The Lost Symbol  

  The Search for Eternity

The Divine Reflection

 

 

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The Lost Symbol book

The secrets of ancients

Ancient Philosophers and the Golden Ratio

Figure 1

The Golden Ratio

 

 A Golden Symbol of Harmony and Tranquility

Golden spiral silver	Golden spiral gold

The Magical Mystery Tour

The Monad symbol

A Golden Symbol of Harmony and Tranquility

The Monad Ring silver	The Monad Ring gold

The Lost Secret

The Renaissance

The Divine Reflection

 

 

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The Christ Grid pendant

 

 

Christ consciousness - silver	Christ consciousness - gold

   As Beckmann points out, "Archimedes started with a hexagon and progressively doubling the number of sides he arrived at a polygon of 96 sides, which yielded pi as 3 1/7, or 3.142857." ⁷ The importance of relating pi to septenary units is obvious in a Biblical light when we consider God's abundant use of the number seven in His ordering of Creation. Some of this evidence is covered in our website essay on the Calendar of the Israel. This ratio of 22/7 is also intriguing because it expresses the ratio between the 22 letters of the Hebrew alphabet, in relation to its seven vowels. This is a supporting factor in the idea that the roots of writing & the first alphabet originate in the celestial gospel. As the first "written" revelation to mankind, the stars in this gospel were named and numbered by God [Ps. 147:4]. The divine message of the coming redeemer and the means God chose to deliver it, thus provide the sacred foundation of all language and mathematics. As the divine original source of this wisdom, the witness of the stars was above reproach. The pi ratio expressed as 22/7, reflects this perfection of the celestial gospel, in at least the mathematical, geometrical and linguistic contexts.
  This trend continued when God's media of revelation transitioned to the written word, when God first wrote the 10 Commandments in precious stone, which Moses the Lawgiver delivered to the people of the Nation Israel. This marked the start of the Mosaic Law Administration. The Canon of truth for the Patriarchal Administration was the celestial gospel, given directly by God, but is was up to men to apply these truths according to the principles of this system God put into place. Even so the Law began with writings from "the finger of God," but transitioned to the written Scriptures given by revelation from God, to "holy men of God, who spake as they were moved by the holy spirit" [II Pet. 1:21]. During this transition from the Patriarchal to the Law Administrations, men became the carriers of the divine message, and the potential for corruption was introduced into the equation. The Human Will must be freely subject to the Will of God to keep the corruption out in both divine systems of revelation. This brings us to the answer that lies beneath the surface of I Kings 7 as it relates to the ancient Gematria of the Hebrew language. Men like Dr. E.W. Bullinger in his book; Number in Scripture, reveal the details of this subject. We will only scratch the surface here. but before we do let's consider one final point connected with septenary measuring units. 
The following note from Keil and Delitzsch' Commentary on I Kings 7:23 below, adds support to the application of pi relating to septenary units as seen in the brazen sea above, [3.142857]
and the knowledge of its application by the ancient Hebrews, via revelation from God, in the dimensions of the Temple and its sacred furniture and accessories.   

"The brazen sea (cf. 2Ch. 4:2-5). - “He made the molten sea - a water-basin called יָם (mare) on account of its size - ten cubits from the one upper rim to the other,” i.e., in diameter measured from the upper rim to the one opposite to it, “rounded all round, and five cubits its (external) height, and a line of thirty cubits encircled it round about,” i.e., it was thirty cubits in circumference. The Chethib קוה is to be read קָוֶה here and in Zech. 1:16 and Jer. 31:39, for which the Keri has קָו in all these passages. קָוֶה or קָו means a line for measuring, which is expressed in 1Ki. 7:15 by חוּט. The relation of the diameter to the circumference is expressed in whole numbers which come very near to the mathematical proportions. The more exact proportions would be as 7 to 22, or 113 to 355.”⁸  [emphasis mine]

 The septenary relation to pi uncovers the link between the pi and phi ratio, through the popular Fibonacci Series. This link makes it possible to obtain pi without the need for measuring! This is illustrated in the following quote from Livio Stechini:

"It is possible to use the Fibonacci Series to obtain an accurate relation for the diameter of the circle to its circumference, without recourse to pi. In the Fibonnacci series of 21, 34, 55, if 21 is taken as the diameter of a circle, its circumference will be 55 x 6/5 = 66, accurate to the one thousandth part, giving the Great Pyramid value of pi as 22/7 = 3.142857. Higher numbers in the fibonacci series provide increasingly finer values in whole numbers accurate to one ten-thousandth part. Prolonging the series to 80, 144, 233, 377, 610... a diameter of 144 (4 x 576) gives a circumference of 377 x 6/5 or a pi value of 3.1415. A diameter of 233= a circumference of 610 x 6/5 or a pi value of 3.1416..."⁹      
            

