with the Earth and Moon?

At first, it would seem to require too much of a stretch to even start thinking about such a preposterous amalgam.

But if we think of each in terms of their most simple dimensions, then it's not so far out a connection at all.

Since the ratio of their diameters is 7920/2160 = 3 & 2/3, the Earth's diameter is to the Moon's is the same, which is simply 11/3.

Instead, we'll use the well-known traditional approximation of pi as 22/7 (or 3.14285...), which is distorted by less than two feet in a mile.

When the Earth and Moon's dimensions are considered with this value of pi, a curious mathematical situation occurs: a

The Moon has been brought down to Earth's surface. As it rolls around the Earth, the Moon's center leaves a circular blue trail.

The perimeter of the square around the Earth is 4 x 7920 = 31,680 miles.

The circumference of the blue circle is 2 x pi x radius = 2 x 22/7 x (3960 + 1080) = 44/7 x 5040 = 31,680 miles as well.

Thus this ideal description of the Earth and Moon "squares the circle" by producing an equal perimeter and circumference.

Extending this multiplication in an interesting way is that the Earth's diameter 7920 = 8 x 9 x 10 x 11.

Thus, the area of this blue circle = pi x radius squared = 22/7 x (5040 x 5040) = 2 x (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11), double the numbers 1 through 11 multiplied together!

Still another happy coincidence is that 10,080 is a Highly Composite number with exactly 72 divisors, the same as the average number of heartbeats in one minute.

Dividing each measure by 720 (= 1 x 2 x 3 x 4 x 5 x 6 = 8 x 9 x 10) we simplify them into the figures at

Note that the 31,680 mile perimeter of the green square and circumference of the blue circle, when divided by 720, must both be equal to 44 (= 4 X 11).

We thus find that the distance from the center of the Earth to the top of the Moon is to the Earth's diameter as 8.5 is to 11.

This is the paper size familiar to most Americans, found commonly in our printers.

The average maximum stretch of an experienced vatman's arms was 44".

Many molds at that time were around 17" front to back because the laid lines and watermarks had to run from left to right.

Sounds big?...well to maximize the efficiency of paper making, a sheet this big was made, and then quartered, forming four 8.5" x 11" pieces."

To see the dimensions of

At right are some of its measures in miles:

Its two concentric outer rings of stones relate by a "squared circle,"

and its measures reveal the

Its dimensions are 8.5 x 14 inches.

These too can be found in the dimensions of the Earth and Moon, where Legal paper's dimensions are found as follows:

This size is equal to two Letter-size sheets.

They are also both found in the relationship between the diameter of the Earth and the full distance between opposite Moons:

(in his highly recommended books

It's to him that I dedicate this little investigation about writing paper (albeit American) but ones which derive from traditional times and measures.

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