Saw-tooth Square Diagram

classic Classic list List threaded Threaded
5 messages Options
Reply | Threaded
Open this post in threaded view
|

Saw-tooth Square Diagram

Helios
Dear Calendar People,

The Saw-tooth Square Diagram is the partitioning of 1377 months into 41 parts, hexaseasonal yerms or odd leap month periods.

The average row has 153 months.

The average short row has 135 months. Short rows combined in unlike pairs make a Double Tritos; 2*I - 2*S. The longer of the short rows has 136 months equal to 11 years.

There are 4 non-center long rows or Common Long rows that combined in like pairs equal 27 years. This is a barely possible eclipse; 32*S - 19*I.

33 35 33 33 33
35 33 33 35
33 33 35 33 33
33 35 33 33
35 33 33 33 35
33 33 35 33
33 33 35 33 33
35 33 33 35
33 33 33 35 33

Reply | Threaded
Open this post in threaded view
|

Re: Saw-tooth Square Diagram

Helios
Dear Calendar People,

I am trying an html correction

33 35 33 33 33
- 35 33 33 35 -
33 33 35 33 33
- 33 35 33 33 -
35 33 33 33 35
- 33 33 35 33 -
33 33 35 33 33
- 35 33 33 35 -
33 33 33 35 33

Reply | Threaded
Open this post in threaded view
|

Re: Saw-tooth Square Diagram

Karl Palmen - UKRI STFC

Dear Helios and Calendar People

 

I don’t see any point of such an arrangement. A more useful arrangement would be rows of a whole number of years.

 

This can be done by noting that ‘33’ is 2 & 2/3 year and ‘35’ is 2 & 5/6 years. One can count the number of hexaseasons, each falls short of 3 years, then ‘35’ counts as 1 and ‘33’ counts as 2. Then a whole number of years occurs, whenever this total of 1s and 2s is divisible by 6.  I do this with

 

33 35 33 33 33 35 33

33 35 33

33 35 33 33 33 35 33

33 35 33 33 33 35 33

33 35 33 33 33 35 33

33 35 33

33 35 33 33 33 35 33

 

3 times to form a 334-year cycle.

 

33 35 33 33 33 35 33  (12)

33 35 33 33 35 33 33  (12)

33 35 33 33 35 33 33  (12)

33 35 33 33 35 33 33  (12)

33 35 33 33 35 33 33  (12)

35 33 33 33 35 33 33  (12)

35 33 33 33 35 33 33  (12)

35 33 33 35 (6)

33 33 33 (6)

35 33 33 35 (6)

33 33 33 (6)

35 33 33 35 (6)

33 33 33 (6)

35 33 33 35 (6)

33 33 35 33 33 33 35 (12)

33 33 35 33 33 33 35 (12)

33 33 35 33 33 35 33 (12)

33 33 35 33 33 35 33 (12)

33 33 35 33 33 35 33 (12)

33 33 35 33 33 35 33 (12)

33 35 33 33 33 35 33 (12)

 

The 33 33 33 in the middle of each Metonic cycle forms an Octaeteris of 8 years. The Metonic cycle can split into two parts of a whole number of years if and only if this Octaeteris begin on a new year. This occurs near the middle of the 334-year cycle. There it splits into an octaeteris of (33 33 33) and an 11-year cycle of 35 33 33 35. Every whole year period must have an even number of 35s and the difference between the number of 33s and 35s must be divisible by three. A similar arrangement would occur with the Grattan-Guinness cycle as suggested in previous note.

 

 

Karl

 

15(01(27

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Helios
Sent: 13 July 2015 05:29
To: [hidden email]
Subject: Re: Saw-tooth Square Diagram

 

Dear Calendar People,

I am trying an html correction

33

35

33

33

33

-

35

33

33

35

-

33

33

35

33

33

-

33

35

33

33

-

35

33

33

33

35

-

33

33

35

33

-

33

33

35

33

33

-

35

33

33

35

-

33

33

33

35

33

 


View this message in context: Re: Saw-tooth Square Diagram
Sent from the Calndr-L mailing list archive at Nabble.com.

Reply | Threaded
Open this post in threaded view
|

Re: Saw-tooth Square Diagram

Helios
Dear Karl and Calendar People,

Instead of inserting odd leap month periods, I've tried 33m and 34m into the arrangement. Now the important eclipses DO reveal themselves by rows.

rows 4th and 6th = Tritos
middle 7 rows = Triad ( triple inex )

34 33 34 33 34
34 33 34 33
34 33 34 34 33
34 33 34 34
33 34 33 34 33
34 34 33 34
33 34 34 33 34
33 34 33 34
34 33 34 33 34 = 1377 months

41 is a centered square number or saw-tooth square. Each row averages to 153 months.

Reply | Threaded
Open this post in threaded view
|

Re: Saw-tooth Square Diagram

Karl Palmen - UKRI STFC
Dear Helios and Calendar People

Thank you Helios for your reply.

With 33 & 34, I prefer

34 33 34 33 34
34 33 34 33 34 33 34
34 33 34 33 34
34 33 34 33 34 33 34
34 33 34 33 34
34 33 34 33 34 33 34
34 33 34 33 34 = 1377 months = 334/3 years

Each row is a yerm-like period.
The rows are arranged into a yerm-like period.
Each long row is a Metonic cycle.
The middle 5 rows = Triad ( triple inex )
The last 3 of any row and the first 1 of next row = Tritos
Also, the last 1 of any row and the first 3 of next row = Tritos.


I look into whole-year rows.
All 7 in the Metonic cycle begin on different months:
01 10 06 03 11 08 04 and so the Metonic cycle can never be split into shorter periods of a whole number of years no matter what month it begins, unlike the cycle of 33 35 33 33 33 35 33, which can be split 33 33 33 | 35 33 33 35.
This ensures every whole-year row has at least 19 years. Some are longer than 19 years because the first 7 have 5 34s instead of the usual 4 34s.
If a row has 3*M 33s and 4*N 34s, then it has 8*M + 11*N years.


Finally. I mention that the shorter cycle of

34 33 34 33 34
34 33 34 33 34 33 34 = 403 months = 391/12 years

is one 1/12 of a Grattan-Guinness cycle.
Any five rows beginning (and ending) with a long row = Triad (triple Inex). As before;
The last 3 of any row and the first 1 of next row = Tritos
Also, the last 1 of any row and the first 3 of the next row = Tritos.


Karl

15(01(28

|
-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Helios
Sent: 14 July 2015 04:40
To: [hidden email]
Subject: Re: Saw-tooth Square Diagram

Dear Karl and Calendar People,

Instead of inserting odd leap month periods, I've tried 33m and 34m into the
arrangement. Now the important eclipses DO reveal themselves by rows.

rows 4th and 6th = Tritos
middle 7 rows = Triad ( triple inex )

34 33 34 33 34
34 33 34 33
34 33 34 34 33
34 33 34 34
33 34 33 34 33
34 34 33 34
33 34 34 33 34
33 34 33 34
34 33 34 33 34 = 1377 months

41 is a centered square number or saw-tooth square. Each row averages to 153
months.





--
View this message in context: http://calndr-l.10958.n7.nabble.com/Saw-tooth-Square-Diagram-tp16006p16014.html
Sent from the Calndr-L mailing list archive at Nabble.com.