — Edokter (talk) — 20:50, 19 September 2012 (UTC)

"Times" is a proprietary font, I think. Wikipedia is part of the open-content movement, broadly construed, and should not be making decisions based on the way proprietary systems render things. --Trovatore (talk) 21:15, 19 September 2012 (UTC)

It doesn't. As I said, the template (and math) uses sans-serif, which on most systems (even open source ones!) maps to Times. — Edokter (talk) — 21:22, 19 September 2012 (UTC)

Edokter more or less hit this one on the head, but I think there are a few misconceptions here that need addressing. First and foremost, Wikipedia doesn't choose the glyph to be displayed. It can't. (Well, except when using images -- which is what the <math>\pi</math> tags do -- but that's undesirable in running text.) Your browser chooses the glyph (more precisely, it chooses the font which gives the glyph), based on what Wikipedia says it should do.

Secondly, contrary to what the anonymous user at the top of this section appears to be saying, there is no "mathematical symbol" pi. There is only the Greek letter, which is subject to different styles of writing. There are conventions for which style should be used, but that's analogous to the convention that we write e in italics for its mathematical meaning -- it's still a lowercase Latin letter E. (Unicode accordingly has just one codepoint for the pi character in both its alphabetic and mathematical meanings, so that can't be the source of Imaginatorium's problems.)

The preferred style for "mathematical" pi, with the horizontal stroke overhanging the (usually) curved legs, is the style used in serif typefaces, and (with individual variations, of course) in handwritten Greek. On the other hand, the "square" pi that Imaginatorium describes, which looks like three sides of a rectangle, is a perfectly standard sans-serif letter form, suitable for everyday Greek text, but not for mathematical expressions. I don't know why it's appearing for Imaginatorium, but Trovatore's statement that we should be using a sans-serif face instead is the opposite of solving the problem.

Here's where Edokter was wide of the mark; we don't use serif typefaces for mathematical typesetting because it makes characters like 1, I and l easier to distinguish (though that's often true and a worthy benefit). We use serif fonts because that's the style that's customary in maths. Specifically, it's very often customary to use italic characters, and there's another reason to avoid sans-serif typefaces; oblique type is not the same thing as italic type. Having a bit of visual dissonance between the typeface of the maths expression and that of the text around it is better than violating this convention and having a sans-serif "square" pi!

Which is why Wikipedia tells your browser it should use a serif typeface to write pi. Actually, the {{pi}} template doesn't try to directly manage the appearance of pi; it applies a style called "texhtml". I'm not fully certain of what magic this style applies (aside from requesting a serif typeface)... but I'm fairly sure it will make some suggestions to the browser to try and get a font suitable for mathematical typesetting (as hinted by the mention of "tex" in the style name). I'm pretty sure it's more than just asking for the default serif typeface (which, by the way, is more likely to be Times New Roman than Times per se; in many *nix systems it'll probably be something like DejaVu Serif unless the Microsoft web fonts have been installed). -- Perey (talk) 17:22, 8 October 2012 (UTC)

There’s no magic going on. If I didn’t miss anything, all texhtml does in the default skin is to set "font-family: serif" (common/shared.css), "white-space: nowrap" (MediaWiki:Common.css), and "font-size: 118%" (MediaWiki:Vector.css).—Emil J. 17:45, 8 October 2012 (UTC)

OK, first of all, I disagree with Perey and Edokter that "a little visual dissonance" is not so bad. I think it looks completely unprofessional. But that's a general consideration and maybe more important in the rendering of e (a separate gripe) than for this article.

So getting down to specifics, here's what I see:

Anticipating Edokter's response, this is on a bog-standard (at least, for these purposes) installation of Ubuntu 12.4, running Firefox. Ubuntu is probably the most popular free-software operating system, version 12.4 is the latest long-term stable version, and Firefox the most popular browser for it. There is nothing unusual in my setup; presumably, this is what most people running Ubuntu 12.4 see. --Trovatore (talk) 19:15, 8 October 2012 (UTC)

(I hope that not the bog-standard font size on your system...) If I'm not mistaken, that's DejaVu Sans. I can't tell what the default serif font on your system is, but I guess that would be DejaVu Serif. These fonts do have a funny way of displaying pi, using pillars in serif, yet having a decent sans-serif pi. I don't know how to handle this properly. All I can tell is that I try to cater to most systems on the planet, and I cannot please them all. What would help is reset your font-size for .texhtml to 100%, as DejaVu fonts have the same x-height, and/or possibly actually use Times or Computer Modern as you maths font. — Edokter (talk) — 20:19, 8 October 2012 (UTC)

