Dear Helios and Calendar People
The 146ths and 244ths can be paired up to form 73rds and 122nds that are
normally of constant length.
I've already suggested the 122nds to Victor, where each 122nd has 3 days
except every 161st 122nd which has one day less. Giving a 161-year cycle
with mean year 365 39/161 days (365.242236 days)
For the 73rds, each has 5 days except every 301st, which has one day
more.
Giving a 301-year cycle mean year of 365 73/301 days (365.242525 days).
The 17ths cannot be so paired, because 17 is an odd-number.
Karl
10(08(27
-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:
CALNDR-L@...] On Behalf Of Helios
Sent: 21 May 2009 14:47
To:
CALNDR-L@...
Subject: Re: Alternating Periodic Sequences
I now count three cases in which there is an endless repetition of the
same
yerm. Quite surely these are the only possibilities of this scheme.
17ths = 21, 22, 21, 22, 21, 22, 21, 22, 21, ... ( 33 cells )
146ths = 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, ... ( 301 cells )
244ths = 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, ... ( 161 cells )
To calculate the mean yerm
mean yerm of 17ths = 1 / [ ( 731 / Y ) - 2 ]
mean yerm of 146ths = 1 / [ 2 - ( 730 / Y ) ]
mean yerm of 244ths = 1 / [ ( 732 / Y ) - 2 ]
or ( C = cell )
mean yerm of 17ths = 1 / [ ( 43 / C ) - 2 ]
mean yerm of 146ths = 1 / [ 2 - ( 5 / C ) ]
mean yerm of 244ths = 1 / [ ( 3 / C ) - 2 ]
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