Top Document: [sci.astro] Time (Astronomy Frequently Asked Questions) (3/9) Previous Document: C.07.1 When is Easter? Next Document: C.08 What is a "blue moon?" See reader questions & answers on this topic!  Help others by sharing your knowledge John Horton Conway (the Princeton mathematician who is responsible for "the Game of Life") wrote a book with Guy and Berlekamp, _Winning Ways_, that describes in Volume 2 a number of useful calendrical rules, including How to Calculate the Day of the Week, Given The Date, and Easter. Here's a brief precis of how to calculate Easter: G(the Golden Number) = Year_{mod 19} + 1 (never forget to add the 1!) C(the Century term) = +3 for all Julian years (i.e., if using the Julian Calendar) 4 for 15xx, 16xx } 5 for 17xx, 18xx } Gregorian 6 for 19xx, 20xx, 21xx } The general formula for C in a Gregorian year Hxx is C = H + [H/4] + [8*(H+11)/25] (brackets [] mean integer part) 1) The Paschal Full Moon is given by the formula (Apr 19 = Mar 50)  (11*G+C)_{mod 30} Except when the formula gives Apr 19 you should take Apr 18, and when it gives Apr 18 and G>=12 you should take Apr 17. Easter is then the following Sunday, since Easter always falls on the next Sunday that is _strictly later_ than the Paschal Full Moon. Example: 1945 = 7 mod 19, so G = 8 and we find for the Paschal Full Moon Mar 50  (886)_{mod 30} = Mar 50  22 = Mar 28. This happens to be a Wednesday (by Horton's "Doomsday" rule for Day of the Week, see below). Therefore, Easter 1945 took place on Sunday, April 1. Conway's "Doomsday" method for finding the day of the week, given the date, is needed for his Easter method. To every year there is a distinguished day of the week, which Conway calls the "Doomsday", D. In any year, if March 0 (the last day of February) falls on a particular DOW, then the following dates also fall on the same DOW: 4/4, 6/6, 8/8, 10/10, 12/12. Also 5/9, 9/5, 7/11, 11/7 (for which he has devised the mnemonic "I went to my ninetofive job at the SevenEleven. Note to nonUS readers: "SevenEleven" is the name of a ubiquitous chain of convenience stores.) In nonleap years, Jan 3 and Feb 0 (Jan 31) also fall on that DOW; in leap years, Jan 4 and Feb 1. Conway calls this DOW the "doomsday" for that year. For example, in 1995 Doomsday is Tuesday. Columbus Day (10/12) is two days after 10/10, a Tuesday, so 10/12 is a Thursday. All that remains is a rule for calculating the Doomsday for any year. In any century, this is done by taking the last two digits of the year, call them xx, dividing by 12 to get a quotient Q and remainder R. Divide R by 4 to get a second quotient Q2. Then this century, the Doomsday for that year is given by Wednesday + Q + R + Q2. In 1995, for example, we have 95/12 = 7 with remainder 11; 11/4 gives quotient 2; Wednesday + 7 + 11 + 2 = Tuesday (cf. above). In other years on the Gregorian calendar, one uses instead of Wednesday, the century day as follows: 16xx and 20xx: Tuesday; 17xx and 21xx: Sunday; 18xx and 22xx: Friday; 15xx, 19xx and 23xx: Wednesday. The cycle repeats over a 4 century period. If you need the DOW on the Julian calendar, the rules are the same except that the century rule is different: for a date in the year ccxx, use cc for the century day of week, where Sunday = 0. For example, October 4, 1582 (the last day of the Julian calendar in countries that followed Pope Gregory's institution of the Gregorian calendar) took place as follows: 82/12 = 6 remainder 10; 10/4 gives remainder 2; 6+10+215= 3, which is Wednesday. 10/10 was Wednesday, 10/3 was Wednesday, so 10/4/1582 (Julian) was a Thursday. The following day was October 15, 1582 (Gregorian). Again we can check: 6+10+2+Wed = Sunday. 10/10 was a Sunday (Gregorian) so 10/15/1582 (Gregorian) was a Friday. The nice thing about these algorithms is that they can easily be done in one's head with a little practice (OK, mod 19 for the Golden Number is a bit hairy for me, but I can still do it!). The DOW calculation is very useful if you are caught without a calendar, and it makes a good party trick. Additional information is available at <URL:http://quasar.as.utexas.edu/BillInfo/doomsday.html> and <URL:http://quasar.as.utexas.edu/BillInfo/ReligiousCalendars.html>. User Contributions:Comment about this article, ask questions, or add new information about this topic:Top Document: [sci.astro] Time (Astronomy Frequently Asked Questions) (3/9) Previous Document: C.07.1 When is Easter? Next Document: C.08 What is a "blue moon?" Part0  Part1  Part2  Part3  Part4  Part5  Part6  Part7  Part8  Single Page [ Usenet FAQs  Web FAQs  Documents  RFC Index ] Send corrections/additions to the FAQ Maintainer: jlazio@patriot.net
Last Update March 27 2014 @ 02:11 PM
