# Talk:Liu Hui's π algorithm

## Limits

Archimedes made arguments that hold with a formal modern definition. Liu Hui may have understood the *property* of convergence, but Archimedes actually made limit arguments and *solved* convergences. Those are two very different things. — Preceding unsigned comment added by 2620:0:1009:3:A057:29E1:13B5:BBE4 (talk) 21:27, 23 February 2016 (UTC)

## References?

I would be great if someone would add references to all of the information found. It seems odd that both Archimedes (Measurement of a Circle) and Liu Hui both used a 96-gon to find the area of a circle. Was it really his own calculation? --pbroks13talk? 17:01, 7 July 2008 (UTC)

Cancel that, I didn't read the whole way through; however, this article still needs more references and in-line citations. --pbroks13talk? 17:05, 7 July 2008 (UTC)

## Original research

That impressive figure from a ${\displaystyle (6\times 2^{1000})}$-gon and alike and that "check with spreadsheet" stuff are certainly original research. Will figure out how to fix them. —Kxx (talk) 04:30, 22 March 2009 (UTC)

• 1) Liu Hui never wrote a word in English, therefore this article certainly belongs to "original research" category.

2) In his writing about pi calculation, Liu Hui did not draw any diagrams, all the colorful diagrams included heare are my "origina research".

3) Ha, Liu Hui did not expressed his algorithm in modern algebraic form, all those algebra formulars are my "orginal research" --Gisling (talk) 14:14, 23 March 2009 (UTC)

## Calculation

For the 3072-gon I've got numerical value of approximation directly as:

${\displaystyle \pi \approx 3.1415904632280500957384585059309517235542823086757970500\ldots ,}$

but article says differently:

${\displaystyle \pi \approx 3.141590463236763.}$

What is correct, or should I ask in this way - how computation was done? xJaM (talk) 22:13, 15 February 2011 (UTC)

Interesting. A quick check with Windows calculator agrees with your value (to about 28 decimal places, anyway). Maybe the value given in the article is incorrect. Gandalf61 (talk) 13:11, 16 February 2011 (UTC)

It's probably machine error: https://en.wikipedia.org/wiki/Floating_point#Common_Values_of_Rounding_Error — Preceding unsigned comment added by 2620:0:1009:3:A057:29E1:13B5:BBE4 (talk) 21:24, 23 February 2016 (UTC)

## Explanation of move from "π" to "pi"

It is unconventional to use a math symbol in a title even when that symbol is common usage. It's Three Blind Mice, not "3 Blind Mice", a Dirac delta function, not a δ function, and so forth. In this case, "pi" is a far more common usage than "π". On Google books, pi algorithm -wikipedia gets vastly more hits than π algorithm -wikipedia. CNN uses "pi", the BBC uses "pi", and the New York Times uses "pi". Math journals can go either way. Check here and here for journal articles with "pi" in their titles. Kauffner (talk) 02:31, 19 April 2011 (UTC)

## Requested move

The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the move request was: Pages moved. CRGreathouse carried out the requested moves on April 27 & 28. Despite having been premature, the discussion below supports the action. -- Hadal (talk) 06:16, 1 June 2011 (UTC)

Liu Hui's pi algorithmLiu Hui's π algorithm – These moves were part of an undiscussed program to remove the symbol π from the titles of articles involving the mathematical constant. Based on a discussion here, consensus is clearly against these moves. So I would like to request that the original titles be restored. Sławomir Biały (talk) 07:12, 27 April 2011 (UTC)

