Gaussian Formulae

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In these formulae, mod indicates the [http://mathworld.wolfram.com/Modulus.html 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 these formulae, mod indicates the [http://mathworld.wolfram.com/Modulus.html 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>.
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In addition, int indicates the [http://mathworld.wolfram.com/IntegerPart.html 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>.
 
In addition, int indicates the [http://mathworld.wolfram.com/IntegerPart.html 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).
 
Year indicates the year of interest (AD).
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The formulae:
 
The formulae:
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a = Year mod 4
 
a = Year mod 4
 +
 
b = Year mod 7
 
b = Year mod 7
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c = Year mod 19
 
c = Year mod 19
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d = (19c + 15) mod 30
 
d = (19c + 15) mod 30
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e = (2a + 4b - d + 34) mod 7
 
e = (2a + 4b - d + 34) mod 7
 +
 
f = Int((d + e + 114) / 31)
 
f = Int((d + e + 114) / 31)
 +
 
g = ((d + e + 114) mod 31) + 1
 
g = ((d + e + 114) mod 31) + 1
  
 
f is the month of Pascha.
 
f is the month of Pascha.
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g is the day of Pascha. For example, if f is 3 and g is 27, then Pascha occurs on March 27.
 
g is the day of Pascha. For example, if f is 3 and g is 27, then Pascha occurs on March 27.
  
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Source: Hieromonk Cassian, ''A Scientific Examination of the Orthodox Church Calendar''
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* Source: Hieromonk Cassian, ''A Scientific Examination of the Orthodox Church Calendar''
Programs using these formulae: [http://www.duke.edu/~aa63/menologion.html ''Menologion'']
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* Programs using these formulae: [http://www.duke.edu/~aa63/menologion.html ''Menologion'']

Revision as of 17:04, August 29, 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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