From: mjd@saul.cis.upenn.edu ("[*] Thomas Pynchon's Little Brother")
Newsgroups: talk.bizarre,alt.folklore.computers
Subject: Re: Top tips
Date: 18 Aug 92 22:02:41 GMT
Followup-To: alt.folklore.computers
Organization: Eaters of Wisdom
In-reply-to: tskelly@ccvax.ucd.ie's message of 17 Aug 92 09:12:43 GMT

In article <1992Aug17.091243.49502@ccvax.ucd.ie> tskelly@ccvax.ucd.ie writes:
>   Oh, by the way, you'll have to eat 366 apples for a leap year -
>   that's every fourth year if the year number is divisible by 4 except
>   if it's a century year, e.g., the year 2000.

Bless you.  2000 IS a century year.

    There are approximately 365.2422 days in a mean solar year.  Good
approximations to 365.2422 include, in order of accuracy, 365 1/4, 365
8/33, and 365 97/400.

    To construct an intercaltaion schedule, one finds a fraction whose
value is close to .2422; the denominator of this fraction is the length
of the intercalation cycle, in years, and the numerator is the number of
intercalations (`leap days') to insert in this period.  For example, the
fraction (1/4) suggests an intercalation schedule of 1 intercalation
every four years; the Julian calendar used such an intercalation
schedule.  A more accurate schedule is to have 8 intercalations every 33
years; the Medieval Arabs did this for a time.

    The Gregorian calendar, in use in most of Europe since the 16th
Century and in the Colonies since 1752, schedules 97 intercalations per
400 years, thus adding, on the average, .2425 days to each calendar
year.  This is about .0003 days per year too much, and so the Gregorian
Calendar slips ahead with respect to the seasons by one day every 3300
years or so.

Given that the Gregorian Calendar schedules 97 intercalations per 400
years, one can easily remember that the rule is:

	Every fourth year has an intercalation,
	except those century years 
		not also divisible by 400.    
	(100 - (4-1)) = 97; 97 / 400 = 0.2425 .

Some people have suggested that the rule be
	Every fourth year has an intercalation, 
	except those century years not also divisible by 400,
	but nevertheless including those that are also divisible by 4000.
	(1000 - (40-(10-1)) = 967;  967 / 4000 = 0.24225 .
	

This would add back one intercalation every 4000 years (for example, the
year A.D. 4,000 would be a leap year, although it is not in the present
Gregorian Calendar), yielding an average of 365.24225 days per calendar
year.  Under this calendar the calendar year would lose a day on the
seasons every 20,000 years or so.

    Nevertheless, it seems that the existing rule is too complicated,
since people always forget it, and adding a third-order exception would
only confuse matters further.  I therefore call for a switch to the 8/33
system.  To decide if a year is a leap year, divide the year by 33 and
find the remainder.  If this remainder is a positive multiple of 4, the
year is a leap year.  Under this schedule, 1980, 1984, 1988, 1992, 1996,
2000, 2004, 2008, and 2012 will be leap years; this will give us a long
time to make the switch.  After 2012 the next intercalation will be in
2017.  This calendar gains a day only every 4500 years.

    I have directed discussion of this topic into
alt.folklore.computers, since they found this topic so interesting the
last time it came up there.



--

                And for to see, and eke for to be seye
Mark-Jason Dominus 	  			    mjd@central.cis.upenn.edu 
Newsgroups: talk.bizarre