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Math

Calculating the Date of Easter 336

Posted by kdawson from the computus-giganticus dept.
The God Plays Dice blog has an entertaining post on how the date of Easter is calculated. Wikipedia has all the messy details of course, but the blog makes a good introduction to the topic. "Easter is the date of the first Sunday after the first full moon on or after March 21... [T]he cycle of Easter dates repeat themselves every 5,700,000 years. The cycle of epacts (which encode the date of the full moon) in the Julian calendar repeat every nineteen years. There are two corrections made to the epact, each of which depend[s] only on the century; one repeats (modulo 30, which is what matters) every 120 centuries, the other every 375 centuries, so the [p]air of them repeat every 300,000 years. The days of the week are on a 400-year cycle, which doesn't matter because that's a factor of 300,000. So the Easter cycle has length the least common multiple of 19 and 300,000, which is 5,700,000 [years]."
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Calculating the Date of Easter More

Calculating the Date of Easter

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  • Metric School Terms (Score:5, Funny)

    by 26199 ( 577806 ) * on Sunday March 23, 2008 @01:35PM (#22837672) Homepage

    In the UK the academic year is split according to the date of Easter. I recall hearing about an effort to move to a "metric" system which doesn't depend on Easter. This suddenly makes a lot of sense...

    • Re:Metric School Terms (Score:5, Interesting)

      by Corsix ( 1178253 ) on Sunday March 23, 2008 @01:57PM (#22837826) Homepage
      My school (south-west UK) seems to have detached term times from Easter. This is Easter weekend at the moment, so we get the Friday and Monday off as they are bank holidays, but the two week long "Easter break" isn't for another two weeks yet.

      • Re: (Score:3, Funny)

        by 26199 ( 577806 ) *

        Ah! The march of progress. Hasn't happened in the north-west yet, to my knowledge...

      • Re: (Score:2)

        by CSMatt ( 1175471 )
        You guys get two weeks off? Lucky Brits.

        • Re:Metric School Terms (Score:5, Informative)

          by 26199 ( 577806 ) * on Sunday March 23, 2008 @02:11PM (#22837924) Homepage

          In the UK school is split into three terms ... in the middle of each, you get a week off, and between them, you get two weeks off. Except over the summer when it's six weeks.

          So there's more holiday through the year, but the summer vacation is shorter.

          (This is probably because we don't have as much summer.)

        • Re: (Score:2, Informative)

          by Anonymous Coward
          Yeah, those of us above school age also get a statutory 28 days paid holiday. Which seems a lot compared to the US 11 or 12(?) but if you think that's good I believe the Dutch get 35 days and every 2nd Friday. To take it to the extreme the French are forced to work at most on 35 hours [thedailymash.co.uk] and get four weeks but have to take them in August. Hurrah for the EU!

          • Re:Metric School Terms (Score:5, Funny)

            by Foobar of Borg ( 690622 ) on Sunday March 23, 2008 @03:27PM (#22838494)

            Yeah, those of us above school age also get a statutory 28 days paid holiday. Which seems a lot compared to the US 11 or 12(?)
            I think 11 or 12 days is about what Americans in the professional class wind up getting on average, but *statutorily* we get somewhere between jack and shit.

            To take it to the extreme the French are forced to work at most on 35 hours and get four weeks but have to take them in August.
            So basically, if you want to invade France make sure to do it in August. That way, they won't notice until they come back from vacation :-).

            • Re: (Score:2, Funny)

              by Anonymous Coward

              So basically, if you want to invade France make sure to do it in August. That way, they won't notice until they come back from vacation :-).


              Not that this will have any effect on the outcome of invading ...

    • Re: (Score:3, Interesting)

      by acroyear ( 5882 )
      could be worse. In the early 600s, Easter as calculated by Patrick's Irish/Celtic church was on a different day some years than the Roman church. In one particularly odd incident, the King of Northumbria celebrated Easter on a different day from his wife.

      The Council of Whitby resolved this, supposedly.

