Talk:Determination of the day of the week

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Errors

Khennacy changed Alaska's previous owner from Russia to Canada as part of other changes. The sentence is awkward (Russia switched when Alaska was bought by the US from Russia) so I left it alone.

Comment: Whoever entered this statement is falsely reporting the change.

Algorithms

I don't agree with the pages claims concerning all algorithms. They could always be an algorithm that is a counterexample.

I don't this the paragraph heading The Algorithm. There are other algorithms.

I'd like the page to be about various algorithms and perhaps have a sepate page for each algorithm that is described in detail.

Other algorithms include the Doomsday algorithm which take avantage of the fact that 4 April, 6 June, 8 August, 10 October and 12 December are all the same day of week in a given year.

Also the article may be in violation of copyright. See [[1]], but actually appears to be quite different.

User:Karl Palmen 29 April 2004

• Hi, Karl, I'm the one who mentioned the copyright issue. This actually applied to just a section that was added by a user sometimes known as Hosamsherif who just copied that text from that page. It appears he has now readded that section, but rephrased it enough not to be a copyvio.
If we add another algorithm, this page could get quite large. Maybe it should just discuss the general idea, and link to a few different algorithms? Kevin Saff 14:50, 29 Apr 2004 (UTC)

Kevin Saff said that if we add another algorithm, this page could get quite large. That is why I suggested putting detailed algorithms on separate pages. The page itself could talk about various ways in which the day of the week is or has been worked out without having to show all the details there.

To be comprehensive and encyclopeadic, it should mention all reasonably well known algorithms.

User:Karl Palmen 30 April 2004

Lazy alternatives using Wikipedia itself

Now that some brilliant programmers at Wikipedia have done lots of legwork - er - fingerwork, most dates that most people could really want to check up on can be checked with a 4-digit search for the year then (if the calendar isn't displayed) a click on the link that goes to the calendar.

And now we have the marvellous new system of showing month calendars whenever we want to with a deceptively simple set of templates. I'm translating them into Maori, starting with mi:2005. Gets easier as you go on, for at least two reasons, one being that you find shortcuts if your lateral thinking is up to scratch. Talk to me if you want to do it for your language and can't find a guide anywhere. But if anyone has seen such a guide, please point me to it! Where's the best place to create such a guide if we don't have one? Robin Patterson 01:30, 6 Jun 2005 (UTC)

Centuries error?

The method of calculation in the "Centuries" heading is wrong. You can't obtain correct values using that method. —Preceding unsigned comment added by 129.97.233.144 (talkcontribs)

It is correct: In the article you stated that you could not obtain 6 from 20xx using the Centuries method. 20/4 yields a quotient of 5 and a remainder of 0. 3−0=3, 3×2=6. QED. You have probably confused the quotient with the remainder. — Joe Kress 04:39, 5 October 2006 (UTC)
The wording was confusing - I made the same mistake. I've reworded it. --... and m@ (talk) 01:14, 31 January 2008 (UTC)
I've rewritten the section explaining the algorithm. The part calculating the months was inconsistent with the examples below it, so I deleted that explanation. For the year and month, I've put mathematical equations in, because they are easier to read than an English sentence. I've removed examples in the instructions, the examples which already are included below are sufficient. I personally would refactor this section so that the explanation of the algorithm is separate from the definition, but I think I've modified the article enough for now. --... and m@ (talk) 02:11, 31 January 2008 (UTC)

The formula does give the results shown at the centuries table, but those values are wrong because:
1st of January of 1700 starts on friday (5), not thursday (4)
1st of January of 1800 starts on wednesday (3), not tuesday (2)
1st of January of 1900 starts on monday (1), not sunday (0)
Only the 1st of January of 2000 is correct, as it starts on saturday (6). —Preceding unsigned comment added by 189.180.105.160 (talk) 00:08, 30 June 2009 (UTC)

Another one

I got this one out of a maths book: $x = (date + (year - [\frac{14 - month}{12}]) + [\frac{31 \times (month + 12[\frac{14 - month}{12}]}{12}] + [\frac{year - \frac {14 - month}{12}]}{4}] -$
$[\frac{year - \frac {14 - month}{12}]}{100}] + [\frac{year - \frac {14 - month}{12}]}{400}])\operatorname{mod} 7$

Then convert x to day:

x= day
0 Sunday
1 Monday
2 Tuesday
3 Wednesday
4 Thursday
5 Friday
6 Saturday

Obviously the formula is a bit big and scary, but you can get rid of a lot of it by doing the algorithm in five steps.

