Mac Oglesby asked how one might begin to calculate the statistics for Easter as recently indicated by Frank.
Now, I always thought that the algorithm which applies to any year since the introduction of the Gregorian Calendar, and which in Britain was in September 1752 is as given below. For those uninterested in its programming it can (I believe!) be found as a calculator for any year at: http://www.ely.anglican.org/cgi-bin/easter Whether it's correct I do not know but Frank indicated an Easter Cycle of 5,700,000 years and so to check, I entered the year 5702008. It yields Ash Wednesday 6 February 57002008 Palm Sunday 16 March 57002008 Good Friday 21 March 57002008 Easter Day 23 March 57002008 Ascension Day 1 May 57002008 Pentecost 11 May 57002008 Trinity Sunday 18 May 57002008 Advent Sunday 30 November 57002008 which is, as Frank points out, the same as for 2008, viz: Ash Wednesday 6 February 2008 Palm Sunday 16 March 2008 Good Friday 21 March 2008 Easter Day 23 March 2008 Ascension Day 1 May 2008 Pentecost 11 May 2008 Trinity Sunday 18 May 2008 Advent Sunday 30 November 2008 Patrick ___________________ Here's the algorithm that I think is used by the calculator: We refer to the year number as y, and use it to calculate the Golden number, g: g = y mod 19 + 1 Next we calculate the date of the Paschal full moon, that is, the full moon which Easter is the Sunday after. This is done in several stages. First we calculate two values called the solar correction, s, and the lunar correction, l. s = (y - 1600) div 100 - (y - 1600) div 400 l = (((y - 1400) div 100) × 8) div 25 Next we calculate an uncorrected date for the Paschal full moon, p'; then we apply a minor correction to get the exact date, p, as the number of days after 21st March. p' = (3 - 11g + s - l) mod 30 if (p' == 29) or (p' == 28 and g > 11) then p = p' - 1 else p = p' Now we need to determine the date of the following Sunday. First we calculate the 'Dominical number', d: d = (y + (y div 4) - (y div 100) + (y div 400)) mod 7 Note that this is the number from which the Dominical letter is determined, and we calculate d', which is the date on which the first Sunday of the year falls: d' = (8 - d) mod 7 We already have p, the date of the Paschal full moon in days after 21st March. Next we determine p'' the first date in the year which falls on the same day of the week as the Paschal full moon. First we determine the 'day number' of p with respect to 1st January. This is 31 + 28 + 21 + p = 80 + p. (Note that we can disregard possible occurences of 29th February, because the calculation of d has already taken this into account, and we shall see that these two values will cancel each other out.) p'' is then given by the formula: p'' = (80 + p) mod 7 = (3 + p) mod 7 The difference between d' (the first Sunday in the year) and p'' (the day of the week when the Paschal full moon falls) gives us the number of days that must be added to p to get the date of the following Sunday, which is Easter Day. There is one further subtlety. This number must lie in the range 1-7, rather than 0-6, since Easter is not allowed to fall on the same day as the Paschal full moon. We first determine x', the difference between d' and p'': x' = d' - p'' = (8 - d) mod 7 - (3 + p) mod 7 = (8 - d - (3 + p)) mod 7 = (5 - d - p)) mod 7 To force this to lie in the range 1-7, we calculate x x = (x' - 1) mod 7 + 1 = (4 - d - p)) mod 7 + 1 We can now calculate e, the number of days Easter falls after 21st March: e = p + x or e = p + 1 + (4 - d - p) mod 7 In other words Easter Day is: if e < 11 then (e + 21) March else (e - 10) April _______________- --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