      • Re:Metric School Terms (Score:5, Informative)

        by psychodelicacy ( 1170611 ) <bstcbn@gmail.com> on Sunday March 23, 2008 @03:55PM (#22838650)
        Absolutely - the Anglo-Saxons had a lot to say about the dating of Easter. See http://faculty.virginia.edu/OldEnglish/aelfric/detemp.html [virginia.edu] for an original text on the subject if you're wildly interested. Melvyn Bragg's novel "Credo" dramatises the Synod of Whitby and gives a sense of exactly how serious an issue this was for people. Since Easter is the major Christian feast, it was a matter of orthodoxy to date it correctly. Interesting to think that being bad at math could make you a heretic!

        • Re: (Score:3, Insightful)

          by drew ( 2081 )
          Interesting - I always assumed that "choosing" the date of Easter was a simple and fairly straightforward affair - it should always be the Sunday following the Jewish passover feast. How the date for that is determined, I am not really sure off the top of my head, but it doesn't seem like it should have been that hard to figure out for any Christian leader who was particularly interested, since the Christians included most of the Jewish scriptures and proscriptions in their own.

          • Re: (Score:3, Informative)

            by psychodelicacy ( 1170611 )
            Well, I can only really speak about the Anglo-Saxons on this, but you need to remember that books were scarce, and literacy was by no means universal. There's no guarantee someone would have had access to the whole Bible at any one time, or could read it even if they did. Add to this the fact that there was a great distrust of Jews - I doubt most Anglo-Saxon thinkers would have accepted that Christianity "included" Jewish scriptures and proscriptions; they would say that Christianity fulfilled the Hebrew sc

    • Er, mods ... I was being completely serious.

      Do not laugh at us! Or we will become more powerful than you can possibly imagine...

  • how is it... (Score:2, Insightful)

    by MousePotato ( 124958 ) *
    This is not a science article. Arguably it is a math article to the interested christians on /. but certainly not science.

    • Re:how is it... (Score:5, Funny)

      by Otter ( 3800 ) on Sunday March 23, 2008 @01:45PM (#22837744) Journal
      Calculating the Date of Easter Finds Possible Cure For Cancer

      There, now it's an official Science article.

      • Re: (Score:3, Funny)

        by popmaker ( 570147 )
        Yep, it goes along with the article on how to find out which weekday "seven days before yesterday" is without using your fingers.

        • Re:how is it... (Score:5, Insightful)

          by Otter ( 3800 ) on Sunday March 23, 2008 @02:23PM (#22838022) Journal
          Your grasp of astronomical chronology far exceeds mine, then. I'm not a Christian and have no interest in the holiday per se, but thought this article was a fascinating piece of science history, and certainly learned more science from the underlying astronomy and the computation thereof than I would have gotten from any ten Roland Piquepaille rehashings of press releases he doesn't understand.

    • Comment removed (Score:4, Funny)

      by account_deleted ( 4530225 ) on Sunday March 23, 2008 @01:47PM (#22837764)
      Comment removed based on user account deletion

      • Re: (Score:2, Funny)

        by ParaShoot ( 992496 )

        These sort of articles, besides showing Christians when their religious day falls, also explain when to expect such mechandise in your local stores.
        At the rate the appearance of the merchandise moves further and further back from the official date each year, I wouldn't be surprised if the said gelatin chicks turn up sometime this July. Buy now for Easter '09!

      • Re: (Score:2)

        by Snorpus ( 566772 )
        Gelatin chicks? Chocolate bunnies? Don't kids get real chicks (dyed yellow, purple, etc.) and bunnies at Easter any more?

      • Re:how is it... (Score:5, Interesting)

        by Phroggy ( 441 ) <slashdot3@@@phroggy...com> on Sunday March 23, 2008 @03:03PM (#22838300) Homepage

        Arguably it is a math article to the interested christians on /.

        Methinks many families that profess no especial religion nonetheless buy their children bunny figures, chocolate, and disgusting gelatin chicks in the springtime. These sort of articles, besides showing Christians when their religious day falls, also explain when to expect such mechandise in your local stores.

        Don't forget about Mardi Gras!

        Mardi Gras (Fat Tuesday, Shrove Tuesday, Pancake Day, etc.) is the day before Ash Wednesday, which is the first day of Lent, which begins 40 days (excluding Sundays) before Easter. So, once you've calculated the date of Easter, subtract 47 to get the date of Mardi Gras [wikipedia.org].