1. $f = [\frac{14 - month}{12}]$
2. $y = year - f$
3. $m = month + 12f - 2$
4. Then put into new formula:
$(date + y + [\frac{31m}{12}] + [\frac{y}{4}]-[\frac{y}{100}]+[\frac{y}{400}])\operatorname{mod}7$
5. Convert (see table)

Jake95(talk!) 16:00, 20 January 2007 (UTC)

• $[\frac{31 \times (month + 12[\frac{14 - month}{12}]}{12}]$ should be $[\frac{31 \times (month + 12[\frac{14 - month}{12}]- 2)}{12}]$

Q5968661 (talk) 00:44, 18 December 2012 (UTC)

• This algorithm is similar to Gaussian algorithm: w = (d + [2.6m – 0.2] + y + [y/4] + [c/4] - 2c) mod 7
When month is 1 or 2, the term (f) [(14 - month)/12] = 1, which means y = year – 1 for January or February and y = year for the rest of the year.
[31m/12] = [2.6m – 0.2]: 2 5 0 3 5 1 4 6 2 4 0 3 (0 3 2 5 0 3 5 1 4 6 2 4).
(y + [y/4] + [y/400] - [y/100]) mod 7 = ([c/4] - 2c) mod 7: 5 3 1 0 (when y = 100, 200, 300, 400 and c = 1, 2, 3, 4).Q5968661 (talk) 05:57, 18 December 2012 (UTC)

Extending the century table

Could someone extend the century table backwards to 1000 ? —Preceding unsigned comment added by 74.230.150.150 (talk) 19:58, 9 September 2007 (UTC)

If you didn't notice, there's a pattern for centuries. You could fill it in yourself. Reywas92Talk 20:04, 9 September 2007 (UTC)
I noticed, but before 1700 the pattern is different (due to calendar changes). I added in the new values from 1000 to 1600, however years between 1699 and 1752 are going to produce incorrect results. Someone else should check this. —Preceding unsigned comment added by 74.230.150.150 (talk) 20:24, 9 September 2007 (UTC)
If you use 1 for 1700-1752, and 4 for 1753-1799 then everything seems to be okay. I'd appreciate it if someone else would check on this. —Preceding unsigned comment added by 74.230.150.150 (talk) 02:38, 10 September 2007 (UTC)
I extended the Centuries' table back to 1000, but only after regretting on 18 Sep. my having
removed all the Julian material that somebody went to a lot of trouble to add to this article.
So I decided to put it back, and extend it, esp. since back in 2006 I was accused of vandalism
for having removed material from an article that I helped to create. But now it seems like
wikipedia is taking the side of the vandals, who are either out to remove material, or replace
it w/bogus material, such as from Pokajanje, who posted a method that doesn't work--and one
that he knew might not work, or he'd have posted examples, such as Saturday, January 1st,
2000, that his method says occurred on a Sunday! Yet he accused the old method of not
working, when he could have verified for himself that it did work, even if it was explained
poorly. He also knew that his method was not tabular, since it required divisions to be
performed, yet claimed that it was tabular. The other method was fully tabular in that one
could use the tables to avoid division at each stage. However, what is even worse is how
wikipedia is now dominated by the vandals, who help out their fellow vandals as in a tag-team
wrestling match, so making vandalism an official sport to see how much damage they can get
away with, or to see how far they can accuse others of the acts that they themselves are
perpetrating! They are the ones now removing material, which a wikipedia calendar expert,
Karl_Palmen, found nothing wrong with, and himself restored after one of the vandals tried to
remove the Centuries' table. But at wikipedia nowadays, an expert user evidently can't get any
respect. Or they move the goalposts by modifiying their guidelines so that they can protect
those who are verifiably wrong, rather than spend a minute to verify it for themselves. Things
have changed for the worse over 6 years here.
Agree with what you said. but the formula d + m + y + y/4 mod 7 per se is definitely right. According to the formula, the 1st of January, 2000 occurred on a Saturday not a Sunday! Because the year 2000 is a leap year, we should substract 1 from the results or the values of m for the first two months. Q5968661 (talk) 11:12, 15 December 2012 (UTC)
Excuse me? Your first post claims that my method says it occurred on Sunday, your second that it occurred on a Saturday. It was a Saturday, and I can prove it with my method:
• Last two digits of year/4 + last 2 digits of year: 0
• Day of month: 1
• Month number: 0 (January of a leap year)
• Century code: 6
The total is 7, and since 7 mod 7 is 0, the date was a Saturday. Please stop making such accusations; all my edits have been made in good faith. And let me apologize for stating that the method did not work. I was wrong in that respect. It does indeed work, but it is rather complicated. It requires that one memorize two extremely large tables, one of which (the years') has no regular pattern.
I have just discovered that my formula is valid for Julian dates, provided that the centuries' table of 6 for 1200, 5 for 1300, etc. is followed. I will soon be adding my method to the article, with examples. Pokajanje|Talk 01:02, 23 December 2012 (UTC)

