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Squaring the Circle - The Great Pyramid
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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).
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The Great Pyramid of Egypt
(Sphinx in foreground)
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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.
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(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.
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Construct square (i JKD),
thus creating double square (JKE f).
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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
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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.
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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).
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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.
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Squaring the Circle - The Earth & the Moon
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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
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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.
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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)!
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The Math:
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1
(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
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2
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.
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3
(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!)
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Well before the development of sophisticated arithmetic compilations, geometry was an important tool for solving the types of problems that today we solve easily as a consequence of our mathematical understanding. It was realised by our ancestors that three geometric figures -the square, circle and the triangle -formed the foundation of nearly all their particular problem solving. The circle was the most revered of all the geometric symbols, being a line which had no definable beginning and therefore no end, and as such represented infinity. The centre of the circle was the most revered point, being that from which every part of the circumference was equidistant, the centre of creation and therefore infinite in its power. In addition the easiest of the three symbols to construct was the circle. A peg could be hammered into the ground, a length of cord or material loosely tied to the stake at one end and a stick at the other, and then whilst holding the cord or material taut, one could scratch a circle in the ground by walking around the stake. However it was derived, the circumference of the circle could then be used to establish the four faces of a square.![[Afbeelding: kgest1.jpg]](http://www.freemasons-freemasonry.com/kgest1.jpg) The principles of geometry were recorded in a series of theorems expounded by the Greek mathematician Euclid around 300 BCE. One of the first principles he alludes to is a process of dividing a straight line into two equal parts. This is done by taking the line, AB, and drawing two circles of equal diameter, one circle at each end of the line, so that they overlap.![[Afbeelding: kgest2.jpg]](http://www.freemasons-freemasonry.com/kgest2.jpg) Drawing a vertical line between the points C & D will bisect the line AB into two equal lengths. This concept can be taken one stage further when the circles, both of equal diameter, are drawn such that the circumference of one circle touches the centre of the other circle. This geometric pattern was well known to the ancients and has been passed down to us with the title Vesica Piscis. The resultant area where the two circles overlap is known as the Vesica.It produces some interesting characteristics. For example, it is possible from this use of the two circles to determine an angle of 30° and 60°. This is shown in the diagram below ![[Afbeelding: kgest3.jpg]](http://www.freemasons-freemasonry.com/kgest3.jpg) through the points where the 60° is defined by the points ACB. The bold line at an angle represents the hypotenuse of a right angle triangle, CBA. Thus, the opposite angle, BAC, is 30°. By turning this simple relationship into a rectangle (as shown by the dotted lines) and bisecting the angles with a pair of compasses, it is possible to create the angles 15°, 30°, 45°, 60°, 75° and 90°. Thus, with a simple pair of compasses and a straight edge, eg 24 inch gauge, our ancestors were able to determine the primary geometric angles regularly used.This simple geometric structure immediately lends itself to the construction of another important figure -the equilateral triangle![[Afbeelding: kgest4.jpg]](http://www.freemasons-freemasonry.com/kgest4.jpg) So, our ancestors, through their knowledge of geometry, were able to produce, with considerable accuracy, the three most common geometric forms in their construction armoury -the circle, the square and the equilateral triangle -the latter two being derived from the basic form -the circle. Thus, the circle became a highly regarded geometric device. But, more importantly, it was the point at the centre of the circle which was most revered, for no circle could be constructed without it.And, as the circle became the form for the origins of so much other geometry, which in turn provided the basis for the construction of many of the temples, palaces and significant buildings of ancient times, so this point within the circle was seen as the centre from which all creation emanated. One can imagine how, through their knowledge of the interlinked macro-cosmos, and a belief that God had designed and implemented every last element of it himself, our ancestors believed that He must have used the same geometric principles. So, too, it can be imagined that the centre of the circle, infinite in the wisdom and knowledge that could be derived from it, was revered as God himself.The vesica, or central area of the interlocked circles, was treated not only with reverence but as a sacred entity. It was an area from which so much else, geometrically, could be created. With their knowledge of the macro-cosmos, it was not lost on our ancestors that the shape was not dissimilar to that of the female vulva, the origins of intelligent form -the origins of all of us. It thus represented the geometry of life. http://www.freemasons-freemasonry.com/se...emple.html
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The Vesica Piscis
The vesica piscis is a figure that arises out of the intersection of two circles. Technically, the vesica piscis is the almond-esque inner form that comes into being when two circles intersect in such a way that the center point of each circle intersects the perimeter of the other. The shape of this inner form is similar to the shape of a fish bladder—thus its Latin name, vesica piscis. The Vesica Piscis is one of relatively few symbols of sacred geometry. When taken all together—two wholes coming together to create a third unique whole—the form becomes an irresistible metaphor suggesting and informing many of the nuances that are found in the holistic approach to health, healing & bodywork.
