Eclipse Magic Square

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Eclipse Magic Square

Helios
Dear Calendar People,

I'm back from a computer failure. I've worked on things about luni-solar eclipse cycles during this computer-less time. I was eager to check the lunar tables on the internet to confirm my findings.
Here's a magic square that shows years with midwinter solar eclipses. I've developed a set of years that include a center date and a certain selection of eleven best near misses that are symmetrical about the center date. The central date is nearest to the winter solstice.

1777 2001 1954 1629 1759
1936 1582 1759 2038 1805
1675 1908 1824 1740 1973
1843 1610 1889 2066 1712
1889 2019 1694 1647 1871

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Re: Eclipse Magic Square

Karl Palmen

Dear Helios and Calendar People

 

Welcome back Helios.

 

It would be interesting to know the Saros numbers of these eclipses. Do the Saros numbers form a magic square with the eclipses in the same positions?

 

I sort the years in order to find what kind of sequence they form.

1582, 1610, 1629, 1647, 1675, 1694, 1712, 1740, 1759, 1777, 1805, 1824, 1843, 1871, 1889, 1908, 1936, 1954, 1973,  2001, 2019, 2038, 2066.

 

I see more than three types of interval  (18, 19 & 28 years) so it does not form a Helios cycle.

 

I do see an absolutely asymmetrical 65-year sub-cycle, which is reversed at the centre year.

 

1582, 1610, 1629,

1647, 1675, 1694,

1712, 1740, 1759,

1777, 1805, 1824,

 

1824, 1843, 1871,

1889, 1908, 1936,

1954, 1973, 2001,

2019, 2038, 2066.

 

The 65-year cycle would correspond to the Unidos of two Saros cycles and one Inex cycle, which is slightly more than 65 years and equal to 67 twelve-month lunar years. It is subdivided into three intervals of 28, 19 and 18 years.

See https://www.staff.science.uu.nl/~gent0113/eclipse/eclipsecycles.htm

 

The mirror image years of 1759 & 1889 are the only years repeated in the magic square.

 

By an absolutely asymmetrical cycle, I mean a cycle that cannot be made symmetrical by changing the start year. Most calendar cycles are not absolutely asymmetrical. Probably, the most well-known example of an absolutely asymmetrical cycle in the 400-year cycle of years with 53 ISO weeks.

 

Karl

 

16(02(23

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Helios
Sent: 24 October 2016 09:22
To: [hidden email]
Subject: Eclipse Magic Square

 

Dear Calendar People,

I'm back from a computer failure. I've worked on things about luni-solar eclipse cycles during this computer-less time. I was eager to check the lunar tables on the internet to confirm my findings.
Here's a magic square that shows years with midwinter solar eclipses. I've developed a set of years that include a center date and a certain selection of eleven best near misses that are symmetrical about the center date. The central date is nearest to the winter solstice.

1777

2001

1954

1629

1759

1936

1582

1759

2038

1805

1675

1908

1824

1740

1973

1843

1610

1889

2066

1712

1889

2019

1694

1647

1871

 


View this message in context: Eclipse Magic Square
Sent from the Calndr-L mailing list archive at Nabble.com.

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Re: Eclipse Magic Square

Karl Palmen

Dear Helios and Calendar People

 

I can work out the Saros numbers of Helios’s eclipses relative to the Saros number of the eclipse in the centre year of 1824.

 

For this I’ll assume that

(1) the 18-year interval is a Saros (S),

(2) the 19-year cycle is a Metonic cycle (10I-15S)

(3) the 65-year sub-cycle is a Unidos (I+2S)

All three are listed at

https://www.staff.science.uu.nl/~gent0113/eclipse/eclipsecycles.htm

From this the 28-year interval is an unlisted cycle of (-9I+16S). It has 65.005-19.000-18.030 = 27.975 years.

 

The coefficient of ‘I’ is equal to the increment of the Saros number. So therefore we have the following increments of the Saros number

18 years 0

19 years +10

28 years -9

 

So now I put the Saros numbers relative to the 1824 eclipse in [].

 

1582 [-04], 1610 [-13], 1629 [-03],

1647 [-03], 1675 [-12], 1694 [-02],

1712 [-02], 1740 [-11], 1759 [-01],

1777 [-01], 1805 [-10], 1824 [000],

 

1824 [000], 1843 [+10], 1871 [+01],

1889 [+01], 1908 [+11], 1936 [+02],

1954 [+02], 1973 [+12], 2001 [+03],

2019 [+03], 2038 [+13], 2066 [+04].

 

Hopefully, these relative Saros numbers will be confirmed when Helios checks the eclipses.

There is the possibility of a difference of 38, which corresponds to the eclipse occurring a month before or after the assumed new moon.

 

Karl

 

16(02(24

 

 

From: Palmen, Karl (STFC,RAL,ISIS)
Sent: 24 October 2016 16:10
To: 'East Carolina University Calendar discussion List'
Subject: RE: Eclipse Magic Square

 

Dear Helios and Calendar People

 

Welcome back Helios.

 

It would be interesting to know the Saros numbers of these eclipses. Do the Saros numbers form a magic square with the eclipses in the same positions?

 

I sort the years in order to find what kind of sequence they form.

1582, 1610, 1629, 1647, 1675, 1694, 1712, 1740, 1759, 1777, 1805, 1824, 1843, 1871, 1889, 1908, 1936, 1954, 1973,  2001, 2019, 2038, 2066.

 

I see more than three types of interval  (18, 19 & 28 years) so it does not form a Helios cycle.

