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For example, September and December correspond, because 1 September falls on the same day as 1 December (as there are precisely thirteen 7-day weeks between the two dates). Months can only correspond if the number of days between their first days is divisible by 7, or in other words, if their first days are a whole number of weeks apart.
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:
The doomsday's anchor day calculation is effectively calculating the number of days between any given date in the base year and the same date in the current year, then taking the remainder modulo 7. When both dates come after the leap day (if any), the difference is just 365 y + y / 4 (rounded down).
Microsoft Excel uses number of days (with decimals, floating point) since January 1, 1900. All these systems present time for the user using traditional units. None of these systems is strictly linear, as they each have discontinuities at leap seconds .
Subtract the weekday number from the ordinal day of the year. Add 10. Divide by 7, discard the remainder. If the week number thus obtained equals 0, it means that the given date belongs to the preceding (week-based) year. If a week number of 53 is obtained, one must check that the date is not actually in week 1 of the following year. Formula
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The Long-Sabbath Calendar, by Rick McCarty (1996), extends to 36 hours the last Saturday of the year and the subsequent first Sunday of the new year. Seventy-two hours are thereby covered with two weekdays instead of the usual three, which shortens the year to 364 calendar days without interrupting the weekday cycle.
The number of days between two dates, which is simply the difference in their Julian day numbers. The dates of moveable holidays, like Christian Easter (the calculation is known as Computus) followed up by Ascension Thursday and Pentecost or Advent Sundays, or the Jewish Passover, for a given year. Converting a date between different calendars.