Difference between revisions of "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 | ||
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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 | ||
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f = Int((d + e + 114) / 31) | f = Int((d + e + 114) / 31) | ||
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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'' | + | * Source: Hieromonk Cassian, ''A Scientific Examination of the Orthodox Church Calendar'' |
| − | Programs using these formulae: [http://www.duke.edu/~aa63/menologion.html ''Menologion''] | + | |
| + | * Programs using these formulae: [http://www.duke.edu/~aa63/menologion.html ''Menologion''] | ||
Revision as of 01:04, August 30, 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
- Programs using these formulae: Menologion