209 vandal

Lots of edits have been made lately by the 209.xxx.xxx.xxx vandal. They include:

• Replacing and with &
• In the paragraph about Corresponding years, changing "...but after February, corresponds to" with simply "...and ends corresponding to". "...but after February, corresponds to" is more natural when it comes to knowing when the year changes.
• Adding "March and November" and "April and July" to the All years section. You notice that this is redundant when it comes to their locations in the Common year and Leap year sections. Georgia guy (talk) 13:29, 30 September 2008 (UTC)

Gaussian algorithm

Just to mention, I took most of it form the German WP. Richiez (talk) 12:49, 19 June 2011 (UTC)

And it's none other than wikipedia that prevented you referencing it in square brackets.
As for other algorithms cited below, they are ALL externally referenced in the References section.
As for the tabular method, it had references to other sources, such as the Doomsday_algorithm,
that over time became unsuitable; it can still be derived from the "standard approach" as described in
general in the Intro. So it was culled from other sources, such that the old tabular method was an
implementation, rather than an algorithm; and as a result of being derived, it was not original research.

Protection

1. Per our Wikipedia:No original research policy, you are not in the business of inventing your own algorithms and publishing them first in Wikipedia.
2. Per our Wikipedia:Verifiability policy, you must show where you are getting these algorithms from.
3. Per our Wikipedia:Edit warring policy, this edit warring stops right now.

I've protected the article, and entirely removed the disputed section, in the hopes that some competent writers, who know more than simply the "undo" tool, will come up with a proper encylopaedic treatment of the subject on this talk page. Readers want to know who invented and published the algorithms, why they work, and how they work. If the answers are "I invented it.", "It has not been published outwith Wikipedia beforehand.", and "Because I say it does." then you have no business here at Wikipedia. I and other administrators shall be feeling free to revoke the editing privileges of people who continue to not understand that, and behave like, we are writing an encyclopaedia here, for the benefits of readers. Now get on with doing this properly. Uncle G (talk) 07:08, 13 December 2012 (UTC)

