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A perpetual calendar is a
calendar A calendar is a system of organizing days. This is done by giving names to periods of time, typically days, weeks, months and years. A date is the designation of a single and specific day within such a system. A calendar is also a phy ...
valid for many years, usually designed to look up the
day of the week In many languages, the names given to the seven days of the week are derived from the names of the classical planets in Hellenistic astronomy, which were in turn named after contemporary deities, a system introduced by the Sumerians and lat ...
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: # 14 one-year calendars, plus a table to show which one-year calendar is to be used for any given year. These one-year calendars divide evenly into two sets of seven calendars: seven for each common year (the year that does not have a February 29) with each of the seven starting on a different day of the week, and seven for each leap year, again with each one starting on a different day of the week, totaling fourteen. (See Dominical letter for one common naming scheme for the 14 calendars.) # Seven (31-day) one-month calendars (or seven each of 28–31 day month lengths, for a total of 28) and one or more tables to show which calendar is used for any given month. Some perpetual calendars' tables slide against each other so that aligning two scales with one another reveals the specific month calendar via a pointer or window mechanism. The seven calendars may be combined into one, either with 13 columns of which only seven are revealed, or with movable day-of-week names (as shown in the pocket perpetual calendar picture). # A mixture of the above two variations - a one-year calendar in which the names of the months are fixed and the days of the week and dates are shown on movable pieces which can be swapped around as necessary. Such a perpetual calendar fails to indicate the dates of
moveable feast A moveable feast is an observance in a Christian liturgical calendar which occurs on different dates in different years.John Ayto ''Oxford Dictionary of English Idioms'' 2010 p123 019954378X "a movable feast an event which takes place at no reg ...
s such as
Easter Easter,Traditional names for the feast in English are "Easter Day", as in the '' Book of Common Prayer''; "Easter Sunday", used by James Ussher''The Whole Works of the Most Rev. James Ussher, Volume 4'') and Samuel Pepys''The Diary of Samue ...
, which are calculated based on a combination of events in the
Tropical year A tropical year or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky of a celestial body of the Solar System such as the Earth, completing a full cycle of seasons; for example, the time ...
and lunar cycles. These issues are dealt with in great detail in ''
computus As a moveable feast, the date of Easter is determined in each year through a calculation known as (). Easter is celebrated on the first Sunday after the Paschal full moon, which is the first full moon on or after 21 March (a fixed approx ...
''. An early example of a perpetual calendar for practical use is found in the ''
Nürnberger Handschrift GNM 3227a Codex 3227a of the in Nuremberg (also known as ''Hs. 3227a'', ''GNM 3227a'', ) is a manuscript of 169 folia, dated to the close of the 14th century. Its text is written in Latin and German. The German portions have been identified as in East ...
''. The calendar covers the period of 1390–1495 (on which grounds the manuscript is dated to c. 1389). For each year of this period, it lists the number of weeks between
Christmas day Christmas is an annual festival commemorating the birth of Jesus Christ, observed primarily on December 25 as a religious and cultural celebration among billions of people around the world. A feast central to the Christian liturgical year, ...
and Quinquagesima. This is the first known instance of a tabular form of perpetual calendar allowing the calculation of the moveable feasts that became popular during the 15th century.


Other uses of the term "perpetual calendar"

