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Re: Pairing: Alternating Periodic Sequences

by Brillig :: Rate this Message:

And the 122nds can be further paired to make 61sts.

Here is a picture of one Metonic cycle crocheted out of such 244ths. The color changes after each run of 161 cells. The row joins the previous row at the start of a new year, so there are 19 rows making up the Metonic cycle.

http://the-light.com/cal/vecrochet0.jpg

This was crocheted using single stitches and double stitches alternating with each other. For more detail, consult the archives.

Victor

On Thu, May 21, 2009 at 11:14 AM, Palmen, KEV (Karl) <karl.palmen@...> wrote:

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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