The translation in the Chinese Wikipedia article is not a source

Yes, "Readers want to know who invented and published the algorithms", but "why they work, and how they work" is more important. There are various methods to calculate the day of the week and the principles behind them are the same. Determination of the day of the week is very simple, if we know the basic facts and the rules of calendars. There are 7 days in a weak, there are 28/29/30/31 days in a month, and there are 365/366 days in a year. Given that 28/29/30/31/365/366/century mod 7 = 0/1/2/3/1/2/5(6), we get the months table (from January to December) 0/3/3/6/1/4/6/2/5/0/3/5, the years table (from 0 to 27, y mod 28) (6)0/1/2/3/(4)5/6/0/1/(2)3/4/5/6/(0)1/2/3/4/(5)6/0/1/2/(3)4/5/6/0/(1)2/3/4/5 (numbers in () for January and February in a leap year), and the centuries table (from 0 to 3, c mod 4) 6/4/2/0 for the Gregorian calendar and (from 5 to 4, mod 7) 6/5/4/3/2/1/0 for the Julian calendar. source Q5968661 (talk) 13:17, 13 December 2012 (UTC)

• I am getting my formula from here, and here, though I am unsure of those sources' reliability. I made the original edit that started this war because the "tabular method" is complex, poorly written, and hard to follow. I made the subsequent reverts because all the users who had reverted me were anonymous. Pokajanje|Talk 21:19, 13 December 2012 (UTC)
• Are you sure that you are unsure of those sources' reliability and made the original edit that started this war? Q5968661 (talk) 05:56, 14 December 2012 (UTC)
• Yes. Yes. Not anymore; one of the sources comes from a mathematics professor at the University of Waterloo.
• For the records, here is how the war transpired. After I had made the original edits on December 6, I was reverted two days later by 208.54.39.x (several very similar addresses, but clearly the same person because of the similar nature of the edit summaries), who called my good-faith edits vandalism. On December 9 I reverted to an old revision of the page, but a day later I was reverted by 71.48.32.58, who called me a "total liar" in his edit summary. Tbhotch and 71.48.32.58 then went back and forth twice, after which Materialscientist reverted 71.48.32.58. My edits were reverted on the 11th by 24.121.112.225, and I undid his revision seventeen minutes later. 192.94.73.30 first reverted back to the original version, and then to a version from October 30, mentioning something about Karl_Palmen, after which administrator Uncle G removed the disputed section and fully protected the page. The last stages of the war were interspersed with minor edits from Ukexpat, 58.23.218.199, and Thumperward.
• In summary, the involved parties are myself (Pokajanje), Tbhotch, MaterialScientist, 208.54.39.x, 71.48.32.58, 24.121.112.225, and 192.94.73.30. I suggest that all of these users be contacted. Pokajanje|Talk 16:29, 14 December 2012 (UTC)
• Also, it seems very convenient that most of us here can't read Chinese, and that that article cites no sources. Pokajanje|Talk 16:32, 14 December 2012 (UTC)
• Not anymore for the edit war. Why does it need sources for the thing almost everyone can do it? 183.250.0.247 (talk) 00:38, 15 December 2012 (UTC)

Pokajanje, I am amazed that you don't recognize the Chinese Wikipedia when you see it. Since you show yourself capable of reading an edit history, you should realize straightaway that the Chinese Wikipedia article has no sources because it is a translation of this article, as it stood on 2006-07-06, which of course cites no sources for most of its content. The translation notice is right there in the first revision of the Chinese Wikipedia article. Q5968661, what did I say about writing properly? Stop mucking around with non-sources. Wikipedia articles are not their own sources. Uncle G (talk) 19:20, 15 December 2012 (UTC)

Warning

I have lowered the protection to allow editing during the AFD discussion. I shall therefore be taking an extremely dim view of any resumption of the edit warring, and resorting more quickly to use of the blocking tool against edit warriors. Uncle G (talk) 19:20, 15 December 2012 (UTC)

With your permission, I would like to reinstate the material I added, with the method given at the University of Waterloo as a source. Also, I did recognize the Chinese Wikipedia, but did not realize that it was a translation of the English article. Pokajanje|Talk 23:19, 15 December 2012 (UTC)
IMO we shouldn't be basing Wikipedia articles on personal pages of academic staff. If the material was published in an academic paper, that would be different. But it isn't. Sionk (talk) 13:31, 19 December 2012 (UTC)

An analysis of the edit warring

Let's review the revision history first.

