It's 2010 and you have a full calendar for that year. You decide to keep your calendars until you have a full set from which you can choose one that will work for any given year whatsoever. What will be the final calendar year that will complete your collection?

I believe Justin's reasoning is correct, although of course the 'perpetual' calendar will be correct only as to the 'Gregorian' date.

The lunar cycle repeats about every 49 months, so in theory would repeat after 49 years; however the lunar phase quite often falls sufficiently close to midnight for the exact dates of the equnoxes etc. to be unpredictable: such events will occur at the new moons of 28 September 2057, 4 September 2089 and 7 August 2097, the Winter Solstice of 2021, Vernal Equinox of 2051, and Vernal Equinox of 2084.

The date of Easter is a related, but additional complication. 'Gregorian' Easter can fall on 35 possible dates - between March 22 and April 25 inclusive. It last fell on March 22 in 1818, and will not do so again until 2285. It fell on March 23 in 2008, but will not do so again until 2160. Easter last fell on the latest possible date, April 25, in 1943 and will next fall on that date in 2038. However, it will fall on April 24, just one day before this latest possible date, in 2011. The cycle of Easter dates repeats after exactly 5,700,000 years.

Similarly, the Chinese Year, Metal Tiger, will recur in 2070, but the first lunar month will commence on 11th February - in contrast, the current lunar year started on 14th February.

So perhaps the true solution is the collection will never be really complete - no doubt a source of considerable comfort for calendar makers!

 

Posted by broll on 2010-09-17 14:40:58