 

I do see an absolutely asymmetrical 65-year sub-cycle, which is reversed at the centre year.

 

1582, 1610, 1629,

1647, 1675, 1694,

1712, 1740, 1759,

1777, 1805, 1824,

 

1824, 1843, 1871,

1889, 1908, 1936,

1954, 1973, 2001,

2019, 2038, 2066.

 

The 65-year cycle would correspond to the Unidos of two Saros cycles and one Inex cycle, which is slightly more than 65 years and equal to 67 twelve-month lunar years. It is subdivided into three intervals of 28, 19 and 18 years.

See https://www.staff.science.uu.nl/~gent0113/eclipse/eclipsecycles.htm

 

The mirror image years of 1759 & 1889 are the only years repeated in the magic square.

 

By an absolutely asymmetrical cycle, I mean a cycle that cannot be made symmetrical by changing the start year. Most calendar cycles are not absolutely asymmetrical. Probably, the most well-known example of an absolutely asymmetrical cycle in the 400-year cycle of years with 53 ISO weeks.

 

Karl

 

16(02(23

 

 

From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Helios
Sent: 24 October 2016 09:22
To: [hidden email]
Subject: Eclipse Magic Square

 

Dear Calendar People,

I'm back from a computer failure. I've worked on things about luni-solar eclipse cycles during this computer-less time. I was eager to check the lunar tables on the internet to confirm my findings.
Here's a magic square that shows years with midwinter solar eclipses. I've developed a set of years that include a center date and a certain selection of eleven best near misses that are symmetrical about the center date. The central date is nearest to the winter solstice.

1777

2001

1954

1629

1759

1936

1582

1759

2038

1805

1675

1908

1824

1740

1973

1843

1610

1889

2066

1712

1889

2019

1694

1647

1871

 


View this message in context: Eclipse Magic Square
Sent from the Calndr-L mailing list archive at Nabble.com.

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Re: Eclipse Magic Square

Felix Verbelen
In reply to this post by Helios
Hello!

Years ago I computed lists of the Saros/Inex series for both Solar and
Lunar eclipses, which could useful in this case.

They are available at

- http://users.skynet.be/felixverbelen/public/SarosSeries_Sun.txt
- http://users.skynet.be/felixverbelen/public/SarosSeries_Moon.txt

Kind regards.

Felix


Op 2016-10-24 om 10:22 schreef Helios:

> Dear Calendar People,
>
> I'm back from a computer failure. I've worked on things about luni-solar
> eclipse cycles during this computer-less time. I was eager to check the
> lunar tables on the internet to confirm my findings.
> Here's a magic square that shows years with midwinter solar eclipses. I've
> developed a set of years that include a center date and  a certain selection
> of eleven best near misses that are symmetrical about the center date. The
> central date is nearest to the winter solstice.
>
> *1777* *2001* *1954* *1629* *1759*
> *1936* *1582* *1759* *2038* *1805*
> *1675* *1908* *1824* *1740* *1973*
> *1843* *1610* *1889* *2066* *1712*
> *1889* *2019* *1694* *1647* *1871*
>
>
>
>
> --
> View this message in context: http://calndr-l.10958.n7.nabble.com/Eclipse-Magic-Square-tp17230.html
> Sent from the Calndr-L mailing list archive at Nabble.com.
>
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Re: Eclipse Magic Square

Karl Palmen
Dear Felix and Calendar People

I found the 1824 eclipse with Saros number 129 having found the 1582 eclipse with Saros number 125 in accordance with the relative Saros numbers:

1582 [-04], 1610 [-13], 1629 [-03],
1647 [-03], 1675 [-12], 1694 [-02],
1712 [-02], 1740 [-11], 1759 [-01],
1777 [-01], 1805 [-10], 1824 [000],

1824 [000], 1843 [+10], 1871 [+01],
1889 [+01], 1908 [+11], 1936 [+02],
1954 [+02], 1973 [+12], 2001 [+03],
2019 [+03], 2038 [+13], 2066 [+04].

Karl

16(02(24

-----Original Message-----
From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Felix Verbelen
Sent: 25 October 2016 16:24
To: [hidden email]
Subject: Re: Eclipse Magic Square

Hello!

Years ago I computed lists of the Saros/Inex series for both Solar and
Lunar eclipses, which could useful in this case.

They are available at

- http://users.skynet.be/felixverbelen/public/SarosSeries_Sun.txt
- http://users.skynet.be/felixverbelen/public/SarosSeries_Moon.txt

Kind regards.

Felix


Op 2016-10-24 om 10:22 schreef Helios:

> Dear Calendar People,
>
> I'm back from a computer failure. I've worked on things about luni-solar
> eclipse cycles during this computer-less time. I was eager to check the
> lunar tables on the internet to confirm my findings.
> Here's a magic square that shows years with midwinter solar eclipses. I've
> developed a set of years that include a center date and  a certain selection
> of eleven best near misses that are symmetrical about the center date. The
> central date is nearest to the winter solstice.
>
> *1777* *2001* *1954* *1629* *1759*
> *1936* *1582* *1759* *2038* *1805*
> *1675* *1908* *1824* *1740* *1973*
> *1843* *1610* *1889* *2066* *1712*
> *1889* *2019* *1694* *1647* *1871*
>
>
>
>
> --
> View this message in context: http://calndr-l.10958.n7.nabble.com/Eclipse-Magic-Square-tp17230.html
> Sent from the Calndr-L mailing list archive at Nabble.com.
>