Gaussian Formulae

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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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