The vesica piscis is an unmistakably feminine or yonic symbol and thus implies the mystery and potency that occurs when two wholes come together to give birth to a third unique entity. So, for instance, when two people work together in a healing relationship, they manifest an ineffable yet critical field that forms as the two coherent bioenegetic fields interact with each other. In another example, the triune of body, mind and spirit can be reconsidered from the perspective of the vesica piscis: the whole of the body and the whole of the mind can be seen as interacting to give rise to the spirit—a dynamic that is found and leveraged in the practice of yoga.
The vesica piscis represents the unique and independent field that is created by any two beings; yet paradoxically it is fully dependent upon the interaction of those unique and independent fields. It is thus a paean to our interdependence. Two people are both necessary and sufficient to create the birth of the vesica piscis. The energy of the vesica piscis occurs all the time between two people, yet with intention, this energy can be grown to encompass all of the world and the beings that inhabit it. Indeed it fully suggests to us that together we can and do change our world.
http://www.howweheal.org/About%20Me/TheVesicaPiscis.html |
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books.google.com.ar/books?isbn=0307557790
VESICA PISCIS Phi is also generated by the most widely used and most ... and,
according to John Michell, an expert in sacred proportion, the Great Pyramid at ...
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www.brucerawles.com/.../00823aa2620d2acf62471e93aebad37c-53.htm
18 Jan 2007 ... Sri Yantra, Great Pyramid, Golden Ratio and Vesica Piscis ... 1-Phi-Square Root
of Phi triangle (cross section of the Great Pyramid and primary ...
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www.dudeman.net/siriusly/cyd/city.html
Pyramids on Mars - composite of original Viking I frames 70A13 and 35A72, from
..... In rounded values, Pi is 3.1416, Phi is 1.618, the Square Root of Two is 1.414,
the ... The Square Root of Three (1.732) is demonstrated in the Vesica Pisces ...
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www.starwheels.com/infopage.php?pagename=ayalogo
PN = 1, ON = 1/Phi ES = 1, SO = 1/Phi; Radius circle (4) = height of large pyramid
. Circle (3) and circle (3') form a Vesica Piscis figure. Square OSQN = Phi ...
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www.spiraloflight.com/ls_sacred.html
Vesica Piscis. Flower of Life. Tree of Life and .... The height of this pyramid is in
Phi ratio (e.g. the Golden Mean Ratio) to its base. In fact, the geometry in this ...
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www.magic-point.org/phi-φ/
Phi Φ. 1.6180339887 4989484820 4586834365 6381177203 0917980576 ...
Cube · The geometry of vibration/light · Playing with the vesica piscis · Pyramids ...
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www.sacred-geometry.es/en/content/flower-life
The resulting cosntruct is known as the Vesica Piscis. After that, the next steps
involve turning around the original circle, find the intersecting point between the ...
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www.gabitogrupos.com/.../template.php?nm=1400449439
6 Oct 2013 ... NUMERO 153/ VESICA PISCIS / DISEÑO DEL OJO EN FUNCION AL ...... (Phi),
was also recorded into the dimensions of the pyramid itself.
- [PDF]
www.rosicrucian.org/publications/digest/digest1.../ws_05_francini.pdf
Vesica Piscis), became the core of all solids. Following this .... pyramid. The Great
Pyramid of Giza was built in approximately 2560 BCE, at the time of the Old ...
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books.google.com.ar/books?isbn=1883319420
PHI AND THE GIZA PYRAMID It is claimed that a temple priest told the ancient ...
This almond looks like a vesica piscis, but its 0 parameters differ from a V3 ...
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- Did the ancient designer(s) of pyramids at Giza knew precisely the size of our planet, the moon and the sun?
- Do ancient units of length express advanced knowledge about our solar system?
