I was looking at Omid K. Rad's implementation of calendar, and have a
few comments on calculating leap years.
1. The implemented algorithm uses a 128 year period, although the
comments say it uses a 2820 year period. While I need to ask for this
discrepancy be resolved, it is important to understand that the 128
year period and the 2820 year period only differ once every 2820
years. In other words, the current implementation does not differ from
the 2820 year method until year 3294 A.P (or H.S.).
2. However, it seems to me that the 2820 Birashk method -- the one
with 21 128 year period and one 132 year period -- will start showing
discrepancies with the observed norouz as early as 1788 A.P. The
reason, is that the Birashk method tries to be in sync with the 128
year method as much as possible, and adjust the extra leap year at the
end of 2820 years. However, the earth does not care about this
assumption, and will rotate around the sun constantly (see caveat
below), unless Birashk has considered the variation of length of years
The correct 2820 year formula will then be: (based on the assumption
that there are 683 evenly spread leap years in 2820 years, and also
aligning the leap years with the largest extent of years around today)
Here, variable year refers to year in A.P or H.S.
Ordak's 2820 year method:
bool isLeap2820ODC = ((683*year+542) % 2820) < 683;
in comparison to:
Birashk's 2820 year method:
bool isLeap2820Birashk = ((year % 2820) == 474) ||
(((31 * ((year+2345) % 2820)) % 128) > 96);
The discrepancies will be in:
years that Ordak considers leap but not Birashk
603, 731, 859, 1787, 1915, 2043, 2171, 2299, 2427, 2460, 2555, 2588,
2683, 2716, 2811, 2844, 2939, 2972, 3067, 3100, 3133, 3195, 3228,
3261, 3295
and
years that Birashk considers leap but not Ordak
602, 730, 858, 1788, 1916, 2044, 2172, 2300, 2428, 2461, 2556, 2589,
2684, 2717, 2812, 2845, 2940, 2973, 3068, 3101, 3134, 3196, 3229,
3262, 3294
Caveat:
According to:
http://scienceworld.wolfram.com/astronomy/TropicalYear.html
The length of year is decreasing each year. According to graphs in
http://www.angelfire.com/dc2/calendrics/
The real length of vernal equinox year (Iranian year) is increasing
each year (from 351 BC to 3175 A.D.) According to Iranian tradition,
vernal equinox should happen before noon (I think it means
astronomical noon). So, there is not much we can do with simple
algorithms other than trying to approximate the real world, and
understanding the fact that ALL calendar algorithms are only
APPROXIMATIONS.
--
ODC
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