    • Re: (Score:2)

      by CSMatt ( 1175471 )

      This is not a science article. Arguably it is a math article to the interested christians on /. but certainly not science.
      Which is why it isn't tagged with the "science" tag and the picture of Einstein is missing.
    • If it is (I think it is) then the calculation of the date of Easter is an interesting demonstration of how the patriarchal Jewish religion has in fact got roots in a matriarchal religion, since its calendar is based on a lunar rather than a solar cycle. (I'm simplifying). There are plenty of clues in the OT for the educated - but educating a few Protestant fundies as to the real underpinnings of their religion might hopefully get them thinking, and thinking helps cure ignorance, and curing ignorance helps d

    • Re: (Score:3, Interesting)

      by wickerprints ( 1094741 )
      I'm not Christian and don't observe Easter, but I am a mathematician, and even I found the calculation interesting. In particular, I was interested to see the variety of algorithms used, as well as their relationship to astronomy.

      One should not forget that astronomy--and much of science in general--historically were motivated by religious belief, not just in Western Judaeo-Christian cultures, but all cultures. That this is no longer the case speaks to the power of rational thought over pre-rational m
    • Math isn't science?
    • Perhaps you fail to notice that this is a long term pseudo-random number generator. A subject near and dear to the hearts of every /.er. Not bad considering the hardware they back in the day had was only slide rules and abacuses.
  • I always thought it was based on when the Hebrew calendar said the week of Passover was.

    • Re:Huh. (Score:4, Informative)

      by sonicdevo ( 899106 ) on Sunday March 23, 2008 @01:49PM (#22837786)
      "Easter is termed a moveable feast because it is not fixed in relation to the civil calendar. Easter falls at some point between late March and late April each year (early April to early May in Eastern Christianity), following the cycle of the moon. After several centuries of disagreement, all churches accepted the computation of the Alexandrian Church (now the Coptic Church) that Easter is the first Sunday after the first fourteenth day of the moon (the Paschal Full Moon) that is on or after the ecclesiastical vernal equinox. Easter is linked to the Jewish Passover not only for much of its symbolism but also for its position in the calendar. The Last Supper shared by Jesus and his disciples before his crucifixion is generally thought of as a Passover meal, based on the chronology in the Synoptic Gospels..."

      http://en.wikipedia.org/wiki/Easter [wikipedia.org]Wikipedia
    • Of course, you are correct. The (Greek) Orthodox get this - the Last Supper was a Passover feast - case closed.

      Meanwhile, I prefer the Flying Spagetti Monster [wikipedia.org]
    • Not this year, they're pretty far off - a month or so? Perhaps a result of this year's Hebrew calender having an extra month to prevent drift? So, essentially, yeah, but it seems like the early Church felt the need to create their own calculation so it didn't look like they were just copying the Jews. Awkward . . .

  • Spring equinox (Score:5, Interesting)

    by wile_e_wonka ( 934864 ) on Sunday March 23, 2008 @01:42PM (#22837722)
    I've always thought that it is more fun to say the date of Easter is "the first Sunday after the first full moon after the Spring Equinox," rather than March 21st.

    It sounds so much more Pagan my way.

    • Re:Spring equinox (Score:5, Informative)

      by AndrewRUK ( 543993 ) on Sunday March 23, 2008 @02:16PM (#22837968)
      Only problem is, your way isn't always right, because the date of Easter is always calculated from March 21st even if (as this year) the northern hemisphere spring equinox doesn't fall on that date.
  • Science ? Yea, right. By that logic astrology would be science too.
  • now, does all that fancy mathematics and statements about the repetition cycle of days include the Leap Year's Lead Day, as well as the fact that it didn't exist the last time this cycle started?

    • Re: (Score:3, Informative)

      by the_other_chewey ( 1119125 )
      now, does all that fancy mathematics and statements about the repetition cycle of days include the Leap Year's Lead Day, as well as the fact that it didn't exist the last time this cycle started?

      Yes, the formula by Gauß does. That's one of the reasons the mathematics have to be so fancy.
  • Would people care very much is we just settled for the first sunday in april?
  • Hope we see a followup article on how Passover is calculated - after all, they roughly conincided at least once 2000 years ago.....
    • It's very easy: Passover comes on exactly the same dates every year in the Jewish Calendar. The Jewish and Gregorian calendars are different, so the date wanders around the Gregorian Calendar to a small extent while remaining fixed in the Jewish one.