Offices and retail establishments often display devices containing a set of elements to form all possible numbers from 1 through 31, as well as the names/abbreviations for the months and the days of the week, to show the current date for convenience of people who might be signing and dating documents such as checks. Establishments that serve alcoholic beverages may use a variant that shows the current month and day but subtracting the legal age of alcohol consumption in years, indicating the latest legal birth date for alcohol purchases. A common device consists of two cubes in a holder. One cube carries the digits zero to five. The other bears the digits 0, 1, 2, 6 (or 9 if inverted), 7, and 8. This is sufficient because only one and two may appear twice in date and they are on both cubes, while the 0 is on both cubes so that all single-digit dates can be shown in double-digit format. In addition to the two cubes, three blocks, each as wide as the two cubes combined, and a third as tall and as deep, have the names of the months printed on their long faces. The current month is turned forward on the front block, with the other two month blocks behind it. Certain
calendar reform Calendar reform or calendrical reform is any significant revision of a calendar system. The term sometimes is used instead for a proposal to switch to a different calendar design. Principles The prime objective of a calendar is to unambiguo ...
s have been labeled perpetual calendars because their dates are fixed on the same weekdays every year. Examples are The
World Calendar The World Calendar is a proposed reform of the Gregorian calendar created by Elisabeth Achelis of Brooklyn, New York in 1930. Features The World Calendar is a 12-month, perennial calendar with equal quarters. Each quarter begins on a Sunday ...
, the
International Fixed Calendar The International Fixed Calendar (also known as the IFC, Cotsworth plan, the Cotsworth calendar and the Eastman plan) is a proposed calendar reform designed by Moses B. Cotsworth, first presented in 1902. The solar calendar divides the year into ...
and the
Pax Calendar The Pax calendar was invented by James A. Colligan, SJ in 1930 as a perennializing reform of the annualized Gregorian calendar. Design The common year is divided into 13 months of 28 days each, whose names are the same as in the Gregorian cal ...
. Technically, these are not perpetual calendars but perennial calendars. Their purpose, in part, is to eliminate the need for perpetual calendar tables, algorithms, and computation devices. In watchmaking, "perpetual calendar" describes a calendar mechanism that correctly displays the date on the watch 'perpetually', taking into account the different lengths of the months as well as leap years. The internal mechanism will move the dial to the next day.


Algorithms

Perpetual calendars use algorithms to compute the day of the week for any given year, month, and day of the month. Even though the individual operations in the formulas can be very efficiently implemented in software, they are too complicated for most people to perform all of the arithmetic mentally.But see the formula in the preceding section, which is very easy to memorize. Perpetual calendar designers hide the complexity in tables to simplify their use. A perpetual calendar employs a table for finding which of fourteen yearly calendars to use. A table for the Gregorian calendar expresses its 400-year grand cycle: 303 common years and 97 leap years total to 146,097 days, or exactly 20,871 weeks. This cycle breaks down into one 100-year period with 25 leap years, making 36,525 days, or ''one'' day less than 5,218 full weeks; and three 100-year periods with 24 leap years each, making 36,524 days, or ''two'' days less than 5,218 full weeks. Within each 100-year block, the cyclic nature of the Gregorian calendar proceeds in the same fashion as its Julian predecessor: A common year begins and ends on the same day of the week, so the following year will begin on the next successive day of the week. A leap year has one more day, so the year following a leap year begins on the ''second'' day of the week after the leap year began. Every four years, the starting weekday advances five days, so over a 28-year period, it advances 35, returning to the same place in both the leap year progression and the starting weekday. This cycle completes three times in 84 years, leaving 16 years in the fourth, incomplete cycle of the century. A major complicating factor in constructing a perpetual calendar algorithm is the peculiar and variable length of February, which was at one time the ''last'' month of the year, leaving the first 11 months March through January with a five-month repeating pattern: 31, 30, 31, 30, 31, ..., so that the offset from March of the starting day of the week for any month could be easily determined.
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 ...
, a well-known algorithm for finding the day of the week for any date, explicitly defines January and February as the "13th" and "14th" months of the ''previous'' year to take advantage of this regularity, but the month-dependent calculation is still very complicated for mental arithmetic: :\left\lfloor\frac\right\rfloor \mod 7, Instead, a table-based perpetual calendar provides a simple lookup mechanism to find offset for the day of the week for the first day of each month. To simplify the table, in a leap year January and February must either be treated as a separate year or have extra entries in the month table:


Perpetual Julian and Gregorian calendar tables


Table one (cyd)

The following calendar works for any date from 15 October 1582 onwards, but only for Gregorian calendar dates.


Table two (cymd)


Table three (dmyc)


See also

* Determination of the day of the week *
Doomsday rule 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 ...
* Long Now Foundation *
Year 10,000 problem In computer science, time formatting and storage bugs are a class of software bugs that may cause time and date calculation or display to be improperly handled. These are most commonly manifestations of arithmetic overflow, but can also be the ...


References


External links


Sliding Perpetual Calendar on one sheet of paper (U.S. version, PDF)

Sliding Perpetual Calendar on one sheet of paper (non U.S. version, PDF)

Conical or Pyramidal Year Calendar (with "First of March table", PDF)

New Perpetual Calendar for any year

Perpetual Calendar in JavaScript
{{Authority control Calendars