“The Jewish calendar is a combined solar/lunar calendar, in that it strives to have its years coincide with the tropical year and its months coincide with the synodic months. This is a complicated goal, and the rules for the Jewish calendar are correspondingly fascinating.”

http://webexhibits.org/calendars/calendar-jewish.html

I think this is an incredible thing. By having a seven day week (the Torah) we are able to have twelve four week months where twelve is the most divisible number by whole numbers, for its size. Like this there are twelve new moons between the time it takes for the Earth to go about the sun once.

I did a little number juggling and found that,

Earth-moon distance: 3.84E10cm=R
Earth-sun distance: 1.496E13cm=r
Earth radius: 6.38E8cm=E_r
Moon radius: 1.738E8cm=M_r

(E_r)/(M_r)=11/3 r/R=4675/12

((E_r)(r))/((M_r)(R)(360))=4

This last equation is significant because,
360 are the degrees in a circle and
4 weeks is a complete revolution of the moon
about the earth more or less on the average
(time between new moons). 360 degrees are
convenient for the units in which to divide a circle,
because of its divisible properties. (i.e. it is divisible by
120, 60, 45, 30, and 90, into whole numbers which are the angles in special
triangles.)

Is what this last equation says is that the radius of the earth compared to the radius of the moon, by a factor of the earth-sun distance compared to the earth-moon distance, is equal to 360 times four. It just so happens that after four 360 degree rotations of the earth around the sun, we have a leap year to make the whole calendar work!!!

quote:

Originally posted by Ian Beardsley:
“The Jewish calendar is a combined solar/lunar calendar, in that it strives to have its years coincide with the tropical year and its months coincide with the synodic months. This is a complicated goal, and the rules for the Jewish calendar are correspondingly fascinating.”

http://webexhibits.org/calendars/calendar-jewish.html

I think this is an incredible thing. By having a seven day week (the Torah) we are able to have twelve four week months where twelve is the most divisible number by whole numbers, for its size. Like this there are twelve new moons between the time it takes for the Earth to go about the sun once.

I did a little number juggling and found that,

Earth-moon distance: 3.84E10cm=R
Earth-sun distance: 1.496E13cm=r
Earth radius: 6.38E8cm=E_r
Moon radius: 1.738E8cm=M_r

(E_r)/(M_r)=11/3 r/R=4675/12

((E_r)(r))/((M_r)(R)(360))=4

This last equation is significant because,
360 are the degrees in a circle and
4 weeks is a complete revolution of the moon
about the earth more or less on the average
(time between new moons). 360 degrees are
convenient for the units in which to divide a circle,
because of its divisible properties. (i.e. it is divisible by
120, 60, 45, 30, and 90, into whole numbers which are the angles in special
triangles.)

Is what this last equation says is that the radius of the earth compared to the radius of the moon, by a factor of the earth-sun distance compared to the earth-moon distance, is equal to 360 times four. It just so happens that after four 360 degree rotations of the earth around the sun, we have a leap year to make the whole calendar work!!!

Also, 360 plus four is the Earth year. Is this divine harmony? Gotta be.

Did you have to quote the whole of your previous message? Not being of a mathematical bent, I'm afraid it did not become any clearer the second time around.

quote:

Originally posted by Stephen Phillips:
Did you have to quote the whole of your previous message? Not being of a mathematical bent, I'm afraid it did not become any clearer the second time around.

I thought that if I quoted the whole post, one might be able to print out just the reply and have the whole idea, but I don't think one can, I tried.
--Ian

quote:

Originally posted by Ian Beardsley:
“The Jewish calendar is a combined solar/lunar calendar, in that it strives to have its years coincide with the tropical year and its months coincide with the synodic months. This is a complicated goal, and the rules for the Jewish calendar are correspondingly fascinating.”

http://webexhibits.org/calendars/calendar-jewish.html

I think this is an incredible thing. By having a seven day week (the Torah) we are able to have twelve four week months where twelve is the most divisible number by whole numbers, for its size. Like this there are twelve new moons between the time it takes for the Earth to go about the sun once.

