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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.
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:
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).
27 week years are 5 days longer than the month years (371 − 366), 6.75%. 44 week years are 6 days longer than the month years (371 − 365), 11%. 70 week years are 2 days shorter than the month years (364 − 366), 17.5%. 259 week years are 1 day shorter than the month years (364 − 365), 64.75%. The table shows the long years in a 400-year ...
This convention accounts for days in the period based on the portion in a leap year and the portion in a non-leap year. The days in the numerators are calculated on a Julian day difference basis. In this convention the first day of the period is included and the last day is excluded. The CouponFactor uses the same formula, replacing Date2 by Date3.
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Since in the Gregorian calendar there are 146,097 days, or exactly 20,871 seven-day weeks, in 400 years, the anchor day repeats every four centuries. For example, the anchor day of 1700–1799 is the same as the anchor day of 2100–2199, i.e. Sunday. The full 400-year cycle of doomsdays is given in the adjacent table.
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