• Comment. Simply saying that mixed script is not allowed isn't an argument. The reason that there is a ban on mixed script is because of move vandalism, not legitimate uses like this one. That said, I would agree that mixed script should probably be avoided for stylistic reasons in many cases. For instance, if one part of a title were written in Arabic and the other in Latin characters, such a juxtaposition would just look strange. But in this case, we're talking about the easily-recognizable mathematical symbol π. If anything, spelling it out looks stranger than using the standard symbol. Regarding your second point, the only part of the MoS section you linked to that seems to be relevant here is the part that suggests having redirects in place if a symbol appears in an article title that is not commonly found on keyboards. Well, a move will leave a redirect in place. The only other point that could conceivably be relevant is the worry that a browser will render an ordinary Greek letter as a square box. I don't think this would ever happen. Sławomir Biały (talk) 14:02, 1 May 2011 (UTC)
• Comment. Many of the Google books hits for "pi" are for a proper name, and sometimes the Greek letter π is written as [pi], with square brackets. Also, many of those hits are not about the mathematical constant, but are publications of fraternities, etc., so not really relevant to this discussion. It's hard to say what the relative proportion of relevant uses is in each case, so we shouldn't place much stock in such search results. More on the issues with using naive Google searches in this way can be found in the WPM thread. In regards to your second search, the reason "Pi algorithm" gets more hits than "π algorithm" is because the power inversion algorithm is an actual algorithm (usually abbreviated "PI algorithm"), unrelated to the mathematical constant π, whereas there is no single "π algorithm". Finally, it's unclear what bearing if anyGreek letters used in mathematics, science, and engineering has on this discussion. That includes the name and symbol of each Greek letter. Sławomir Biały (talk) 14:13, 1 May 2011 (UTC)
Greek letters used in mathematics, science, and engineering has a long list of article titles with spelled-out Greek letters, but very few titles with actual Greek script. You can compare the results for "pi" and "π" on Google Books with your own qualifiers. (I've tried "approximations" and "irrational".) Spelled-out pi is typically ahead of the pi symbol by at least 10X. Kauffner (talk) 12:53, 2 May 2011 (UTC)
• Support. Argumentum ad Googlum? With a non-ASCII symbol? Xanthoxyl < 08:33, 1 May 2011 (UTC)
• Support. The title with the symbol is clearly preferable - using "pi" looks odd. Chaosdruid may be right that some rule says such-and-such, but that's why we have WP:IAR - so that rules don't force us to do silly things. And I can't believe Kauffner is seriously using Google hits for a symbol. --Zundark (talk) 09:49, 1 May 2011 (UTC)
• Prefer the current title, I do not find the argument to change compelling. The use of the symbol π is just as reasonable as the use of latin letters with diacritics, and is probably more recognizable than some of the more rare diacritics such as Ł, which we also allow in article titles. — Carl (CBM · talk) 11:50, 1 May 2011 (UTC)
Diacritics don't usually obscure the underlying Latin character, yet they are highly controversial all the same. Kauffner (talk) 12:53, 2 May 2011 (UTC)
We have been using diacritics for years, in both article bodies and titles, and there seems to be little chance of that changing. Saying diacritics are "controversial" overstates the issue. — Carl (CBM · talk) 13:03, 2 May 2011 (UTC)
Some have argued to avoid using diacritics when there is an alternative supported in standard English (e.g., Moebius for Möbius). As a general rule, I support the use of diacritic marks in titles: "Moebius" seems like a philistine spelling to me. Added: WP:DIACRITICS basically says that the use of diacritics depends on what is used in most English-language sources, so we prefer Möbius to Moebius, but Weierstrass to Weierstraß. The key point, however, is that there is nothing wrong with diacritic marks per se. It's just an issue of WP:COMMONNAME. Sławomir Biały (talk) 13:29, 2 May 2011 (UTC)
If the standard is which version gets the most ghits, you would never use diacritics (or π for that matter). Sadly, the even more philistine "Mobius strip" gets far more hits than "Möbius strip" and "Moebius strip" combined.[1] Kauffner (talk) 15:41, 2 May 2011 (UTC)
Well, I think it's safe to say that google ngrams is not a reliable indicator of what we should do. We should look at reliable, scholarly sources, rather than quantitative statistics from Google, that mindlessly indexes every random bit of junk in the cosmos. Sławomir Biały (talk) 17:36, 2 May 2011 (UTC)
• Support. "Pi" is an approximation of the proper symbol to denote the number we're discussing. We should use π when that doesn't lead to confusion or ambiguity. Ozob (talk) 12:45, 1 May 2011 (UTC)
• Support per extensive discussion at WikiProject Mathematics. CRGreathouse (t | c) 16:11, 1 May 2011 (UTC)
You moved the articles after the vote opened and now you vote on the move that you already made. I'm sure what you are doing is regular and proper. I just want to clarify things so that everyone can follow this unusually complex vote. Kauffner (talk) 17:05, 1 May 2011 (UTC)
I wasn't aware of this discussion. In the future, if you'd like to have me participate on a !vote, feel free to leave a message on my User Talk page.
CRGreathouse (t | c) 17:33, 1 May 2011 (UTC)
• Support the π version of the title per discussions above and at WT:WPMATH. Ben (talk) 02:49, 2 May 2011 (UTC)

### Discussion

Huh....So what happened to the seven-day voting period? Is only User:CRGreathouse allowed to vote? Or perhaps we can still vote and the articles can be moved again at the end the voting period? Kauffner (talk) 09:46, 28 April 2011 (UTC)

