# 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*