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Subject:
Recurring calendar years
Category: Science Asked by: click17-ga List Price: $5.00 |
Posted:
12 Aug 2004 09:08 PDT
Expires: 11 Sep 2004 09:08 PDT Question ID: 386963 |
I was recently informed that a 1973 Calendar can be used again in 2007 because days and dates are the same. Is this true and does it work for most years, i.e a 74 calendar being exactly the same as 2008. |
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There is no answer at this time. |
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Subject:
Re: Recurring calendar years
From: touf-ga on 12 Aug 2004 09:21 PDT |
A standard 365 day year has 52 weeks plus one day. (52 x 7 = 364). So, a given year is offset by one day from the year preceding it. The only fluke in this system is when leap years are involved, because then the following year is offset by 2 days. Anyway, because of the leap year fluke, it's not a simple 34 year correlation. (If we didn't have leap years, you could re-use a calendar every 7 years) Instead, you have two asynchronous cycles; a four-year leap year cycle and a 7 year "daily offset" cycle. Plus on top of this, you have one more fluke -- every year ending in 00 does not have a leap year, with the exception where the first 2 numbers are divisible by 4. This means that 1700, 1800, and 1900 had no leap year, but 2000 did. So actually, you have three asynchronous cycles: leap year; daily offset; century leap year; Eventually, you get them all to line up and calendars repeat themselves, but it's not a simple one to one mathematical correlation. To answer your question, a 1974 definitely cannot be used as a 2008 calendar, because 2008 is a leap year, while 1974 is not. However, up through Feb 28, the calendars are the same. |
Subject:
Re: Recurring calendar years
From: nelson-ga on 12 Aug 2004 16:11 PDT |
There are only 14 possible calendars. You have one set of seven calendars for each possible day that Jan. 1 can fall on (Sunday through Saturday) for non-leap years. You then have another set of seven calendars for leap years. |
Subject:
Re: Recurring calendar years
From: pinkfreud-ga on 12 Aug 2004 16:17 PDT |
This site may interest you: http://www.koshko.com/calendar/calendar-lookup-gregorian.shtml |
Subject:
Re: Recurring calendar years
From: jml104-ga on 17 Aug 2004 12:05 PDT |
Yes, the 1973 and 2007 calendars are the same. As already noted, this 34-year recurrence doesn't always work. The only absolute guarantee is that a calendar will work again every 400 years. See below for an explanation. If you want to reuse your calendars sooner than that, calendars usually recur every 28 years, except when the 28 year period contains a year (like 1700, 1800, or 1900) that is divisible by 100 but not by 400. Again, see below for an explanation. Two years have the same days and dates when two conditions are met: (1) Jan 1 of the two years are on the same day, and (2) the two years are either both leap years or both not. Condition (1) occurs when the number of days between Jan 1 of one year and Jan 1 of the other is a multiple of 7. We tend to think of leap years as following a 4-year cycle, but in actuality they follow a 400-year cycle: a leap year every 4 years, except when a year is divisible by 100 but not by 400. Thus there are 97 leap years every 400 years. So the number of days in 400 years is 365 x 4 + 97 = 146097, which is a multiple of 7. So every 400 years both conditions are satisfied, and the calendars match. If it weren't for the "divisible by 100 but not by 400" rule, then leap years would be a four year cycle, and days of the week would be a seven year cycle, so the two would match every 4 x 7 = 28 years. That's why if a 28 year period doesn't contain one of those "divisible by 100 but not by 400" years, then the calendars will repeat. So 1973 is the same as 2001, 1974 is the same as 2002, 1975 is the same as 2003, 1976 as 2004, etc up until 2072 (which is NOT the same as 2100). |
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