- Was the Giza Pyramids project a tribute to Geometry, Metrology and Astronomy?
Introduction
by Ernest Moyer
To say that we have in the Egyptian Royal Cubit an uncanny mathematical and geodetic display is inadequate to the reality.
Unseen forces created, and preserved, a record in our earthly social system that is stunning in its implications.
Somewhere in our past, before the Egyptians of 6,000 BC, and the Babylonians who followed, was a social influence that left a permanent imprint on mankind. But that imprint was buried; it was not visible to the social eye. Only hints of it came from the ancient philosophers who wrote about it.
In his book, Science Awakening, B. L. Van der Waerden attempted to portray science coming to life under a philosophical model of slow evolution out of primitive savagery . For him, and for most of the modern intellectual world, these were the beginnings of civilized man. But Van der Waerden failed to grasp the phenomenon he was attempting to assess. This was not Science Awakening; it was Science Going to Sleep. Only in more recent centuries has science come to life again, after many millennia of slumber.
I shall not engage in a dissertation on the historic record of those ancient events. However, it is important to recognize that this uncanny influence did not derive from a world that had a common civilization. The influence came from a highly cultured social group that existed in relative isolation in the regions of the Near East. That group was intended to uplift primitive man. Their work was hardly begun when a great default took place. The members of that group scattered to other parts of the world and left a record of their influence in various ways, from linguistic, to social practices, to such scientific displays.
How unfortunate that modern man, with his self-created and conceited philosophies, cannot admit to the key that would open his eyes to the true history of the world, and a higher reality.
The phenomenon of the Royal Egyptian Cubit was buried until such time as later man would become aware of its existence. This awakening took more than five thousand years. We cannot penetrate this mystery without invoking an intelligence behind the design that led to such startling reappearance. But even more, the preservation of components that included the definition of the measure of the radius of the earth, the definition of the surface measure, and the unique measuring system of the Egyptians, could not have been accomplished without some unknown and unacknowledged power.
At some point in time, if mankind did not first destroy himself, some human being would come along who would penetrate this mystery.
– Ernest Moyer
Cosmic Coincidence?
1,000 x 360 x 365.24 = 131,486,400
131,486,400 feet = 40,077 km = 24,902.7 miles = Equatorial Circumference of the Earth
Official value for equatorial circumference of the Earth is 40,075 kilometers and the mean length of the year is 365.2425 days
Perhaps unit of length called foot did not originate from a part of anatomy of an ancient king or pharaoh but from circumference of our planet???
1 Degree of arc
A circle has 360 degrees (each degree has 60 minutes and each minute has 60 seconds.)
One degree of arc has length = Circumference /(360) = (2*Pi*R)/360
For equatorial circumference of the Earth = 40,077,000 m (radius= 6,378,453 m )
1 degree of arc / 1,000 = 111.325 m = 365.24 feet
There are 1,296,000 seconds of arc in a circle. If we divide it by 2*Pi we get Radius of earth equal 206,264.81 seconds of arc.
Curiously, this is the length of the Royal Cubit in English inches multiplied by 10,000. (10,000 X 20.625 = 206,250.)
It is not by coincidence that feet and inches and Royal Egyptian Cubit are connected with dimensions of our planet!
Ancient Units of Length
Interest in ancient metrology was triggered by research into the various Megalith building cultures and the Great Pyramid of Giza.
In 1637 John Greaves, professor of geometry at Gresham College, made his first of several studies in Egypt and Italy, making numerous measurements of buildings and monuments, including the Great Pyramid. These activities fuelled many centuries of interest in metrology of the ancient cultures by the likes of Isaac Newton and the French Academy.
The first known description and practical use of a physical pendulum is by Galileo Galilei, however, Flinders Petrie, a disciple of Charles Piazzi Smyth, is of the opinion that it was used earlier by the ancient Egyptians. Writing in an article in Nature, 1933 Petrie says:
If we take the natural standard of one day divided by 105, the pendulum would be 29.157 inches (0.7405878 m) at lat 30 degrees. Now this is exactly the basis of Egyptian land measures, most precisely known through the diagonal of that squared, being the Egyptian double cubit. The value for this cubit is 20.617 inches, while the best examples in stone are 20.620±0.005inches.
It seems that the Architect who designed Giza Pyramids used very special unit of measure called Royal Egyptian Cubit, which like the nautical mile and the meter, also originated from dimensions of our planet.