Plate 1. The Pi and Phi Ratios in the Great Pyramid

  This mathematical affinity between pi and phi (pi= ز x 6/5, equivalent to 2.618 x 6/5 = 3.1416) will be further expounded in our essay on the Great Pyramid, especially in the relation between its base and height as seen in Plate 1 above. Now lets look beneath the surface of I Kings 7. The Hebrew word for "line" in verse 23 is normally spelled with two Hebrew letters, but as Jochen Katz points out; this word is written with an extra letter.¹⁰ A subject that has gotten much attention of late is "Bible codes." These codes are revealed with the use of the numerical values of the letters of the Hebrew and Greek languages, used in the Bible. E.W. Bullinger captured the essence of this referring to "the supernatural design in the use of number both in the Works of God and in the Word of God." He delineates four topics below in his book Number in Scripture:

1. Numbers of things mentioned.
2. Numbers of words and things.
3. Numbers of words used for a thing.
4. Numbers formed by the letters of the words themselves.

 The last category above, the ancients called Gematria.¹¹ Since the letters of the Hebrew alphabet are used instead of numbers, each letter has a numerical value. As Jochen Katz points out: "we can take the ratio of (the gematriacal value of "qav") in its unusual word form (having three letters), to the regular word form with two letters which is 111/106."¹² The value of this ratio (1.047198) when multiplied by the Bible's basic value of pi; (3) gives the result of 3.1415, or pi accurate to five digits! This formula is revealing because it employs the computation of a ratio hidden in the number values of the Hebrew language, to yield a higher degree of mathematical accuracy for the pi ratio, than its surface value of 3. This information is useful when we consider the application of pi in the Great Pyramid, and in light of the other Biblical uses of this word "qav," that we have just touched upon.
   This sub-surface enlightening of how pi is used in the Bible again stretches the envelope of the historical awareness of the scientific sophistication in the ancient world. Since this expertise is revealed as an aspect of the dimensions of the sacred furniture of the Temple and Tabernacle, it makes sense that God's knowledge of these matters would far exceed human knowledge. This is exactly what Isaiah tells us: 

Phi and the Solar System

The dimensions of the Earth and Moon are in Phi relationship, forming a Golden Triangle

The illustration above shows the relative sizes of the Earth and the Moon to scale.

• Draw a radius of the Earth (1)
• Draw a line from the center point of the Earth to the center point of the Moon (square root of Phi)
• Draw a line to connect the two lines to form a Golden Triangle (Phi).

Using dimensions from Wikipedia and geometry's classic Pythagorean Theorem, this is expressed mathematically as follows:

This geometric construction is the same as that which appears to have been used in the construction of the Great Pyramid of Egypt.

Source:  Hidden Nature by Alick Bartholomew.  Thanks to Sathimantha Malalasekera for bringing this to my attention.

Certain solar system orbital periods are related to phi

Saturn reveals a phi relationship in several of its dimensions

The diameter of Saturn is in a phi relationship with the diameter of its rings, as illustrated by the green lines. The inner ring division is in a phi relationship with the diameter of the rings outside the sphere of the planet, as illustrated by the blue lines. The Cassini division in the rings of Saturn falls at the Golden Section of the width of the lighter outside section of the rings. Note:  Phi grid showing Golden Ratio lines provided by PhiMatrix software.

A closer look at Saturn's rings reveals a darker inner ring which exhibits the same  golden section proportion as the brighter outer ring.

Venus and Earth reveal a phi relationship

Venus and the Earth are linked in an unusual relationship involving phi.  Start by letting Mercury represent the basic unit of orbital distance and period in the solar system:

 Curiously enough we find:

Ö Period of Venus * Phi = Distance of the Earth 

Ö 2.5490 * 1.6180339 = 1.5966 * 1.6180339 = 2.5833

In addition, Venus orbits the Sun in 224.695 days while Earth orbits the Sun in 365.242 days, creating a ratio of 8/13 (both Fibonacci numbers) or 0.615 (roughly phi.)  Thus 5 conjunctions of Earth and Venus occur every 8 orbits of the Earth around the Sun and every 13 orbits of Venus.

Mercury, on the other hand, orbits the Sun in 87.968 Earth days, creating a conjunction with the Earth every 115.88 days.  Thus there are 365.24/115.88 conjunctions in a year, or 22 conjunctions in 7 years, which is very close to Pi!

See more relationships at the Solar Geometry site.

