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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 determination of the day of the week (1 January 2000, Saturday) the day of the month: 1 ~ 31 (1) the month: (6) the year: (0) the century mod 4 for the Gregorian calendar and mod 7 for the Julian calendar (0). adding 1+6+0+0=7. Dividing by 7 leaves a remainder of 0, so the day of the week is Saturday. The formula is w = (d + m + y + c) mod 7.
The 8-day week with 21 hours per "day" is a general concept for full week coverage where the 168 hours of the week are grouped differently. It can be used as a base for several shift plans, e.g. three 7-hour shifts per day where every employee works six shifts for a total of 42 hours per week, but to get whole days off groups work alternating ...
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).
is the number of days since Jan 1st, 2000 12:00. is the Julian date; 2451545.0 is the equivalent Julian year of Julian days for Jan-01-2000, 12:00:00. 0.0008 is the fractional Julian Day for leap seconds and terrestrial time (TT). TT was set to 32.184 sec lagging TAI on 1 January 1958. By 1972, when the leap second was introduced, 10 sec were ...
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 ...
They also find an asymptotic formula +, where , and . It has been estimated that the observable universe contains around 10 80 atoms, far fewer than the number of possible legal positions of regular board size (m=n=19).
If the mean daily temperature is above 65 °F, the mean degrees Fahrenheit above 65 °F are counted as the cooling degree day. The heating and cooling degree days are tallied separately to calculate monthly, seasonal, and yearly total heating and cooling degree days. Heating and cooling degree days closely correlate with heating and cooling demand.