• 22:33, 6 December 2012‎ Pokajanje (13,682 bytes) (-5,631)‎ (A tabular method to calculate the day of the week: Completely rewrote section. The old method was confusing, too technical, and might have contained misinformation.)
• 06:39, 8 December 2012‎ 208.54.39.196‎ (19,313 bytes) (+5,631)‎ (Undid vandalism to purely Tabular Method 526778968 by Pokajanje)
• 01:09, 9 December 2012‎ Pokajanje (13,694 bytes) (-5,386)‎ (208.54.39.x, please provide reasons for your reverts other than simply "vandalism". The method before my edits was confusingly worded and incorrect, and section headings are not capitalized.)
• 01:48, 10 December 2012‎ 71.48.32.58 (19,080 bytes) (+5,386)‎ (Undid vandalism by a total liar 527109363 by Pokajanje)
• 02:24, 10 December 2012‎ Tbhotch (13,694 bytes) (-5,386)‎ (Undid revision by 71.48.32.58 (talk) I suggest you to read WP:NOTVAND, also WP:EW, and expressions like "Now let's try" don't have encyclopaedic value. Use the talkpage instead)
• 02:39, 10 December 2012‎ 71.48.32.58 (19,080 bytes) (+5,386)(Undid vandalism by another non-anglo user 527280764 by Tbhotch)
• 02:44, 10 December 2012‎ Tbhotch (13,694 bytes) (-5,386)‎ (Undid revision 527282872 by 71.48.32.58 (talk) My nationallity is totally irrelevant to you, this article or Wikipedia in general. This is WP:NOTVAND. WP:NPOV, WP:MOS, WP:EW)
• 02:45, 10 December 2012‎ 71.48.32.58 (19,080 bytes) (+5,386)‎ (Undid revision by nazi 527283651 by Tbhotch)
• 02:49, 10 December 2012‎ Materialscientist (13,694 bytes) (-5,386)‎ (Reverted edits by 71.48.32.58 to last version by Tbhotch)
• 21:27, 11 December 2012‎ 24.121.112.225 (19,069 bytes) (+5,386)‎ (Undid revision 527284548 by Materialscientist restore material relating to Dodgson's mistake)
• 21:44, 11 December 2012‎ Pokajanje (13,683 bytes) (-5,386)‎ (Undid revision 527600102 by 24.121.112.225 That method does not work)
• 06:06, 12 December 2012‎ 192.94.73.30 (18,983 bytes) (+5,337)‎ (Undid revision 527602955 by Pokajanje method wasn't fully tabular and gave the wrong day for original "Friday the 13th" 1307-10-13)
• 23:26, 12 December 2012‎ Pokajanje (13,628 bytes) (-5,337)‎ (Undid revision 527661561 by 192.94.73.30) That is because, as stated, it is valid for the Gregorian calendar only.)
• 04:28, 13 December 2012‎ 192.94.73.30 (18,965 bytes) (+5,337)‎ (Redid antivandalism restoration of 30oct by inhouse calendar expert Karl_Palmen)
• 07:07, 13 December 2012‎ Uncle G (12,201 bytes) (-6,764)‎ (A tabular method to calculate the day of the week: Removed disputed section entirely.)
• 19:03, 15 December 2012‎ Uncle G (12,629 bytes) (+428)‎ (afd by request of ElKevbo)

Now some questions

1. What are the reasons for revision?
2. How many does it involve?
3. Are they all vandalism?
4. How to avoid and manage it?
to be continued... --Q5968661 (talk) 02:39, 23 December 2012 (UTC)
It seems like we've reached a compromise with the current algorithm. Now we simply need to find a source, and it's hard to find where this algorithm originated. Pokajanje|Talk 17:08, 23 December 2012 (UTC)
Where is the source for 1 + 1 = 2? It is in the human brain! Q5968661 (talk) 11:24, 24 December 2012 (UTC)

A tabular and mental method to calculate the day of the week (prototype)