What would help would be to stop using these misguided templates. --Trovatore (talk) 20:21, 8 October 2012 (UTC)

That would help for you, but it would also be detrimental to the majority of users/readers. I'm still looking for a way to have better font managment on Wikipedia, either in the form of an extension or gadget, so people don't have to mess with their local font setup on skin files. — Edokter (talk) — 20:31, 8 October 2012 (UTC)

What would help everyone is to get rid of the idea of mixing serif and sans-serif fonts inline. That was an unfortunate decision from the get-go and needs to be reversed. Without that, there is little rationale left for the templates. --Trovatore (talk) 20:56, 8 October 2012 (UTC)

Please don't asume that what's good for you is good for everyone; too many people make that mistake. I go what is good for most. The situation is not ideal, but it is better then having math displayed in a sans-serif font that strips it of all meaning and context. Readability outweighs any aesthetical motivations. — Edokter (talk) — 21:40, 8 October 2012 (UTC)

It seems to me that you're the one who's assuming you know what is good for most. I dispute the accuracy of your claim; I do not think it is in fact good for most, though even if it were, you have not established that that is the correct criterion to use. --Trovatore (talk) 22:30, 8 October 2012 (UTC)

Edokter is right -- you are seeing DejaVu Sans and DejaVu Serif, Trovatore. And it does look bad for the serif. The serif pi lacks the slightly "cursive" look customary in mathematical rendering (and it doesn't have a true italic, just an oblique). But have a look at this selection of free fonts (and Times New Roman), all available for Ubuntu (I can no longer remember how many of these were pre-installed and how many I added).

Asana Math	Computer Modern	DejaVu Sans	DejaVu Serif	Liberation Sans	Liberation Serif	STIXGeneral	Times New Roman	Nimbus Roman No9 L	Ubuntu
π	π	π	π	π	π	π	π	π	π
π	π	π	π	π	π	π	π	π	π

If you have all, or even some of these fonts installed, you should be able to see what I mean. The DejaVu Serif pi is uniquely unsuitable for mathematical use. Yes, the DejaVu Sans pi is better, but that's because almost anything is better than DejaVu Serif. ;-) It's emphatically not a reason to go and switch to sans-serif typefaces for pi. Most of the sans-serif pi glyphs look acceptable for mathematical use, but not good, compared with serif fonts (even those not made with mathematical typesetting in mind), and some sans-serif typefaces are definitely not suitable (like Ubuntu) -- they have the simple three-sided rectangular pi. -- Perey (talk) 14:00, 9 October 2012 (UTC)

(Reply to Trovatore) I do not asume to know what's best; my findings are based on extensive research in web typography (and it's shortcomings). I gather statistical data from here, here, here and here among other places, combine these with other data like this and make an analysis that would suit most users. Not so long ago, .texhtml was hardcoded to use Times New Roman; it may be a good idea to go back to that, as it now turns out that DejaVu Serif sucks as a default serif font. But it will always be impossible to make it perfect for all users. — Edokter (talk) — 16:30, 9 October 2012 (UTC)

Who bloody asked you? You do have an impressive array of facts about typography at your fingertips, and I acknowledge your expertise in that sense. But what is "best" for "most users" is a value judgment, and I do not agree with yours. --Trovatore (talk) 17:52, 16 October 2012 (UTC)

No-one "bloody" asked me, and I resent that tone. This is Wikipedia, remember? I'm sorry if my aproach does not meet your preference, but it does enjoy the approval of most editors here. It has been discussed before and there is consensus for using serif for pi and formulae in general. — Edokter (talk) — 18:10, 16 October 2012 (UTC)

It's a response to your ownership attitude, which I resent. --Trovatore (talk) 19:04, 16 October 2012 (UTC)

You're welcome to start an RFC then. I certainly do not see an ownership issue here; this is simply a matter of someone's preference clashing with consensus, one I happen to defend. You just continue to complain about how you don't like how it looks, without providing any rational arguments. So at this point I have nothing more to say to you. — Edokter (talk) — 21:11, 16 October 2012 (UTC)

If I may interject... Trovatore, perhaps what you're seeing as Edokter's "ownership attitude" of this issue stems from the fact that Edokter is an administrator and is involved with maintaining Wikipedia's CSS styles. In that sense, he/she does "own" this issue; if there's a problem with how pi appears, Edokter is in a position to fix it, and has the right to use his/her judgement to decide on a solution. You, in turn, have the right to dispute Edokter's decision. Edokter mentioned RFC as an option, to which I'll add that Dispute Resolution lists a number of alternatives. -- Perey (talk) 17:10, 20 October 2012 (UTC)