You boldly renamed this article without previous discussion. Apparently you thought there would be a consensus for that move, but quite clearly there isn't. It's standard practice to undo such moves before any formal discussion. (Exceptions would be in case of serious policy violations or maybe when just nobody feels strongly about the matter. Neither applies here.) That the move proposal was formulated the other way round is not really a problem. See WP:BURO. Hans Adler 10:31, 28 April 2011 (UTC)
But why were the moves done in such an unusual way? After all, they were never likely to be voted down. But even if editors voted for these titles, they would still have trouble getting approved because they are blacklisted. Kauffner (talk) 06:08, 29 April 2011 (UTC)
There is no conspiracy against you, just lots of editors acting independently without any coordination. Titles containing π are affected by the move blacklist (I just verified this by creating a test page of that type with no problem), not by the creation blacklist, so there isn't much of a problem. Once an article exists, there is a natural locus for discussing any new name and asking for admin help. It's just a minor inconvenience – so long as there is no misguided editor going around and making all such titles artificially contentious. As you may have noticed, you haven't had much, if any, support yet but a lot of opposition. At some point it might be a good idea to just accept reality and disengage. Hans Adler 06:30, 29 April 2011 (UTC)
Use it on the redirect, if you can prove there will be many people using that in the search, but not the actual article. Chaosdruid (talk) 20:10, 29 April 2011 (UTC)
There is no reason to do it that way. There is a consensus at WikiProject Mathematics that using "pi" in an article title is eccentric and should not be done. Hans Adler 06:55, 30 April 2011 (UTC)
@Chaosdruid The attempt to rename the main Pi article failed due to lack of consensus, not because of a consensus that it has the right name. The situation is also different because that article needs disambiguation from the letter, and none of the other articles involving the constant do. "mixed script which is not allowed" is nonsense. There is no policy or guideline against mixed script titles, and in fact they can be created with no problem (I created User:Hans Adler/Testing the title blacklist as it concerns π, and then had it deleted as unnecessary, to verify this). There is only a technical measure against renaming existing pages to such title, which exists only to slow down a prolific vandal. So both of your arguments are invalid. Hans Adler 06:54, 30 April 2011 (UTC)
@Hans - Well, so nice to meet you! Maybe you can try a little harder to explain your second sentence? Do not call something nonsense just because you don't like it, get the policy changed, then it won't be on a blacklist and then the impediment will have been removed.
Your arguments are illogical, not having consensus means there was no consensus - you cannot say that because there was a lack of consensus that is different to no consensus and so there was a consensus, dear oh dear...there is also the fact that symbols are discouraged in title names and that screen readers will only read it as "p". Lastly having a consensus of five people in a project does not mean that you can start doing things your way across the whole of the encyclopedia. These comments should be in the discussion section - moving them now... Chaosdruid (talk) 09:36, 30 April 2011 (UTC)
OK, this is my last attempt. If you don't listen now I won't try again (I hope). There is no policy or guideline against mixed titles. If you think otherwise, the onus is on you to say where it is.
The blacklist changes all the time in response to the activities of the pagemove vandals. This is decided more or less privately and discreetly between a small number of admins who try to minimise the unwanted side effects (such as server load, or moves to legitimate mathematical titles involving π requiring admin intervention) and balance them with the disruption caused by the vandals. It is dastardly to present the blacklist as an argument against perfectly legitimate titles, and in fact it borders on siding with the page move vandals.
My second sentence: We have an article about the letter π and an article about the constant π. This complicates matters, as articles on Greek letters are by convention under their names written in Latin letters. (For practical reasons: Some of them are visually indistinguishable from Latin letters, and we should treat them all uniformly.) The situation is much clearer for titles such as "Liu Hui's π algorithm". No typesetter in their right mind would typeset this as "Liu Hui's pi algorithm" without very good reason, as it looks eccentric to the audience of the article. Hans Adler 10:26, 30 April 2011 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── When I say "symbols are discouraged in title names" I am referring to the article titles MoS which says "Do not use symbols:"Wikipedia:Article_titles#Special_characters Chaosdruid (talk) 10:59, 30 April 2011 (UTC)