Days of the month Months Years mod 28 Centuries mod 4/7 Numbers Days of the week
01 08 15 22 29 05 01 07 12 18 24 03 G 1 Monday
02 09 16 23 30 08 02 08 13 19 24 02 02 2 Tuesday
03 10 17 24 31 02 03 11 03 08 14 20 25 01 3 Wednesday
04 11 18 25 06 04 09 15 20 26 00 01 4 Thursday
05 12 19 26 09 12 04 10 16 21 27 06 5 Friday
06 13 20 27 04 07 05 11 16 22 00 05 00 6 Saturday
07 14 21 28 01 10 06 12 17 23 00 04 03 0 Sunday

The algorithm: w = (d + m + y + c) mod 7. Who: anybody. Why and How: simple and easy.

That is completely unclear. Pokajanje|Talk 20:08, 19 December 2012 (UTC)

Unbalanced and OR

This article is seriously unbalanced. The best known algorithms (Gauss, Lewis Carroll, Zeller's and Doomsday), two of them developed in the 19th century and the other two having their own articles, are given short shrift. Meanwhile, another algorithm that Pokajanje has called "my formula" on this talk page - an admission of original research - and is probably a minor variation on the older ones, is called the "basic" algorithm. I am going to remove the "basic" formula. If it belongs in this article at all, it should be provided with sources and put in context. And it should definitely not be called the basic algorithm! RockMagnetist (talk) 17:37, 24 December 2012 (UTC)

I did not invent it. Pokajanje|Talk 22:35, 24 December 2012 (UTC)
to RockMagnetist this may cause another edit war! --Q5968661 (talk) 02:48, 25 December 2012 (UTC)
There is a danger of that. However, anyone wishing to restore that section should be aware of WP:BURDEN: "The burden of evidence lies with the editor who adds or restores material, and is satisfied by providing a reliable source that directly supports the material". Also, I am not necessarily against including this material if it can be provided with reliable sources and put in its proper context. RockMagnetist (talk) 06:33, 25 December 2012 (UTC)
The formula of d + m + y + [y/4] + c mod 7 is based on the basic knowledge and rules of calendars, such as days in a week, days in a month, days in a year, years in a century, leap year rules and so on. They are all belong to common-sense knowledge. Are you sure common-sense knowledge needs sources? --Q5968661 (talk) 11:56, 25 December 2012 (UTC)
Correct. As the formula works, I think it might fall under the category of not needing to cite that the sky is blue. Pokajanje|Talk 17:44, 25 December 2012 (UTC)
If you are correct, there is no need for this article. Shall we PROD it? RockMagnetist (talk) 19:33, 25 December 2012 (UTC)
This article cannot be PRODed; it has already been nominated for deletion once. Pokajanje|Talk 23:54, 25 December 2012 (UTC)
Don't behave like vandalism! --Q5968661
Acceptable examples of common knowledge
• Known time and date relating information (e.g. "There are seven days in a week.")
• Well-known historical fact ("Julius Caesar was a Roman".)
• Geographic pieces of information easily verified by a nonspecialized map ("Dallas is in Texas")
• Plain sight observations that can be made from public property ("A tall spire sits atop the Empire State Building")
• Obvious national associations ("German is the primary language in Germany")
• Mathematical or logical truisms ("1+1=2")
• Universally-accepted everyday orders that are taught in early elementary school ("A comes before B in the English Alphabet" or "January comes before February in the Gregorian calendar"). --Q5968661 (talk) 03:08, 26 December 2012 (UTC)
It appears I was unwise to try irony on this audience. A few mathematicians including Gauss thought it worthwhile to write down their algorithms. It strikes me as pretty cheeky to dismiss each of their methods in a line or two and then devote most of the article to a so-called "basic" method that supposedly does not require any source. It may not require sources for the details of the argument, but it needs sources to place it in the context of those older algorithms. RockMagnetist (talk) 07:01, 26 December 2012 (UTC)
I am working on a more complete description of Gauss's method; I have already added two sources for it. If you're really serious about improving this article, you should choose one of the other three older algorithms and describe it more thoroughly. RockMagnetist (talk) 07:05, 26 December 2012 (UTC)
Note: There are two different ways that modulo can handle negative numbers. For this equation to work properly '$(\cdots)\ \bmod\ 7$' needs to return a positive number if '$(\cdots)$' is a negative number. In case of January and February gives incorrect values. Hence use the corresponding same month's m value for these two months depending on whether it is leap year or not. e.g. leap year for February use m = 6 and January m = 2,similarly for non-leap year in feb m = 1 and jan m = 8.
It has been removed from Gaussian algorithm because of mistakes. Q5968661 (talk) 07:14, 27 December 2012 (UTC)

