Hi all,
The length of the polar circumference is 2.16 billion digits. The length of 24,860 miles is 1,575,129,600 inches and 1,575,129,600 / 2.16 billion = .7292 inches for the length of the digit.
.7292 x 20 = 14.584 inches for the remen, and
14.584 times the square root of 2 = 20.625 inches for the royal cubit.
.7292 x 16 = 11.667 inches for the Roman foot.
.7292 x 24 = 17.50 inches for the Roman cubit.
The Greek cubit is 25/24 of the Roman cubit, giving
.7292 x 25 = 18.23 inches for the Greek cubit, or
18.23 x 2/3 = 12.15 inches for the Greek foot.
In Republic 8:546b, Plato described a perfect number as follows:
(Benjamin Jowett’s translation from the Great Books collection.) “Now that which is of divine birth has a period contained in a perfect number, but the period of human birth is comprehended in a number in which first increments by involution and evolution obtaining three intervals and four terms of like and unlike, waxing and waning numbers, make all the terms commensurable and agreeable to one another. The base of these, with a third added, when combined with five, and raised to the third power, furnishes two harmonies; the first a square 100 times as great; and the other a figure having one side equal to the former, but oblong, consisting of 100 numbers squared upon the rational diameters of a square, the side of which is five, each of them being less by one or less by two perfect squares of irrational diameters; and 100 cubes of three. Now this number represents a geometrical figure which has control over the good and evil of births. For when your guardians are ignorant of the law of births, and unite bride and bridegroom out of season, the children will not be goodly or fortunate.”
(This next translation is from perseus)
[www.perseus.tufts.edu]
“Now for divine begettings there is a period comprehended by a perfect number, and for mortal by the first in which augmentations dominating and dominated when they have attained to three distances and four limits of the assimilating and the dissimilating, the waxing and the waning, render all things conversable and commensurable with one another, whereof a basal four-thirds wedded to the pempad yields two harmonies at the third augmentation, the one the product of equal factors taken one hundred times, the other of equal length one way but oblong,—one dimension of a hundred numbers determined by the rational diameters of the pempad lacking one in each case, or of the irrational lacking two; the other dimension of a hundred cubes of the triad. And this entire geometrical number is determinative of this thing, of better and inferior births.”
“The base of these, with a third added, when combined with five, and raised to the third power, furnishes two harmonies.”
This is generally regarded as giving a triangle, with a short side of three, a long side of 4 (3 with a third of 3, or 1, added), and a hypotenuse of 5.
The area of the triangle 3-4-5 is 6.
Raising to the third power gives 3 cubed + 4 cubed + 5 cubed = 6 cubed = 216
My interpretation of the statement of a square 100 times as great: 100 squared x 216 = 2,160,000.
My interpretation of the statement of the oblong is that the rational (whole number) diameter (diagonal) of a square with side lengths of five: 5 x sq rt 2 = 7.07... or 7 in whole numbers, and Plato says this is less by one, giving 7 + 1 = 8, and then times 100 = 800 for the short sides of the oblong. The long sides of the oblong are 3 cubed x 100, or 2700. The product of this oblong is 800 x 2700 = 2,160,000, the same as 100 squared x 216.
Regardless of what is expressed or implied by Plato,
triangle 3-4-5 = 6 for the area of the triangle,
3 cubed + 4 cubed + 5 cubed = 6 cubed = 216, and
2 cubed x 3 cubed = 6 cubed = 216 (given by Plato as 800 x 2700 = 2,160,000).
216 is the smallest cube that can be represented as a sum of three positive cubes, being the first example of Euler’s sum of powers theory.
216 is the smallest number that can be represented as a sum of any number of cubes in more than one way.
216 is an untouchable number.
According to a theory by Sun Zhiwei, 216 is the only number that can not be written either as a triangular number or as a triangular number plus a prime number.
In base six, 6*6*6 is comparable to 10*10*10 in base 10.
It has been suggested that the meanings of ancient expressions of 666 may have been based on 6*6*6, or 6 raised to the third power, or 216.
Berossus was a Babylonian who wrote a chronology of Babylonia, in Greek, during Alexandrian times. In FOG, Graham referenced the statement by Berossus that the ancient Babylonian chronology gave a period of 2,160,000 years from creation to universal catastrophe. This statement is also found in Archaeological Discussions, published by the Univ. of Chicago, in 1909 (p. 209):
[www.journal.uchicago.edu]
As Graham pointed out, 216 is also a precessional number, with 2,160 years being the age of each of the 12 zodiacal constellations.
2,160,000,000 digits in the polar circumference equals the number of years in 1,000,000 zodiacal ages.
The Greek or Roman stadia, containing 10,000 digits each, gives 216,000 stadia in the polar circumference, or the number of years in 100 zodiacal ages.