Relative planetary distances average to Phi

The average of the mean orbital distances of each successive planet in relation to the one before it approximates phi:

Note:  We sometimes forget about the asteroids when thinking of the planets in our solar system.  Ceres, the largest asteroid, is nearly spherical, comprises over one-third the total mass of all the asteroids and is thus the best of these minor planets to represent the asteroid belt.  (Insight on mean orbital distances contributed by Robert Bartlett.)

2005 unveiled the discovery of a 10th planet called 2003UB313.  It was found at a distance of 97 times that of the Earth from the Sun.  Its ratio to Pluto would thus be 2.47224, much higher than any previous planet to planet orbital distance ratio.  Could it be that this is actually the 11th planet and the 10th planet will be found at an orbit whose ratio is 1.52793 times that of Pluto, preserving the phi average?  Time will only tell, but if it happens remember that you heard it here first.

The shape of the Universe itself is a dodecahedron based on Phi

New findings in 2003 based on the study of data from NASA's Wilkinson Microwave Anisotropy Probe (WMAP) on cosmic background radiation reveal that the universe is finite and shaped like a dodecahedron, a geometric shape based on pentagons, which are based on phi.   The the Universe page for more.

The Golden Ratio

— Arche de Noé amarrée sur les berges du Rhin - Cologne —

— Pas de copyright — Document personnel — Gérard Colombat — Décembre 2011 —

Cliquer sur l'image pour obtenir un agrandissement

On remarque dans ce cas que le nombre 120 est associé au chiffre 5 et le nombre 720 (600 + 120), factorielle de six au chiffre 6, 6 étant le nombre symbolique de jours de la Création, Création que DIEU a décidé de détruire en ordonnant à Noé de construire son arche pendant 120 ans, période pendant laquelle les hommes auraient pu se tourner vers DIEU.

" [...] Alors l'Éternel dit: Mon esprit ne restera pas à toujours dans l'homme, car l'homme n'est que chair, et ses jours seront de cent vingt ans. (Genèse 6/3)

In the 3x3 Magic Square of Saturn featuring the first nine numbers, the constant is 15, the sum of all the numbers of the square is 45. [The letters in the name Adam total to 45.] In the 6x6 Magic Square of the Sun, the magic costant is 111, and the sum of all the numbers of the square is 666.

Chapter 6 of Genesis deals with the description of the dimensions for Noah's Ark. (Bible dimensions are given in the form of length, breadth and height.) For the ark the length is given as 300 cubits, the breadth as 50 cubits and the height as 30 cubits (Gen 6:15). The volume is 300x50x30 or 45 with a bunch of zeros. The area is 300x50 or 15.000. The perimeter is 300+300+50+50 or 7.00. In Genesis 7:20 we read that the water rose 15 cubits, and in 7:24 we see that the water prevailed for 150 days. The periods between the release of birds was seven days each time. ("And he stayed yet other seven days; and again he sent forth the dove out of the ark.")

 

The ratio of the length to the breadth is 6:1 and the length to the height 10:1. Note that 10 is the earth's number and 6 is the sun's number. Note also that obelisks were built with a 1:10 ratio of base to height, and remember that upon raising the pillar stone in Genesis 1:28, Jacob says 'of all you give to me I will give one tenth to thee'. The sum of the first nine numbers is 45, and the sum of the first ten numbers is 55. The Washington Monument is 55.5 at the base x 555.5 feet tall. See Hebrews 7:2, where we read, "For this Melchisedec, king of Salem, priest of the most high God, who met Abraham returning from the slaughter of the kings, and blessed him; To whom also Abraham gave a tenth part of all".

Multiplying both sides of 6:1 by six gives us 360:60. We treat this as a rectangle spread round the globe 60 degrees wide. While the sun moves from 23 degrees north to 23 degrees south of the equator, the moon moves 5 degrees beyond the sun (to 28 degrees) and Mercury, the most eccentric of the planets, moves 7 degrees beyond the sun's extreme position (30+ degrees). A rectangle 6:1 describes the boundary of the visible planets on the globe. The outside dimension represents the range of Mercury, while the inside dimension represents the range of the sun.

 

The sun's 23.5 degree limit forms a border inside the rectangle. Remember that 30 degrees north and south is where a hexagram inscribed in a circle would touch the sides of that. That is the reason that a hexagram is used to depict the planets in the rose cross emblem. Note Saturn is at the top of this image. Saturn is the last sphere that the soul inhabits on its way back to the stars, and Saturn 'rules' Capricorn; also the sun is said to die in Capricorn, so it has been deemed the Gate of Death. The moon, being the last sphere the soul encounters before birth and being the ruler of Cancer, Cancer has been named the Gate of Birth (for this astronomical era).