Yes, RockMagnetist is right. This algorithm requires a source since it achieves a novel synthesis of "common knowledge", which is forbidden under the policy against orignal research. Sławomir Biały (talk) 14:26, 28 December 2012 (UTC)

Some IP editor seemed to think that my removal of a link to a gopher site was vandalism. On the contrary, I stated the policy when I removed it. Links to proxy servers are not allowed per Wikipedia:External_links#Redirection_sites. RockMagnetist (talk) 17:58, 28 December 2012 (UTC)

Links to Google Groups is also not allowed per WP:LINKSTOAVOID (social networking sites). RockMagnetist (talk) 18:00, 28 December 2012 (UTC)

Yet another link is apparently an email address; I removed that. RockMagnetist (talk) 19:40, 31 December 2012 (UTC)

Gauss's algorithm

Before doing any more with the section on Gauss's algorithm, please read the reference by Schwerdtfeger, which has Gauss's original text in an appendix. Gauss's algorithm doesn't look anything like the one discussed in this section. I can't find any reliable source for the version that is shown (it can be found in blogs that may have copied it from this article). Thus, the section will have to be completely rewritten. An illustration of why Wikipedia requires reliable sources! RockMagnetist (talk) 18:05, 29 December 2012 (UTC)

Happy New Year!

Which is the original Gauss's algorithm?

w = (d + e + f + g + [g/4]) mod 7                   ( 1 )
w = (d + e + A + [A/4] + [A/400] - [A/100]) mod 7   ( 2 )
w = (d + e + y + [y/4] + [c/4] -2c) mod 7           ( 3 )
where
A = year
g = y = year mod 100
c = [year/100]
f = [c/4] -2c


Who are we?

"We split the year into the century part and the two digit year inside the century."
(A + [A/4] + [A/400] - [A/100]) mod 7
= (g + [g/4] + (100 + 100/4)c + [c/4] - c/1) mod 7
= (g + [g/4] - c  + [c/4] - c) mod 7, here (100 + 100/4) mod 7 = 6 = -1
= (g + [g/4] + [c/4] - 2c) mod 7
= (y + [y/4] + [c/4] - 2c) mod 7
Finally let e = [2.6m -0.2] or [(13m-1)/5], we have the formula ( 3 ):
w = (d + [2.6m -0.2] + y + [y/4] + [c/4] -2c) mod 7


Which one is the original formula in the world? ! --Q5968661 (talk) 03:38, 1 January 2013 (UTC)

None of them! Gauss only wrote down a formula for the day of the week of Jan 1 in any given year. RockMagnetist (talk) 07:51, 1 January 2013 (UTC)
   If you are right, you may have the chance to make a choice. Let d =1 and e = 0 (January),
w = (1 + f + (g -1) + [(g - 1)/4]) mod 7                                ( 1 )
w = (1 + (A - 1) + [(A - 1)/4] + [(A - 1)/400] - [(A - 1)/100]) mod 7   ( 2 )
w = (1 + (y - 1) + [(y - 1)/4] + [c/4] -2c) mod 7                       ( 3 )
where g ≠ 00, A ≠ 00, y ≠ 00
--Q5968661 (talk) 10:12, 1 January 2013 (UTC)

