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Topic: Julian = Gregorian (Read 476 times) |
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ThudnBlunder
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Julian = Gregorian
« on: Oct 8th, 2003, 6:43pm » |
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In order to effect the change from the old Julian calendar to the new Gregorian calendar, in 1582 Pope Gregory XIII decreed that the Julian date of Thursday October 4th would be immediately followed by the Gregorian date of Friday October 15th.
Given that in the Julian calendar all years evenly divisible by four are leap years, while in the Gregorian calendar years evenly divisible by 100 are not leap years unless they are also evenly divisible by 400, in what year after 1582 will the Julian and Gregorian calendars first be in agreement?
(Edit: That is, when will they both show the same day of the week?)
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| « Last Edit: Oct 9th, 2003, 3:15pm by ThudnBlunder » |
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aero_guy
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Re: Julian = Gregorian
« Reply #1 on: Oct 9th, 2003, 1:38pm » |
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Here is my analysis:
3/4 of every 400 years cause a change of one day between the calendars. Unfortunately that is one extra day in the Julian calendar that is not in the Gregorian, thus causing them to move further apart. So, they are currently 11 days off, and they need to change by 365-11=354 days. 4/3 of this is 472 hundred years. The first possible change is in 1600, but as this is divisible by 400, there is no change. Thus we add 47200 to 1700 and subtract 100 as that last year is the year there was no change, it actually reached the same day 100 years earlier (effect of applying fractions to dates).
So, the answer is the year: 48800, or in reality never as they will definitely have created a new dating system by then.
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ThudnBlunder
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Re: Julian = Gregorian
« Reply #2 on: Oct 9th, 2003, 3:13pm » |
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The question was intended to mean 'When will they both show the same day of the week?' I have therefore reworded it.
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aero_guy
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Re: Julian = Gregorian
« Reply #3 on: Oct 13th, 2003, 10:21am » |
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Hmm, that doesn't seem to make sense. Won't they both show the same day the first day of the change. Both calenders say it should be Friday.
Perhaps you mean, "When will the day of the week for a given date be the same in each calendar?"
This will be a very different questions since, if the answer is say Friday June 6th, the actual time that these two Friday June 6ths occur will be different.
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ThudnBlunder
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Re: Julian = Gregorian
« Reply #4 on: Oct 13th, 2003, 10:33am » |
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Quote:| Hmm, that doesn't seem to make sense. Won't they both show the same day the first day of the change. Both calenders say it should be Friday. |
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In 1582, the Gregorian calendar was started 10 days ahead of the Julian calendar; October 5th of the Julian was the same day as October 15th of the Gregorian. The question is "When does this difference first become zero (mod 7)?"
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