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Zeller's congruence. Zeller's congruence is an algorithm devised by Christian Zeller in the 19th century to calculate the day of the week for any Julian or Gregorian calendar date. It can be considered to be based on the conversion between Julian day and the calendar date.
The Doomsday rule, Doomsday algorithm or Doomsday method is an algorithm of determination of the day of the week for a given date. It provides a perpetual calendar because the Gregorian calendar moves in cycles of 400 years. The algorithm for mental calculation was devised by John Conway in 1973, [1][2] drawing inspiration from Lewis Carroll 's ...
The basic approach of nearly all of the methods to calculate the day of the week begins by starting from an "anchor date": a known pair (such as 1 January 1800 as a Wednesday), determining the number of days between the known day and the day that you are trying to determine, and using arithmetic modulo 7 to find a new numerical day of the week.
A perpetual calendar is a calendar valid for many years, usually designed to look up the day of the week for a given date in the past or future. For the Gregorian and Julian calendars, a perpetual calendar typically consists of one of three general variations: Fourteen one-year calendars, plus a table to show which one-year calendar is to be ...
Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8]. A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms.
Formula. For the avoidance of error, the formulae should be given primarily with respectively +5J & +6J. Zeller included those, albeit secondarily, in the 1882 paper. A note might be added on the conversion between Zeller's day-of-week numbering and that in ISO 8601 - one just exchanges 0 & 7. Algorithm.
The formula reflects the fact that any five consecutive months in the range March–January have a total length of 153 days, due to a fixed pattern 31–30–31–30–31 repeating itself twice. This is similar to encoding of the month offset (which would be the same sequence modulo 7) in Zeller's congruence.
Calendrical Calculations. Calendrical Calculations is a book on calendar systems and algorithms for computers to convert between them. It was written by computer scientists Nachum Dershowitz and Edward Reingold and published in 1997 by the Cambridge University Press. A second "millennium" edition with a CD-ROM of software was published in 2001 ...