I'm not sure what you mean by making a choice. I'll be away for a couple of days. RockMagnetist (talk) 15:33, 1 January 2013 (UTC)
Rather than leave you hanging for a couple of days, I have added the correct description of Gauss's algorithm to the article. The previous section on the algorithm is now labelled Another variation, and someone should find a source for it. My version includes some wikitables. These are recommended by the Manual of Style (see Wikipedia:Manual of Style/Tables). The current formatting of tables in this article does not look very Wikipedia-like. RockMagnetist (talk) 16:37, 1 January 2013 (UTC)
1 + 5R : (A - 1) mod 4 + 4R : (A - 1) mod 100 + 6R : (A - 1) mod 400
= 1 + 5((A - 1) mod 4) + 4((A - 1) mod 100) + 6((A - 1) mod 400) --Q5968661 (talk) 05:07, 3 January 2013 (UTC)
Good catch. Thanks! RockMagnetist (talk) 06:29, 3 January 2013 (UTC)
You are welcome. Would you like to write these into the section for me?
  1 + 5R((A-1),4) + 4R((A-1),100) + 6R((A-1),400)  (1)
= 1 + 5R((A-1),4) + 10R((A-1),100), A-1<100
= 1 - 2R((A-1),4) + 3R((A-1),100)                  (2)
= 1 + 6R(100c,400), A-1=100c
= 1 - 100R(c,4)
= 1 - 2R(c,4)                                      (3)
(2) + (3) - 1
= 1 - 2R((A-1),4) + 3R((A-1),100) - 2R(c,4)        (4)



$w = (d + [2.6m - 0.2] - 2(y \operatorname{mod} 4) + 3(y\operatorname{mod} 100) - 2(c \operatorname{mod} 4)) \operatorname{mod} 7$
--Q5968661 (talk) 06:34, 4 January 2013 (UTC)

Why do you want that in? RockMagnetist (talk) 16:18, 4 January 2013 (UTC)

Q5968661, you removed some material with citations and replaced it with your own work. I am trying to keep properly cited material separate from potential OR. It may be fun to make up your own variations, but it isn't encyclopedic. RockMagnetist (talk) 17:57, 5 January 2013 (UTC)

RockMagnetist, you added Kraitchik's algorithm and Schwerdtfeger's variation into the section of Gauss's algorithm, but neither of them are Gauss's style, especially the first. Maybe Kraitchik's algorithm belong to Zeller’s style. If the term [2.6m - 0.2] belong to Gauss's algorithm, so do Schwerdtfeger's variation in part. --Q5968661 (talk) 01:23, 6 January 2013 (UTC)

I agree that they are not really Gauss's algorithm, and indeed Gauss's algorithm doesn't really solve the complete problem. But at least they are published (although Schwerdtfeger's paper is a little down the reliability scale because it is self-published). For now I'm keeping them in separate subsections until it is clear how they all fit together. RockMagnetist (talk) 01:29, 6 January 2013 (UTC)
"Readers want to know who invented and published the algorithms", but "why they work, and how they work" is more important. There are various methods to calculate the day of the week and the principles behind them are the same. Determination of the day of the week is very simple, if we know the basic facts and the rules of calendars.
The algorithm: w = (d + m + y + c) mod 7. Who: anybody. Why and How: simple and easy.
Who invented the algorithm: anybody (of course including you),
Why it works: simlple,and
How it works: easy. --Q5968661 (talk) 02:08, 6 January 2013 (UTC)
They are the same years table:[2] = [3]. The difference is in months table and centuries table. --Q5968661 (talk) 02:58, 6 January 2013 (UTC)
The similarity between the tables is exactly my reason for saying that we shouldn't be reinventing the wheel. There is no reason for a "basic algorithm" section when it is negligibly different from published versions. RockMagnetist (talk) 23:01, 6 January 2013 (UTC)
Who were reinventing the wheel？Gauss, Zeller, Kraitchik, Schwerdtfeger, ... or Pokajanje? Nothing to say, we are learning! --Q5968661 (talk) 06:28, 7 January 2013 (UTC)