 

"And being turned, I saw seven golden candlesticks; And in the midst of the seven candlesticks one like unto the Son of man, And he had in his right hand seven stars, and his countenance was as the sun shineth in his strength." Noah carries seven passengers with him in the ark. Below we see an Egyptian illustration of that story.

 

 

. . .

In Exodus 25, the Ark of the Covenant is described as 2.5 cubits in length, 1.5 in breadth and in height. Doubling these numbers gives us 5x3x3 which is 45. The end of the ark was a square, while the top and sides were in the 3:5 proportion. Looking again at Noah's Ark we see that the ratio of its breadth to height is also 3:5. The side of the doubled Ark of the Covenant is the end of Noah's Ark, and the ark would be made of ten of these 3x3x5 blocks. In Gen 28:22 Jacob says 'of all that thou give unto me, I will give the tenth unto thee'.

 

The diagonal of the 3x5 rectangle produces a 31 degree angle. That is, a 3x5 rectangle inscribed in a circle touches that circle at 31 degrees from the equator, the point that Mercury ranges to. This is just one hemisphere's view. The outside dimension represents Mercury path, and the inner dimension the sun's path contained therein. The Shekinah (Glory of God) that appeared over the Ark and lit the room of the Most Holy Place has it’s parallel in the sun, which He created for His glory. You can see the notion of the sun's bounded way depicted by the staves.

 

Note that the dimensions given for the ark were 300:50:30. If we multiply these by 6/5 we get 360:60:36, meaning that our map rectangle is conceptually 36 tall? Thirty six is six squared, and the sum of the first thirty six numbers is 666. In the Magic Square of the Sun the constant is 111, three ones. The sum of all the numbers of the square is 666. (The sum of the first 11 numbers is 66, and Pi equals Phi squared x 6/5.)

 

The magic square of the sun (36 cells) can be generated by quartering the nine cells in the magic square of Saturn. (Surveying in the US is done using 6 mile by six mile grids of one square mile sections.) Dividing each of Saturn's nine cells nine times (fractal) gives us the magic square of the moon with 81 cells. Notice that these are the three down the center of the planet hex emblem above. Mercury's square quarter's the squares in the Jupiter square, and the earth's square of ten, quarters the squares in the Mars square (5). 4 and 5 are different takes on life, just as Jupiter and Mars are represent different governing styles. Jupiter rules from a throne with a shephard's crook, while Mars rules from a war chariot with a flail in his hand.

Jupiter is related to Mercury numerically as Mars is related to the earth, and Saturn, the sun and moon all relate to one another. 5 x 5 is an altar number in the Bible. As a matter of fact, one altar was 5x5x3 tall meaning it had a 3x5 profile. In terms of fractions we can say that the square of Saturn represents 1:3, and Jupiter 1:4, etc. All of these but two can be derived without much trouble from the square using a straight edge, as was shown before.

Looking at the epic poem about Gilgamesh, we see that the 'ark' mentioned is cubic and measures 60x60x60 fathoms. The footprint is square and the area of that is numerically 1/6th that of the Noah's ark. 60x60x60 is actually a cubic expression of the 6x6 sun square. The flood in the Bible ends a 600 year period. "And it came to pass in the six hundredth and first year, in the first month, the first day of the month, the waters were dried up from off the earth: and Noah removed the covering of the ark, and looked, and, behold, the face of the ground was dry." Six hundred shekels of gold is the price that David paid for the threshingfloor on which the Temple eas to be built. "So David gave to Ornan for the place six hundred shekels of gold by weight."

This ark takes 7 days to build, and the flood lasts seven days. "I laid out the shape of her sides and joined her together. I provided her with six decks, dividing her (thus) into seven parts. Her floor plan I divided into nine parts." A square divided into nine parts is the square of Saturn. "When the seventh day arrived, The flood (-carrying) south-storm subsided in the battle, Which it had fought like an army."

 

"And the house which king Solomon built for the Lord, the length thereof was threescore cubits, and the breadth thereof twenty cubits, and the height thereof thirty cubits. And the porch before the temple of the house, twenty cubits was the length thereof, according to the breadth of the house; and ten cubits was the breadth thereof before the house." The house was 60x20 and 30 tall. The floor area would be 12.00 like the months, and the volume would be 60x20x30 or 36.000. The 10x20 porch gives us 2, and the 20x20x20 Holy of Holies gives us 4 and 8, the squares and cubes of 2.

http://dcsymbols.com/mastersquare/page10.htm