Happy Holidays,
Jim
The length of the polar circumference is 2.16 billion digits. The length of 24,860 miles is 1,575,129,600 inches and 1,575,129,600 / 2.16 billion = .7292 inches for the length of the digit.
.7292 x 20 = 14.584 inches for the remen, and
14.584 times the square root of 2 = 20.625 inches for the royal cubit.
.7292 x 16 = 11.667 inches for the Roman foot.
.7292 x 24 = 17.50 inches for the Roman cubit.
The Greek cubit is 25/24 of the Roman cubit, giving
.7292 x 25 = 18.23 inches for the Greek cubit, or
18.23 x 2/3 = 12.15 inches for the Greek foot.
In Republic 8:546b, Plato described a perfect number as follows:
(Benjamin Jowett’s translation from the Great Books collection.) “Now that which is of divine birth has a period contained in a perfect number, but the period of human birth is comprehended in a number in which first increments by involution and evolution obtaining three intervals and four terms of like and unlike, waxing and waning numbers, make all the terms commensurable and agreeable to one another. The base of these, with a third added, when combined with five, and raised to the third power, furnishes two harmonies; the first a square 100 times as great; and the other a figure having one side equal to the former, but oblong, consisting of 100 numbers squared upon the rational diameters of a square, the side of which is five, each of them being less by one or less by two perfect squares of irrational diameters; and 100 cubes of three. Now this number represents a geometrical figure which has control over the good and evil of births. For when your guardians are ignorant of the law of births, and unite bride and bridegroom out of season, the children will not be goodly or fortunate.”
(This next translation is from perseus)
[www.perseus.tufts.edu]
“Now for divine begettings there is a period comprehended by a perfect number, and for mortal by the first in which augmentations dominating and dominated when they have attained to three distances and four limits of the assimilating and the dissimilating, the waxing and the waning, render all things conversable and commensurable with one another, whereof a basal four-thirds wedded to the pempad yields two harmonies at the third augmentation, the one the product of equal factors taken one hundred times, the other of equal length one way but oblong,—one dimension of a hundred numbers determined by the rational diameters of the pempad lacking one in each case, or of the irrational lacking two; the other dimension of a hundred cubes of the triad. And this entire geometrical number is determinative of this thing, of better and inferior births.”
“The base of these, with a third added, when combined with five, and raised to the third power, furnishes two harmonies.”
This is generally regarded as giving a triangle, with a short side of three, a long side of 4 (3 with a third of 3, or 1, added), and a hypotenuse of 5.
The area of the triangle 3-4-5 is 6.
Raising to the third power gives 3 cubed + 4 cubed + 5 cubed = 6 cubed = 216
My interpretation of the statement of a square 100 times as great: 100 squared x 216 = 2,160,000.
My interpretation of the statement of the oblong is that the rational (whole number) diameter (diagonal) of a square with side lengths of five: 5 x sq rt 2 = 7.07... or 7 in whole numbers, and Plato says this is less by one, giving 7 + 1 = 8, and then times 100 = 800 for the short sides of the oblong. The long sides of the oblong are 3 cubed x 100, or 2700. The product of this oblong is 800 x 2700 = 2,160,000, the same as 100 squared x 216.
Regardless of what is expressed or implied by Plato,
triangle 3-4-5 = 6 for the area of the triangle,
3 cubed + 4 cubed + 5 cubed = 6 cubed = 216, and
2 cubed x 3 cubed = 6 cubed = 216 (given by Plato as 800 x 2700 = 2,160,000).
216 is the smallest cube that can be represented as a sum of three positive cubes, being the first example of Euler’s sum of powers theory.
216 is the smallest number that can be represented as a sum of any number of cubes in more than one way.
216 is an untouchable number.
According to a theory by Sun Zhiwei, 216 is the only number that can not be written either as a triangular number or as a triangular number plus a prime number.
In base six, 6*6*6 is comparable to 10*10*10 in base 10.
It has been suggested that the meanings of ancient expressions of 666 may have been based on 6*6*6, or 6 raised to the third power, or 216.
Berossus was a Babylonian who wrote a chronology of Babylonia, in Greek, during Alexandrian times. In FOG, Graham referenced the statement by Berossus that the ancient Babylonian chronology gave a period of 2,160,000 years from creation to universal catastrophe. This statement is also found in Archaeological Discussions, published by the Univ. of Chicago, in 1909 (p. 209):
[www.journal.uchicago.edu]
As Graham pointed out, 216 is also a precessional number, with 2,160 years being the age of each of the 12 zodiacal constellations.
2,160,000,000 digits in the polar circumference equals the number of years in 1,000,000 zodiacal ages.
The Greek or Roman stadia, containing 10,000 digits each, gives 216,000 stadia in the polar circumference, or the number of years in 100 zodiacal ages.
Happy Holidays,
Jim