
The Question
(Submitted April 01, 1997)
Any idea how Gauss formulated his method of determining Easter within 3 days
for any year of the Gregorian calendar?
The Answer
I'm not sure how Gauss derived his famous equation for the calculation of
Easter. In general, calculating the dates of festivals which are partially
defined in terms of astronomical events is not difficult. You have to
calculate how a very predictable and regular thing (the astronomical event)
combines with another very predictable and quite regular thing (a human
calendar  Julian, Gregorian, Jewish, Islamic, Mayan, ...). Churches and
other authorities have been calculating festivals well in advance for long
periods. (Often they introduce some simplification of the astronomical
event, such as considering the mean motion of a body, but that's fine 
they are in charge of the festival and can set up the rules for its
occurrence however they want to!). The achievement of Gauss was to come up
with such a simple formula for the calculation of Easter. (His formula can
be readily generalized to give the correct date in many different calendars
and during any desired range of years). I looked at a number of books on
Gauss to see if any had a detailed account of his work on the Easter
formula, but found nothing beyond references to his almost unequaled
ability to recognize patterns, upon which some of his other extraordinary
accomplishments in mathematics were founded. One book (by Schaaf, see
below) gave the following reference to Gauss's first publication of his
Easter work, which isn't in our library and I haven't had time to pursue:
Monatliche Correspondenz, August 1800, page 121.
The books I looked at were:
"Carl Friedrich Gauss, prince of mathematicians" by W.L. Schaaf, and
"Carl Friedrich Gauss, titan of science" by G.W. Dunnington.
There are several good web sites which discuss calendars.
Paul Butterworth
for the "Ask an Astrophysicist" team
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