Dear Mac,
Many thanks for your message...
> If you can find the time, this mailing list member ...
> would much appreciate details about how you derived the
> list of dates.
I am glad you asked this question and equally glad
that Patrick Powers has supplied the algorithm!
I had it in my head that this algorithm was first
published in Butcher's Ecclesiastical Handbook in
1876 and I give this as the (incorrect) citation in
one of my sets of student exercises.
When I Googled "Butcher's Ecclesiastical Handbook"
all I got was a couple of references to plagiarised
versions of my exercises. Tee hee! I wouldn't have
discovered my error had you not prompted me to look
for something else!
I first saw the algorithm in Meeus and now see that he
gives the correct citation "Butcher's Ecclesiastical
Calendar, 1876".
There is a reasonably complete account in:
http://en.wikipedia.org/wiki/Computus
One of my favourite books is "Calendrical Calculations"
by Edward M. Reingold and Nachum Dershowitz. It is
full of good jokes!
This book almost attributes the algorithm to Clavius
and Lilius (key figures in the Gregorian reform of
the calendar).
Once you have implemented the algorithm you can then
have fun determining the length of the cycle. A
naive approach is to start at an arbitrary year and
look for the next year that has Easter on the same
date. You then look to see whether the two following
years match too. They won't! So you look for the
next matching year and keep going until you repeat
indefinitely. Your program will take a long time!!
"Calendrical Calculations" says:
The dates of Easter repeat only after 5,700,000
years, the least common multiple of the 19-year
Metonic cycle, the 400 years it takes for the
Gregorian calendar to return to the same pattern
of days of the week, the 4000 years it takes for
the Gregorian leap-year corrections to add up to
30 days, and the 9375 years it takes for the
correction to the Metonic cycle to amount to
30 days.
If you get to understand the ecclesiastical moon
and the ecclesiastical vernal equinox you will
wonder whether the algorithm works at all. In
fact it does a remarkably good job at predicting
"the first Sunday after the first full moon after
the vernal equinox" which is often given as the
formal definition of Easter.
What I should like to know is what is meant by
Sunday! Sunday begins at different times in
different places. Could it mean Sunday as it
is timed at the longitude of Rome?
Enough from me!
Frank
---------------------------------------------------
https://lists.uni-koeln.de/mailman/listinfo/sundial
