Editing Doomsday rule (section)

{{Short description|Way of calculating the day of the week of a given date}}
{{Use mdy dates|date=August 2024}}
[[File:John H Conway 2005.jpg|thumb|[[John Horton Conway|John Conway]], inventor of the Doomsday algorithm]]

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 Horton Conway|John Conway]] in 1973,<ref>John Horton Conway, {{cite web |url=https://web.archive.org/web/20240907031643/https://www.archim.org.uk/eureka/archive/Eureka-36.pdf|title=Tomorrow is the Day After Doomsday |page=28-32 |date=October 1973 |publisher=Eureka }}</ref><ref>Richard Guy, John Horton Conway, Elwyn Berlekamp : "Winning Ways: For Your Mathematical Plays, Volume. 2: Games in Particular", pages 795–797, Academic Press, London, 1982, {{ISBN|0-12-091102-7}}.</ref> drawing inspiration from [[Lewis Carroll]]'s [[Determination of the day of the week#Lewis Carroll%27s method|perpetual calendar algorithm]].<ref>Lewis Carroll, "To Find the Day of the Week for Any Given Date", ''Nature'', March 31, 1887. {{doi|10.1038/035517a0}}</ref><ref>Martin Gardner, ''The Universe in a Handkerchief: Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Word Plays'', pages 24–26, Springer-Verlag, 1996.</ref><ref>{{cite web |url=https://ww2.amstat.org/mam/2014/calendar/doomsday.html|title=What Day is Doomsday |date=April 2014 |publisher=Mathematics Awareness Month }}</ref> It takes advantage of each year having a certain day of the week upon which certain easy-to-remember dates, called the ''doomsdays'', fall; for example, the last day of February, April 4 (4/4), June 6 (6/6), August 8 (8/8), October 10 (10/10), and December 12 (12/12) all occur on the same day of the week in the year.

Applying the Doomsday algorithm involves three steps: determination of the anchor day for the century, calculation of the anchor day for the year from the one for the century, and selection of the closest date out of those that always fall on the doomsday, e.g., 4/4 and 6/6, and count of the number of days ([[Modular arithmetic|modulo 7]]) between that date and the date in question to arrive at the day of the week. The technique applies to both the [[Gregorian calendar]] and the [[Julian calendar]], although their doomsdays are usually different days of the week.

The algorithm is simple enough that it can be computed mentally. Conway could usually give the correct answer in under two seconds. To improve his speed, he practiced his calendrical calculations on his computer, which was programmed to quiz him with random dates every time he logged on.<ref>{{Cite web |last=Alpert |first=Mark |date=April 1, 1999 |title=Not Just Fun and Games |url=https://www.scientificamerican.com/article/not-just-fun-and-games/ |access-date=April 18, 2024 |website=Scientific American |language=en}}</ref>