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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:
Thus, for any date except February 29, the intervals between common years falling on a particular weekday are 6, 11, 11. See e.g. at the bottom of the page Common year starting on Monday the years in the range 1906–2091. For February 29 falling on a particular weekday, there is just one in every 28 years, and it is of course a leap year.
Mission control center's board with time data, displaying coordinated universal time with ordinal date (without year) prepended, on October 22, 2013 (i.e.2013-295). An ordinal date is a calendar date typically consisting of a year and an ordinal number, ranging between 1 and 366 (starting on January 1), representing the multiples of a day, called day of the year or ordinal day number (also ...
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).
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