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Saturday, 02 April 2005 |
Is there anything that mathematicians DON'T do? Nope!
Gauss developed an algorithm to determine on which date Easter falls given a year:
Let y represent the year of interest. Let mod(x,y) be defined as the remainder when x is divided by y. For the twentieth century, let M=24, and for the 21st century (today), let M=25. Let N=5.
E(y) = Mod(19 Mod(y, 19) + M, 30) + Mod(2 Mod(y, 4) + 4
Mod(y, 7) + 6 Mod(19Mod(y, 19) + M, 30) + N, 7)
The result E(y) is the number of days AFTER March 22 on which Easter Sunday lies for year y. E(y) should range from 0 to 35, since Easter can fall between March 22, and April 26(?). The above is Gauss' algorithm! The algorithm is even correct for the weird March Easter years: E(2005)=5 (March 27), E(2002)=9 (March 31). According to this algorithm (as well as astronomers), the next Easter in March will occur in 2008...even earlier in March than it was this year, ugh: E(2008)=1 (March 23).
Not all is rosey though. A computer programmer recently debunked Gauss' algorithm (I can't recall his name). The algorithm has an obvious failure for y=1981. What happens?
On this programmer's site he refers to another researcher that patched up the algorithm. This algorithm must be the algorithm commonly used today, although Gauss' algorithm will probably be correct for the rest of our lives. My guess is this failure results from a switching of the parameter N. This parameter changes every century. My source does not provide the value for N in 1981. Gauss calculated values for M and N up to the 25th century.
Of course the geniuses at Wolfram Research included a function in Mathematica that calculates the month and day of Easter for any given year, based on the patched algorithm.
Source: http://members.tripod.com/~american_almanac/gauss.htm |
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Last Updated ( Sunday, 02 October 2005 )
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