Squaring the Circle - The Great Pyramid

The square represents the physical. The circle represents the spiritual. All sacred geometers have attempted the impossible: to square the circle (create a square who's perimeter is equal to the circumference of a circle.)

Here is the first of two valiant attempts:
This squaring of the circle works with a right triangle that represents the apothem (ZY) - (a line drawn from the base of the center of one of the sides to top of the pyramid), down to the center of the base (ZE), and out to the point where the apothem touches the Earth (EY).

The Great Pyramid of Egypt
(Sphinx in foreground)

	Now let's look at this in 2D, from directly above. For the purpose of this exercise, the side (AB) of the base equals 2.
	(ABCD) is the base of the Great Pyramid. This is lettered similarly to the wire frame version (above). For the purpose of this exercise, the side (AB) of the base equals 2.
	Construct square (i JKD), thus creating double square (JKE f).
	Create diagonal (EK) which intersects (i D) at (l). iD = 1, therefore the diameter of the circle is also 1. (EK) = (5) = .618 + 1 + .618
	Put the point of your compass at (E) and extend it along the diagonal (EK) to point (m) where the circle intersects (EK), and draw the arc downward to intersect (KD f C) at (n). If (EK) = (5), and (l m/l D) and l i = .5, the diameter of this circle is 1. This makes (E m) = .618 + 1, or 1.618. (E m) is the apothem.
	Draw (E n) which intersects (A i l D ) at (o). Put compass point at (f) and extend it to (n). Again put your point at (E) and draw the circle which happens to have the radius (E o). (f n) is the height of the Great Pyramid. This circle comes remarkably close to having the same circumference as the perimeter of the base (ABCD).

Let's go back to the original right triangle (EYZ)
(EY) = .5

(YZ) = phi

(EZ) = (phi)

EY = .5, The apothem is phi/1.618. This makes the 51 degree + degree angle.

Using a² + b² = c², this makes the height the square root of phi.

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 f

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 larger circle thus created is to the smaller 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 equal to the perimeter of square (ABCD)!

(AB) = 11
(EF) = 1/2 of (AB) = 5.5

(ab) = 3
(eF) = 1.5

Therefore 5.5 + 1.5 = 7

The circumference of a circle is equal to two times the radius (the diameter) times pi (3.1416).

C= 14 x 3.1416
C= 43.9824

In Square (ABCD), (AB) = 11
The perimeter of a square is four times one side. 11 x 4 = 44

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!)

Phi in the Bible

Although perhaps not immediately obvious, phi and the golden section also appear in the Bible. Also see the Theology page.

The Ark of the Covenant is a Golden Rectangle

In Exodus 25:10, God commands Moses to build the Ark of the Covenant, in which to hold His Covenant with the Israelites, the Ten Commandments, saying,

“Have them make a chest of acacia wood-
two and a half cubits long,
a cubit and a half wide,
and a cubit and a half high.”

The ratio of 2.5 to 1.5 is 1.666…, which is as close to phi (1.618 …) as you can come with such simple numbers and is certainly not visibly different to the eye. The Ark of the Covenant is thus constructed using the Golden Section, or Divine Proportion. This ratio is also the same as 5 to 3, numbers from the Fibonacci series.

In Exodus 27:1-2, we find that the altar God commands Moses to build is based on a variation of the same 5 by 3 theme:

“Build an altar of acacia wood, three cubits high; it is to be square, five cubits long and five cubits wide.”

Note: A cubit is the measure of the forearm below the elbow.

Altar of Exodus 27

Noah’s Ark uses a Golden Rectangle

In Genesis 6:15, God commands Noah to build an ark saying,

“And this is the fashion which thou shalt make it of: The length of the ark shall be three hundred cubits, the breadth of it fifty cubits, and the height of it thirty cubits.”

Thus the end of the ark, at 50 by 30 cubits, is also in the ratio of 5 to 3, or 1.666…, again a close approximation of phi not visibly different to the naked eye. Noah’s ark was built in the same proportion as ten arks of the covenant placed side by side.

Noah's Ark

The Number 666 is related to Phi

Revelation 13:18 says the following:

“This calls for wisdom. If anyone has insight, let him calculate the number of the beast, for it is a man’s number. His number is 666.”

This beast, regarded by some as the Anti-Christ described by John, is thus related to the number 666, one of the greatest mysteries of the Bible.Curiously enough, if you take the sine of 666º, you get -0.80901699, which is one-half of negative phi, or perhaps what one might call the “anti-phi.” You can also get -0.80901699 by taking the cosine of 216º, and 216 is 6 x 6 x 6.

The trigonometric relationship of sine 666º to phi is based on an isosceles triangle with a base of phi and sides of 1. When this triangle is enclosed in a circle with a radius of 1, we see that the lower line, which has an angle of 306º on the first rotation and 666º on the second rotation, has a sine equal to one-half negative phi.

The relationship of phi, the golden ratio, and 666

In this we see the unity of phi divided into positive and negative, analogous perhaps to light and darkness or good and evil. Could this “sine” be a “sign” as well?

In addition, 666 degrees is 54 degrees short of the complete second circle and when dividing the 360 degrees of a circle by 54 degrees you get 6.66… The other side of a 54 degree angle in a right angle is 36 degrees and 36 divided by 54 is .666.

Phi appears throughout creation, and in every physical proportion of the human body. In that sense it is the number of mankind, as the mysterious passage of Revelationperhaps reveals.

Also see the Theology page.

The colors of the Tabernacle are based on a phi relationship

The PhiBar program produces the colors that the Bible says God gave to Moses for the construction of the Tabernacle.

As it says in Exodus 26:1, “Make the tabernacle with ten curtains of finely twisted linen and blue, purple and scarlet yarn, with cherubim worked into them by a skilled craftsman.”

Set the primary color of the PhiBar program to blue, the secondary color of the PhiBar to purple and it reveals the Phi color to be scarlet.

This reference to the combination blue, purple and scarlet in the construction of the tabernacle appears 24 times in Exodus 25 through 39, describing the colors to be used in the curtains, waistbands, breastpieces, sashes and garments.

See the Color page for additional information.

Insights on the Ark of the Covenant and 666 contributed by Robert Bartlett.
Insights on the Altar in Exodus 27 contributed by Sir Hemlock.
Insights on the Tabernacle colors contributed by J.D. Ahmanson.

http://www.goldennumber.net/bible/