In what follows we shall consider the distribution of the date of Easter in the Gregorian calendar. Here things are more complicated. When one looks at the frequency of the different calendar dates on which Easter Sunday occurs, some remarkable facts are discovered.
Figure 59.a shows the frequencies as a function of the date for the 1000 successive Easter dates of the years 2000 to 2999. Note the regular occurrence of the maxima. During the third millennium, Easter occurs more often on March 31, and on April 5, 10, 16 and 21, than for instance on April 2, 7, 13 and 18. May we expect that the frequency curve will have the regular shape of the dashed line if much more years are taken into consideration?
To investigate this, let us consider several more millennia — see Table 59. B. In Figure 59.b the distribution curve for the years 2000-2999 is given again, together with that for the next 1000 years. It is clearly visible that in this latter period the maxima take place somewhat earlier in the year than during the period 2000-2999. The maximum of April 5, for instance, now occurs on April 4. After another 1000 years, the displacement again amounts to one day, as is seen in Table 59.B — see the numbers printed in bold.
After approximately 6000 years the maxima will fall again on the initial dates, so here we have a periodicity of about 6000 years for what concerns the position of the maxima in the distribution.
The last column of Table 59. B gives the distribution of the dates of Easter in the period 2000-7999. This is represented in Figure 59.c. For the dates March 28 to April 17, we now have indeed a curve that is more or less flat, with a mean frequency of 200 (per 6000 cases). The frequencies for March 22, 23, ... 27 are equal to 1/7, 2/7, ... 6/7 of this amount, respectively.
The peak with value 231 on April 19 is disturbing, however. During the period 2000-7999, Easter occurs more frequently on April 19 than on any other date. (Surprisingly, this is not the case during the shorter interval 2000-2999, however! See the second column of Table 59. B).
Even if a much longer period is considered, that remarkable peak persists on April 19. Certainly it is not interesting for us to know on what date Easter will fall in that distant future. But our curiosity is a mathematical one only, and to perform a statistical investigation about the distribution of Easter Sunday as calculated by the current ecclesiastical rules, a large number of years must be taken into consideration.
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