Royal Egyptian Cubit
Royal Egyptian Cubit = 20.62 inches = 0.52375 meters.
Where did this ancient unit of measure come from?
Is it connected with dimensions of our planet, like meter and nautical mile?
In Egypt, building overseers required the Royal Egyptian Cubit to be calibrated against a precision standard at regular intervals. Failure to do so was punishable by death. This indicates an important legacy, like a standard handed down from the ‘Gods’. The ‘Gods’ of certain cultures could be early post-flood founders a few generations after Noah.
The anatomical length … cannot possibly be as long as the royal cubit of 525 mm.’24 (Unless, of course, it came from a people taller than the Egyptians.)
Egyptian royal cubits had 7 palms and 28 fingers in a cubit. The Babylonian had 30 divisions.
Both numbers indicate astronomical origin of the cubit (28 or 30 day month with 4 weeks of 7 days).
Since ancient times, people were dividing circle into 360 degrees dividing further degree into 60 minutes and each minute into 60 seconds.
The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, that follows through the ecliptic path over the course of the year, seems to advance in that path by approximately one degree each day. Some ancient calendars, such as the Persian calendar, used 360 days for a year. The Mayans used 20 cycles of 18 plus 5 unlucky days in one of their Maya calendars. The use of a calendar with 360 days may also be related to the use of sexagesimal numbers. One of the earliest recorded use of 360 as the total days in a year is found in the Hebrew Bible, Genesis 8-9 as it describes the duration of the Great Flood over 12 months of 30 days each.
Another theory is that the Babylonians subdivided the circle using the angle of an equilateral triangle as the basic unit and further subdivided the latter into 60 parts following their sexagesimal numeric system. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree.
Aristarchus of Samos and Hipparchos seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes. Eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts.
The division of the circle into 360 parts also occurred in ancient India, as evidenced in the Rigveda.
Another motivation for choosing the number 360 may have been that it is readily divisible: 360 has 24 divisors, making it one of only 7 numbers that have more divisors than any number twice itself .
Furthermore, it is divisible by every number from 1 to 10 except 7. This property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention.
Finally, it may be the case that more than one of these factors has come into play. According to that theory, the number is approximately 365 because of the apparent movement of the sun against the celestial sphere and that it was rounded to 360 for some of the mathematical reasons cited above. [ -- Source: Wikipedia]
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Today, officially accepted around the world as fundamental (standard) unit of measure for length is meter.
meter or metre (m) – the metric and SI base unit of distance.
Originally, the meter was defined as one ten-millionth (1/10,000,000) of a quadrant, the distance between the Equator and the North Pole. In other words, meter was defined as 1/10,000,000 of the distance from the Earth’s equator to the North Pole measured on the circumference through Paris. Distance selected for defining 1m is 1/4 * Earth Circumference (along meridian):
1m = (40,000,000*1/4) / 10,000,000
In other words, there are 40,000,000 meters in circumference of the Earth.
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Another, larger unit of distance which is connected with the size of our planet is Nautical Mile.
The nautical mile (symbol M, NM or nmi) is a unit of length that is approximately one minute of arc measured along any meridian. By international agreement it has been set at 1.852 km (6,076 feet). This unit is based on estimate of Earth circumference equal 40,003.2 km: 1.852 * 360 * 60 = 40,003.2 km
The nautical mile was historically defined as a minute of arc along a meridian of the Earth (north-south), making a meridian exactly 180×60 = 10,800 historical nautical miles. It can therefore be used for approximate measures on a meridian as change of latitude on a nautical chart. The originally intended definition of the metre as 1/107 of a half-meridian arc makes the mean historical nautical mile exactly (2×107)/10,800 = 1,851.851851… historical metres. Based on the current IUGG meridian of 20,003,931.4585 (standard) metres the mean historical nautical mile is 1,852.216 m.
360 deg = 21,600 min of arc (since 1 deg = 60 min of arc).
