Squaring the Circle

Using the Earth & the Moon

Now here's one that compares the Earth to the Moon! I'd like to thank John Michell for first pointing this one out to me.

Create a square (ABCD) with (AB) = 11.
Create diagonals (AC) and (BD) crossing at center point (E).
Construct a circle which is tangent to square (ABCD) at four places.

Construct two 3 • 4 • 5 right triangles, with the 4 • 5 angles at (A) and (D).
Connect the 5 • 3 angles creating square (abcd) with side (ab) = 3.
{4 + 3 + 4 = 11, or side (AD) of square (ABCD)}.
Create diagonals (ac) and (bd) centering at (e).
Create a circle that is tangent to square (abcd) at four places.

Draw line (Ee) which intersects side (AD) at (F).
(EF) = the radius of the larger circle and (eF) = the radius of the smaller circle.

The smaller circle thus created is to the larger circle as the moon is to the Earth!

With your compass point at (E), create a circle with radius (Ee).
This creates a circle whose circumference is very close to the perimeter of square (ABCD) - another squared circle.

The Math

(AB) = 11
(EF) = 1/2 of (AB) = 5.5; and (ab) = 3
(eF) = 5.5 + 1.5 = 7. The circumference of a circle is equal to two times the radius (the diameter) times pi (3.1416). or
C = π d. or
C= 3.1416 x 14. or
C= 43.9824
In Square (ABCD), (AB) = 11
The perimeter of a square is four times one side.
11 x 4 = 44. Very Close, what?

According to the Cambridge Encyclopedia, the equator radius of the Earth is 3963 miles. The equator radius of the Moon is 1080. The claim is that the smaller circle (in square abcd) is to the larger circle (in square ABCD) as the Moon is to the Earth. (EF) = 5.5

(F e) = 1.5
5.5 : 1.5 :: 3963 : 1080
5.5 / 1.5 = 3.66666
3963 / 1080 = 3.6694 - (if it had been 3960, it would have been exact!)

The following carries the reader further into Sacred Geometry. It is mostly text, but worth the effort.