# Difference between revisions of "Gaussian Formulae"

From OrthodoxWiki

m |
|||

Line 13: | Line 13: | ||

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. | ||

− | + | ==External Links== | |

− | * Source: Hieromonk Cassian, ''A Scientific Examination of the Orthodox Church Calendar'' | + | * Source: Hieromonk Cassian, ''A Scientific Examination of the Orthodox Church Calendar'', ISBN 0911165312. Available from [http://users.sisqtel.net/sgpm/ctos/oldcal/SEO.html The Center for Traditionalist Orthodox Studies] |

* 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 19:05, 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.

## External Links

- Source: Hieromonk Cassian,
*A Scientific Examination of the Orthodox Church Calendar*, ISBN 0911165312. Available from The Center for Traditionalist Orthodox Studies

- Programs using these formulae:
*Menologion*