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The Gregorian calendar did not exist before October 15, 1582. Gregorian dates before that are proleptic, that is, using the Gregorian rules to reckon backward from October 15, 1582. Years are given in astronomical year numbering. Augustus corrected errors in the observance of leap years by omitting leap days until AD 8.
In the Gregorian calendar, this is done by adding 1 eight times in 2,500 (Gregorian) years (slightly more than 2500 × 0.003126, or about 7.8), always in a century year: this is the so-called lunar correction (historically called "lunar equation"). The first one was applied in 1800, the next is in 2100, and will be applied every 300 years ...
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).
Alexandrian computus, based on rules established by the Church of Alexandria, was universally used from the beginning of the 8th century until the Gregorian calendar reform of 1582. The Roman Catholic Church has used the Gregorian calendar, and accordingly Gregorian computus, to calculate the dates of Easter since 1583.
The Gregorian calendar, like the Julian calendar, is a solar calendar with 12 months of 28–31 days each. The year in both calendars consists of 365 days, with a leap day being added to February in the leap years. The months and length of months in the Gregorian calendar are the same as for the Julian calendar.
These formulas are based on the observation that the day of the week progresses in a predictable manner based upon each subpart of that date. Each term within the formula is used to calculate the offset needed to obtain the correct day of the week. For the Gregorian calendar, the various parts of this formula can therefore be understood as follows:
For Gregorian dates after 2299, the year in the table which differs by an exact multiple of 400 years should be used. The values "r0" through "r6" indicate the remainder when the Hundreds value is divided by 7 (Julian) or 4 (Gregorian), indicating how the series extend in either direction. Both Julian and Gregorian values are shown for years ...
The practices of the Roman Catholic Church that had become traditional by 1582 for calculating the Easter and lunar calendars became settled when Dionysius Exiguus translated the rules of the Church of Alexandria from Greek into Latin in 525. (Northumbria adopted them at Whitby in 664, the Welsh around 768, and France around 775.