Eikonal Blog

2011.03.28

Universal calendars

Filed under: mathematics — Tags: — sandokan65 @ 16:59

According to Daniel Zwillinger (“Standard Mathematical Tables And Formulae”; 31st ed; 2003; Recipe 10.3.2, but formula 10.3.1) the specific date maps to the following day of the week (in the Gregorian calendar):

    W = \left(k + [2.6 m -0.2] - 2 C + Y + \left[\frac{Y}4\right] + \left[\frac{C}{4}\right]\right) \ (mod \ 7)

Here:

  • W = day of the week (0=Sunday to 6=Saturday)
  • k = the day in the month (= 1 to 31)
  • m = the month (1=March to 12=February)
  • C = century minus one (1997 \rightarrow C=19, 2005 \rightarrow C=20)
  • Y = the year inside century, where the years begining is march 1st (so, 1997 maps to Y=97 except for January and February when it goes to Y=96
  • and [...] is the floor function (the largest integer part of the enclosed real number).

For example, today is March 29th, 2011. That would be:

  • The day’s order number inside this month: k=29
  • This month is, according to Roman counting, the first one in the year: m=1
  • The year inside the century is Y=11 (since it is past February)
  • The century is 21st, so C=21-1 = 20
  • So: [2.6 m -0.2] = [2.6 -0.2] = [2.4] = 2, [Y/4] = [11/4] = [2.25] = 2, [C/4] = [20/4] = 5
  • and W = \left(29 + 2 - 2 \times 20 + 11 + 2 + 5\right) \ (mod \ 7) = (49-40) \ (mod \ 7) = 9 \ (mod \ 7) = 2 i.e. today is Tuesday (correct).

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