Re: [math-fun] Weeks Between Easters
Dave: I'm not sure what or who you're responding to, but I didn't see anyone discussing anything but the standard algorithm for the date of Easter. This is a fixed mathematical function assigning to each Gregorian year (starting in 1583) a date in that year. As such, it has certain mathematical properties, which is all I saw anyone discussing. --Dan Dave Dyer wrote: << You're not taking into account "leap seconds", which are necessary to keep midnight at midnight, and the gradual recession of the moon, which is gradually changing the length of the lunar month. For example, over the quoted span of 5 million years, leap seconds at the rate of one a year would result in 57 fewer days between now and then. .. exposing the futility of calculations about dynamic systems over these time scales. You're really doing the equivalent of arguing how many angels can dance on the head of a pin.
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
Here's John Conway's rendering of the algorithm for the date of Easter (courtesy of http://quasar.as.utexas.edu/BillInfo/ReligiousCalendars.html): The following rules, due to John Conway, allow you to calculate the date of Easter for any year on the Gregorian or Julian calendar. First, calculate the *Golden Number *G. This is fundamental to the calculation of both the date of Easter and the Date of Rosh Hashanah. It is intimately connected with the Metonic Cycle. For any year Y, the Golden Number is defined as G = Remainder(Y|19) + 1. *Don't forget to add the 1!!!* For example, in the year 1996, the Golden Number was 2 because Remainder(1996|19)=1. Next, compute S, where S=Remainder((11G + C)|30), and in the 20th through the 22nd century, C=-6. A table for C and a rule for calculating C are given below. *Important Note: * S must be nonnegative. If you get a negative number, add an appropriate multiple of 30 to make S between 0 and 29 (inclusive). For example, in 1996, S=Remainder((22-6)|30)=16. Then, the *Paschal Full Moon* falls on the date (March 50=April 19) - S, except that if this formula gives April 19, the Paschal Full Moon falls on April 18 instead, and if the rule gives April 18, *and* if G is greater than or equal to 12, the Paschal Full Moon falls on April 17. Then Easter is the first Sunday that falls *after* this date (if the date you calculated is a Sunday, then Easter is one week later). You can use Conway's Doomsday Rule for Day of the Week to determine the day of the week of the Paschal Full Moon. For example, in 1996, the Paschal Full Moon falls on April 19-S = April 19-16 = April 3. Conway's Doomsday Rule<http://quasar.as.utexas.edu/BillInfo/doomsday.html>tells us that April 3 is a Wednesday that year, so Easter is the *next* Sunday, or April 7. Here's how to determine C: - In all Julian Calendar years, C=+3. This gives us Julian Easter. Note that Julian (Orthodox) Easter may not fall on the same actual day as Gregorian Easter, because the rule for Gregorian Easter is different. Julian Easter is celebrated by the Orthodox Church. - In years 15xx, 16xx of the Gregorian Calendar, C=-4 (note the negative sign). - In years 17xx, 18xx of the Gregorian Calendar, C=-5 - In years 19xx, 20xx, 21xx of the Gregorian Calendar, C=-6 For Gregorian dates in other centuries, where the year is Y=Hxx, calculate C as follows: - C = [H/4] + [8(H+11)/25] - H (note the square brackets!)
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Dan Asimov -
victor miller