Perey, I think you misunderstand the role of administrator on Wikipedia. A WP admin has no special authority whatsoever. He has extra tools; that's it. His admin status counts for precisely nothing in disputes. --Trovatore (talk) 19:55, 20 October 2012 (UTC)

I don't think I do. I may disagree somewhat with the idea that admin status counts for nothing -- as they say, with great power comes great responsibility, or in this case, with a little bit of CSS-related power comes a little bit of CSS-related responsibility. ;-) But that's not actually the point. I'm not saying that being an admin makes Edokter right; I'm saying that being an admin justifies any "ownership" of the problem by Edokter. What I described as "the right to use his/her judgement" is not because of any special admin authority -- it's just "Be bold" applied to an admin's tools: "If you can do it, and you think it's right, go ahead and do it." -- Perey (talk) 09:44, 25 October 2012 (UTC)

I don't know what you're talking about. There is nothing here to which the tools are even relevant; neither {{pi}} nor {{math}} is protected. And I reiterate that admin status counts for nothing, zero times zero times zero, in disputes. --Trovatore (talk) 09:47, 25 October 2012 (UTC)

As regards to adminship, Trovatore is absolutely right. Adminship confers no special rights or authority in this context. Paul August ☎ 21:12, 29 October 2012 (UTC)

Both of those templates rely on the texhtml CSS style class, though, which (unless I've been looking at this completely wrong all along) is only editable by admins. -- Perey (talk) 06:52, 29 October 2012 (UTC)

Even if that's so, nothing says the templates need to use that CSS style class, nor that we need to use the templates. --Trovatore (talk) 20:43, 29 October 2012 (UTC)

FWIW, in the table you show above, the only glyphs in IE 7 running on Windows XP that are rendered with serifs or "cursive style" are Times New Roman (all of the rest are sans serif style), and those are the only ones that look "proper" as a mathematical font symbol. (I'm using IE 7 at work, so I assume that the OS fonts are those we got straight out of the box.) — Loadmaster (talk) 16:50, 9 October 2012 (UTC)

That;s normal for IE; it falls back to the parent font if the specified font is not available. Chrome will fall back to it's default webpage font, which is serif. — Edokter (talk) — 17:30, 9 October 2012 (UTC)

I've restored the Times fontstack for .texhtml ("Times New Roman", Times, FreeSerif, serif;), which now includes FreeSerif for Linux. But, I'd rather use Nimbus Roman No9 because it has near 100% installed base on Linux. However, I'm not sure how to exactly reference that font in CSS; there are are multiple versions around. I even have two version installed that like to be called "NimbusRomanNo9" and "NimbusRomNo9L" (they are TrueType versions though). This page lists it as "Nimbus Roman No9 L"; in other words, what is the proper font-family name for this font? — Edokter (talk) — 21:05, 12 October 2012 (UTC)

Never mind. It should be "Nimbus Roman No9 L". — Edokter (talk) — 21:28, 12 October 2012 (UTC)

spelling of Madhava of Sangamagrama

If you'd indicated at the start that spelling without the diacritics is according to the manual of style, and not a "typo", I would not have wasted my time "correcting" it back to "Mādhava of Saṅgamagrāma". Calling the latter a "spelling mistake" is misleading and can be considered inflammatory. --Matt Westwood 22:17, 24 September 2012 (UTC)

Edit request on 3 November 2012

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(There is a bottom)I wish to change the way you think of Pi. As you say in the article, Pi is the number 3.14159, but really its(I typed this):

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When you said "π is an irrational number, which means that it cannot be expressed exactly as a ratio of two integers (such as 22/7 or other fractions that are commonly used to approximate π); consequently, its decimal representation never ends and never repeats."-Pi Article. You didn't really explain it as much as an infinite nubmer. You really should have put something like that. I would like it if you used that in the place of 3.14159 when you began. Thanks. TheGeneralOfFisher 1234567890 (talk) 20:02, 3 November 2012 (UTC)

Pi is not an "infinite number", but it is irrational. This means that writing 3.14159265... (for example) is just as appropriate as your (frankly silly) suggestion. The edit should not be made; and I think your comment should be severely truncated (but I'm not sure if there are "principles" about editing other people's comments). Note that the external links include a reference to the first billion digits of pi. Imaginatorium (talk) 20:17, 3 November 2012 (UTC)

Not done: The top of the article says that PI is approximately 3.14159 and that it goes on forever. There is no need to put a larger approximation into the article. RudolfRed (talk) 20:18, 3 November 2012 (UTC)

Tau is the rival irrational number to Pi. This tells us that Pi is wrong. ElliottBelardo (talk) —Preceding undated comment added 01:59, 19 November 2012 (UTC)