From: kerryg@rice.edu (Kerry Go)
Newsgroups: sci.math
Subject: Easter algorithm
Date: 11 Mar 91 07:40:38 GMT

Several years ago, I came across the following algorithm and found it
interesting.

A = year mod 4
B = year mod 7
C = year mod 19
D = (19C + M) mod 30
E = (2A + 4B + 6D + N) mod 7

In the 20th century, M = 24 and N = 5.
Easter is on the (22+D+E)th of March or the (D+E-9)th of April.

Has anyone seen this before?  If so,
(1) Is there a book containing this algorithm?  If so, what is the name and
author of the book?  I don't know the values for
M and N other than those for this century.
(2) Is there a proof showing why this algoithm works (or doesn't)?

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From: ernie@neumann.une.edu.au (Ernest W Bowen)
Newsgroups: sci.math
Subject: Re: algorithm for date of easter
Date: 6 Jul 93 15:18:54 GMT
Summary: :Z?~?~?An algorithm for date of easter

In article <212cfe$1f3@salyko.cubenet.sub.org>, hadi@salyko.cubenet.sub.org (Hans Dimbeck) writes:
> 
>  
> Who can help me.
> I need a method to calculate the date of easter.
> 
> Thanks Hans.


        According to H.V. Smith in "Mathematical Spectrum," 11 (1978/79),
23-24, the following rule appeared in Butcher's Ecclesiastical
Calendar, 1876.  To find the date of Easter Sunday for year y:

              Divide            by      Quotient  Remainder
        ---------------------------------------------------
                 y               19                   j
                 y              100        k          h
                 k                4        m          n
               k + 8             25        p
             k - p + 1            3        q
        19j + k - m - q + 15     30                   r
                 h                4        s          u
        32 + 2n + 2s - r - u      7                   v
           j + 11r + 22v        451        w
         r + v - 7w + 114        31        x          z

Here x is the number of the month ond 1 + z is the day of that
month upon which Easter Sunday falls in the year y. 

	The following csh shell script does these calculations and
echoes x and 1 + z.  Some signs appear to be wrong because in @
assignments + and - are right-associative.

---

# With argument y, this echoes the month-number and day-number for
# Easter Sunday in year y; e.g. easter 1992 displays  4 19.
@ j = $1 % 19
@ k = $1 / 100
@ h = $1 % 100
@ m = $k / 4
@ n = $k % 4
@ p = ($k + 8) / 25
@ q = ($k - $p - 1) / 3
@ r = (19 * $j + $k - $m + $q - 15) % 30
@ s = $h / 4
@ u = $h % 4
@ v = (32 + 2 * $n + 2 * $s - $r + $u) % 7
@ w = ($j + 11 * $r + 22 * $v) / 451
@ xp = $r + $v - 7 * $w - 114
@ x = $xp / 31
@ d = $xp % 31 + 1
echo '		' $x $d

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