Gaussian Formulae

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The formulae:
 
The formulae:
  
a = Year mod 4
+
  a = Year mod 4<br>b = Year mod 7<br>c = Year mod 19<br>d = (19c + 15) mod 30<br>e = (2a + 4b - d + 34) mod 7<br>f = Int((d + e + 114) / 31)<br>g = ((d + e + 114) mod 31) + 1<br>f is the month of Pascha.<br>g is the day of Pascha. For example, if f is 3 and g is 27, then Pascha occurs on March 27.
 
+
b = Year mod 7
+
 
+
c = Year mod 19
+
 
+
d = (19c + 15) mod 30
+
 
+
e = (2a + 4b - d + 34) mod 7
+
 
+
f = Int((d + e + 114) / 31)
+
 
+
g = ((d + e + 114) mod 31) + 1
+
 
+
f is the month of Pascha.
+
 
+
g is the day of Pascha. For example, if f is 3 and g is 27, then Pascha occurs on March 27.
+
  
 
Important, this returns the date of Pascha ONLY on the [[Old Calendar]]. To get the Gregorian date, add 13 days.
 
Important, this returns the date of Pascha ONLY on the [[Old Calendar]]. To get the Gregorian date, add 13 days.
 
  
 
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Revision as of 11:59, September 8, 2005

The Gaussian Formulae for Pascha were created by the prolific German mathematician Karl Friedrich Gauss (1777-1855).

In these formulae, mod indicates the Modulus, a mathematical operator that returns the remainder from division. For example, <math>8 mod 3 = 2</math> because <math>8 / 3 = 2 remainder 2</math>.

In addition, int indicates the Integer Part of a number. For positive numbers, it returns the greatest integer less than the number. For example, <math>Int(8.25) = 8</math>.

Year indicates the year of interest (AD).

The formulae:

 a = Year mod 4
b = Year mod 7
c = Year mod 19
d = (19c + 15) mod 30
e = (2a + 4b - d + 34) mod 7
f = Int((d + e + 114) / 31)
g = ((d + e + 114) mod 31) + 1
f is the month of Pascha.
g is the day of Pascha. For example, if f is 3 and g is 27, then Pascha occurs on March 27.

Important, this returns the date of Pascha ONLY on the Old Calendar. To get the Gregorian date, add 13 days.


  • Source: Hieromonk Cassian, A Scientific Examination of the Orthodox Church Calendar

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