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Formula for Easter


Date: 06/12/99 at 10:49:49
From: john 
Subject: Formula for Easter

Hi! I was wondering if you have any formula for solving this Easter 
holiday question: If you have the year, how would you figure out the 
month and the day on which Easter occurs that year?

Thank You for your time.


Date: 06/12/99 at 12:15:04
From: Doctor Anthony
Subject: Re: Formula for Easter

Gauss derived a formula to find the day (D) and month (M) on which 
Easter day falls given the year (T)

Below is shown the formula and its application to the year 1999

If   k = Integer part of [T/100]            k = Int[1999/100] = 19
     a = T (mod 19)                         a = 1999 (mod 19) = 4
     b = T (mod 4)                          b = 1999 (mod 4) = 3
     c = T (mod 7)                          c = 1999 (mod 7) = 4
     q = Integer part of [k/4]              q = Int[19/4] = 4
     p = Integer part of [(13+8k)/25]       p = Int[165/25] = 6
     m = (15-p+k-q) (mod 30)                m = 24 (mod 30) = 24
     d = (19a + m) (mod 30)                 d = 100 (mod 30) = 10
     n = (4+k-q) (mod 7)                    n = 19 (mod 7) = 5
     e = (2b+4c+6d+n) (mod(7)               e = 87 (mod 7) = 3

If  d+e <= 9  then  D = 22+d+e and M = 3    d+e = 10+3 = 13

If  d = 29 and e = 6
              then  D = 19 and  M = 4       (not applicable here)

If  d = 28 and e = 6 and a > 10 
              then  D = 18 and  M = 4       (not applicable here)

Otherwise  D = d+e-9  and  M = 4            D = 13-9 = 4,  M=4

So Easter day in the year 1999 was on April 4th.

- Doctor Anthony, The Math Forum
  http://mathforum.org/dr.math/   
    
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