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A calendrical calculation is a calculation concerning calendar dates. Calendrical calculations can be considered an area of applied mathematics. Some examples of calendrical calculations: Converting a Julian or Gregorian calendar date to its Julian day number and vice versa (see § Julian day number calculation within that article for details).
As for example, the year 2697 BC (or −2696, using the astronomical year count), traditionally the first year of the reign of the legendary Yellow Emperor, was the first year (甲子; jiǎzǐ) of a cycle. 2700 years later in 4 AD, the duration equivalent to 45 60-year cycles, was also the starting year of a 60-year cycle. Similarly 1980 years ...
For January, January 3 is a doomsday during common years and January 4 a doomsday during leap years, which can be remembered as "the 3rd during 3 years in 4, and the 4th in the 4th year". For March, one can remember either Pi Day or "March 0", the latter referring to the day before March 1, i.e. the last day of February.
The Lunar Hijri calendar is a lunar calendar consisting of 12 months in a year of 354 or 355 days. The astronomer's mean tropical year, which is averaged over equinoxes and solstices, is currently 365.24219 days, slightly shorter than the average length of the year in most calendars. A year can also be measured by starting on any other named ...
For the Gregorian calendar, the various parts of this formula can therefore be understood as follows: represents the progression of the day of the week based on the day of the month, since each successive day results in an additional offset of 1 in the day of the week. represents the progression of the day of the week based on the year.
The most common way to reconcile the two is to vary the number of days in the calendar year. In solar calendars, this is done by adding an extra day ("leap day" or "intercalary day") to a common year of 365 days, about once every four years, creating a leap year that has 366 days (Julian, Gregorian and Indian national calendars).
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A calendar date is a reference to a particular day represented within a calendar system. The calendar date allows the specific day to be identified. The number of days between two dates may be calculated. For example, "25 December 2024" is ten days after "15 December 2024". The date of a particular event depends on the observed time zone.