There are actually 13 new moons in a year, but (12/13)100=92% accuracy, and as such the calendar on this account is a very accurate approximation. The crux of the idea is not dependent on that accuracy in any case and is:

"Is what this last equation says is that the radius of the earth compared to the radius of the moon, by a factor of the earth-sun distance compared to the earth-moon distance, is equal to 360 times four. It just so happens that after four 360 degree rotations of the earth around the sun, we have a leap year to make the whole calendar work!!!"

I have worked out some glitches in the original post and decided to post the whole work finished, as professor Zeiger of the Torah Science Foundation has got me excited about it. He writes:

Thank you for your insights, Ian!
Indeed, the Jewish calendar is unique on its wisdom, which attest to
the
foresight of our sages that put it together.

Shabbat Shalom and Chodesh Tov!

Eliezer Zeiger

So here is the refined thing:

“The Jewish calendar is a combined solar/lunar calendar, in that it strives to have its years coincide with the tropical year and its months coincide with the synodic months. This is a complicated goal, and the rules for the Jewish calendar are correspondingly fascinating.”
http://webexhibits.org/calendars/calendar-jewish.html
I think this is an incredible thing. By having a seven day week (the Torah) we are able to have twelve four week months where twelve is the most divisible number by whole numbers, for its size. Like this there are twelve new moons between the time it takes for the Earth to go about the sun once, close to it. There are 13, but (12/13)100=92% accuracy.
I did a little number juggling and found that,
Earth-moon distance: 3.84E10cm=R
Earth-sun distance: 1.496E13cm=r
Earth radius: 6.38E8cm=E_r
Moon radius: 1.738E8cm=M_r
(E_r)/(M_r)=11/3 r/R=4675/12
((E_r)(r))/((M_r)(R)(360))=4
This last equation is significant because,
360 are the degrees in a circle and
4 weeks is a complete revolution of the moon
about the earth more or less (time between new moons). 360 degrees are
convenient for the units in which to divide a circle,
because of its divisible properties. (i.e. it is divisible by
120, 60, 45, 30, and 90, into whole numbers which are the angles in special
triangles.)
Is what this last equation says is that the radius of the earth compared to the radius of the moon, by a factor of the earth-sun distance compared to the earth-moon distance, is equal to 360 times four. It just so happens that after four 360 degree rotations of the earth around the sun, we have a leap year to make the whole calendar work!!!
Also, 360 plus 4 is close to the Earth year. (364/365)100=99.7% accuracy.
If you consider that the Earth, Moon and Sun formed from a cloud of gas and dust under its own gravity over perhaps billions of years, this is quite an extraordinary arrangement to have occurred.
Consider that the earth-moon distance (EM) is to the solar radius (SR) as silver (Ag) is to gold (Au). Here is the calculation:

EM/SR=3.84E10cm/6.9599E10=0.55

Ag/Au=107.9/197.0=0.55

Ag and Au are the molar masses of silver and gold respectively. These masses are their relative masses for one atom of each, they do not vary, for all practical purposes, from sample to sample on Earth no matter where the samples were found. Of course gold and silver are the precious metals most used to make fine jewelry. In astrology they have been traditionally the representative elements for the moon and sun respectively, not because of the last relationship, but because of their colors.
Also, the moon as seen from the Earth appears to be the same size as the sun, nearly, allowing for an eclipse of the main solar body so that its outer atmosphere can be studied.
It would seem the mechanics of the Earth-moon-Sun system are structured in harmony with the most elegant of abstract symbolic dynamics, we even structured our systems in accordance with this harmony before we could ever know it existed, most likely because we wanted to divide cycles in a pragmatic manner. That the two are in accordance speaks of the existence of a wonderful mystery, for which we yet have answers.
Though this structure will change and has not always been this way, It has been this way over geologic time while the Titius-Bode rule holds, that predicts the distribution of the planets about the sun, their average orbital radii, as a geometric progression up to Pluto excluding Neptune and counting the asteroid belt as a planet torn apart by Jupiter's gravity.