You are misreading that passage. Obviously the term symbol can be used in a wide sense that includes Latin letters and standard punctuation marks (which is clearly not meant), in a narrow sense that excludes punctuations marks and everything that looks like a letter in some script, and in various senses in between. To see what is meant here one needs to use common sense, look at any examples specified, and read the rule in context. The only example given is ♥, which is a symbol even under the strictest reading of "symbol". That a strict reading is intended is also clear from the following rule, which would otherwise be redundant. The article on ${\displaystyle \wp }$ is called Weierstrass p because many browsers cannot display the special letter ${\displaystyle \wp }$, not because it falls under the previous rule (which it doesn't). Hans Adler 11:20, 30 April 2011 (UTC)
Not to disagree with your general point here, but you might choose a better example. It is a standard practice to spell out the names of symbols and this is not related to browser capabilities. The article title is Dollar sign, although every browser can render a "\$". Kauffner (talk) 13:28, 30 April 2011 (UTC)

@Chaosdruid Simply saying that mixed script is not allowed isn't an argument. The reason that there is a ban on mixed script is because of move vandalism, not legitimate uses like this one. That said, I would agree that mixed script should probably be avoided for stylistic reasons in many cases. For instance, if one part of a title were written in Arabic and the other in Latin characters, such a juxtaposition would just look strange. But in this case, we're talking about the easily-recognizable mathematical symbol π. If anything, spelling it out looks stranger than using the standard symbol. Regarding your second point, the only part of the MoS section you linked to that seems to be relevant here is the part that suggests having redirects in place if a symbol appears in an article title that is not commonly found on keyboards. Well, a move will leave a redirect in place. The only other point that could conceivably be relevant is the worry that a browser will render an ordinary Greek letter as a square box. I don't think this would ever happen. Sławomir Biały (talk) 14:02, 1 May 2011 (UTC)

You didn't click the link I put in then to read the MoS: Article titles where it clearly says not to use symbols in article titles? Also, you put comments here when they should be in the discussion section? (moved discussion to discussion section) Chaosdruid (talk) 16:57, 1 May 2011 (UTC)
That section says "Symbols such as "♥", as sometimes found in advertisements or logos, should never be used in titles. This includes non-Latin punctuation such as the characters in Unicode's CJK Symbols and Punctuation block.". It is not referring to Greek letters, which have been being used in titles for years. A Greek letter is no more a "symbol" than any other letter. — Carl (CBM · talk) 17:11, 1 May 2011 (UTC)
That is not strictly true, the letter is being used as a symbol to represent the number 3.xxxxxxxx. The Greek letter Pi does not mean 3.XXXXX it is a letter, not a number. I have raise the matter at MoS:Article Titles for clarity. Chaosdruid (talk) 17:19, 1 May 2011 (UTC)
Strictly speaking the symbol "P" is a symbol that denotes the letter P, and the symbols "4", "IV", and "" all denote the number four. But that's not what the MOS means by "symbol"; it's referring to dingbats, graphical characters, etc. If it meant "use ASCII" that is what it would say. Each character in ASCII is also a symbol, of course. — Carl (CBM · talk) 17:25, 1 May 2011 (UTC)
Just to reiterate what I said at Wikipedia_talk:Article_titles#Symbols_in_article_titles.2C_specifically_Pi, the (relatively recent) change of the MoS to exclude symbols appears to have been primarily targeted at elements of the unicode symbols code block, which does not include Greek letters. The question of Greek letters seems to be pretty far from what the people discussing that change to the MoS had in mind. Sławomir Biały (talk) 18:05, 1 May 2011 (UTC)

### Canvassing

Note canvassing [2] (Non-neutral notice) by Hans — Preceding unsigned comment added by Kauffner (talkcontribs) 11:06, 9 May 2011

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

## Move discussion in progress

There is a move discussion in progress on Talk:Pi which affects this page. Please participate on that page and not in this talk page section. Thank you. —RM bot 13:15, 2 June 2011 (UTC)

## Significance of Algorithm

The section on significance of the algorithm suggests that it generates better results than Archimedes algorithm. Has anyone checked to see if Liu Hui's superior results are because he made more accurate calculations? The denominators in Archimedes fractions are mostly single digits and generally powers of 2. This made for speedier calculation but less accuracy. Nobody should claim that Liu Hui's method is superior unless this possibility has been investigated.128.68.254.48 (talk) 08:34, 18 January 2016 (UTC) well I guess if you are quoting an RS, which I can't check at present, there isn't much I could do about this. In this case I suspect the RS may be biased, or not cited accurately. I have certainly got better results on a 96-gon on a spreadsheet using Archimedes than Archimedes did and my instinct (if such is acceptable) is that both methods are exactly the same in accuracy. 128.68.254.48 (talk) 09:21, 18 January 2016 (UTC)