  • Easter Island (Score:2, Insightful)

    by drquoz ( 1199407 )
    Could this be the solution to the mystery of Rapa Nui?
  • ...when you said first sunday after the first full moon after the equinox.

  • In Perl (Score:5, Informative)

    by Phroggy ( 441 ) <slashdot3@@@phroggy...com> on Sunday March 23, 2008 @02:46PM (#22838172) Homepage
    sub GetEasterDate {
      my($year)=@_;
      # http://www.smart.net/~mmontes/nature1876.html
      my $a=$year%19;
      my $b=int($year/100);
      my $c=$year%100;
      my $d=int($b/4);
      my $e=$b%4;
      my $f=int(($b+8)/25);
      my $g=int(($b-$f+1)/3);
      my $h=(19*$a+$b-$d-$g+15)%30;
      my $i=int($c/4);
      my $k=$c%4;
      my $l=(32+2*$e+2*$i-$h-$k)%7;
      my $m=int(($a+11*$h+22*$l)/451);
      my $month=int(($h+$l-7*$m+114)/31);
      my $p=($h+$l-7*$m+114)%31;
      my $day=$p+1;
      return (0,0,0,$day,$month-1,$year-1900);
    };

    • GetEasterDate in Perl, huh? My, my, my.

    • In PHP (Score:3, Interesting)

      by JoeCommodore ( 567479 )
      $unixdatenum = easter_date($year);

  • In Vim Script (Score:2, Interesting)

    by Anonymous Coward
    Only valid between 1583 and 4899

    function! s:EasterSunday(year, return_value)

    if a:year 4089
    return 0
    endif
    let a = a:year / 100
    let b = a:year % 100

  • hmm (Score:3, Interesting)

    by thatskinnyguy ( 1129515 ) on Sunday March 23, 2008 @02:56PM (#22838228)
    Is it just me or does it seem like anything posted having to do with politics or religion turns into a mod point black hole?

  • Recommended Reading (Score:5, Interesting)

    by szyzyg ( 7313 ) on Sunday March 23, 2008 @03:01PM (#22838264)
    I won't hesitate to recommend the book 'Marking Time' by Duncan Steel - it's a great book about the history and evolution of calendars. The date of easter is a particularly interesting question and Duncan goes as far as to explain how the date of Easter was at the core of an English plan to attack the legitimacy of the Catholic church and how this plan was what triggered Britain's first attempts to colonize America, great stuff.
  • More East.

    *Ta-da-boom*

    I first saw this in a Tandberg [wikipedia.org] cartoon years and years ago. PIty I can't find the original.

  • Stupid *nix Tricks (Score:5, Funny)

    by Relic of the Future ( 118669 ) <dales@@@digitalfreaks...org> on Sunday March 23, 2008 @03:11PM (#22838364)
    cal 9 1752

    Calendars are funny things.

  • Easter is always either early or late. It's never when it's supposed to be.
  • Why does Easter change date every year and Christmas does not. Were they set based on different calendars? Otherwise it would be indeed weird that the number of months between the two days switches all the time.
  • Of course, when these calculations consider the addition of the Easter Bunny, the Fibonacci sequence, represented as an infinite mathematical set, must be applied to the cycle result. In the end you'll find it's bunnies all the way down.
  • And it was March 19 in California. Leap day made is seem earlier.

  • Catholic Easter != Orthodox Easter (Score:5, Interesting)

    by pz ( 113803 ) on Sunday March 23, 2008 @04:47PM (#22838986) Journal
    There are millions of people who did not celebrate Easter today (23 March 2008) because they will be celebrating on 27 April 2008 (yep, 5 weeks later ... this is an unusual year). Orthodox Easter is computed to always fall after Passover (because, recall, the Last Supper was a Passover Seder).

    Here's a web site that is more, um, shall we say, enlightened: http://www.assa.org.au/edm.html [assa.org.au]

    One of the main differences between the calculations for Roman Catholic Easter and Eastern Orthodox Easter is in which calendar (Gregorian or Julian) is used. Use Google. It's actually quite interesting because of all the history and politics involved. It's not just simple (eg, exactly when is the moon full? over which point on the earth?) as one might think.

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