Using polar circumference of the Earth = 40,008m we get 40,008/21600 = 1.852 km. In other words, circumference of Earth is 360 * 60 = 21,600 Nautical Miles.There are 360 deg in a circle. Nautical Mile is equal 1.85 km
Interestingly, 360 x 1.85 = 666
Link about ancient units of measure:
Ancient Measurements of the Circumference of the Earth
http://www.metrum.org/measures/measurements.htm
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The value of 1.00106 British inches is calculated as 1/500,000,000 of the Earth’s polar diameter (7,900 miles = 12,713.4 km)
Defining the Royal Egyptian Cubit
There are 12 zodiac signs dividing the sky into 12 parts (12×30=360). Also, Giza is located 30 deg North of the equator.
Dividing circumference into 12 parts when Radius = 1 unit results in
2*Pi/12 = 0.5236
This number in meters = 1 Royal Egyptian Cubit
A circle has 360 degrees, each degree has 60 minutes and each minute has 60 seconds.
One second of arc has length = Circumference /(360*60*60) = (2*Pi*R)/1,296,000
Note: Pi = 3.141 592 654, multiplying its numbers results in:
3 x 1 x 4 x 1 x 5 x 9 x 2 x 6 x 5 x 4 = 129600
amazingly this is exactly 1/10 of the number of seconds in a circle 360x60x60 = 1296000.
Circumference in seconds of arc/circumference in radians gives us REC in inches:
360*60*60/(2*Pi*10,000) = 20.6265
this number represents 1 Royal Egyptian Cubit in inches.
The radian is the standard unit of angular measure, used in many areas of mathematics.
An angle’s measurement in radians is numerically equal to the length of a corresponding arc of a unit circle, so one radian is just under 57.3 degrees (when the arc length is equal to the radius). A complete revolution is 2*Pi radians for a circle of radius one.An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian. A full circle corresponds to an angle of 2*Pi radians.
Model of Earth to scale 1:12,000: The radius R of our earth model would be (6,366 km)/12,000 = 0.5305 km which is approximately 1,000 Royal Cubits
The REC is “embedded” in the design of the Giza Pyramids
The design of the Great Pyramid is based on the ratio 11:7
Proportions of any object are always independent of the units of length (meters, feet, cubits etc) we use to measure the object. Once specific unit of measuring length is introduced, dimensions of an object can be expressed by different numbers, however its proportions will remain the same. Although objects with identical proportions can be built to different scale, the “base to height” ratio will stay the same.
11/7 ratio (equal 1.571) is nearly perfect half Pi and excellent approximation of the “squaring the circle” principle.
For the Great Pyramid, Base to Height Ratio 440/280 is exactly 11/7
Most “pyramidologists” appear to be “chasing their tails” uncovering huge amount of “numerical coincidences” embedded in the Great Pyramid…
It is simply unbelievable, however ALL of these numerical coincidences are result of selecting just 2 numbers for the pyramid design:
7, 11 (height to base ratio), 40 as the scale factor, and the measuring unit: Royal Cubit = 20.62 ” = 0.524 m.
Of course big question is: why these numbers were selected for the design of the Great Pyramid?
There are at least 2 likely answers:
- in geometry, 11/7 ratio is the ratio used to perfectly approximate “squaring the circle” , Phi (1.618) and Pi (3.1428)
- in astronomy: Radius of the Earth/Radius of the Moon = 11/3 and this is reflected in the Great Pyramid design (see image below)
Units of measure used in modern times as well in the past seem to be based not on random choices but on dimensions of our planet.
Looking closer at the ancient units of length (some of which are still in use today) we can only admire the advanced knowledge of their creators.
Although very few measuring rods were found, we can discover what units were in use by the ancient architects by measuring their monumental stone structures (pyramids and temples).
For example, the Great Pyramid has base length = 9068.8 inches and height = 5776 inches.
The base in Feet = 755.7333 feet, height = 481.3333 feet.
Both numbers do not tell us much until we convert them to ancient units of length called Royal Egyptian Cubits.
1 REC = 20.62 inches therefore base is 440 REC and height is 280 REC.
Another important quality is locked in the ratio of the pyramid’s dimensions:
base to height = 440/280 = 11/7
Radius of Earth/Radius of Moon = 11/3
1/3 of moon diameter = 720 miles = 1x2x3x4x5x6 miles or 6! miles.
Moon Diameter = 3 units, Earth Diameter = 11 units
Moon plus Earth Radius is 7 units (7x 720=5040 miles)
The ratio 3:11 is 27.3 percent, and the orbit of the Moon takes 27.3 days.
Sidereal rotation period 27.321582 d (synchronous).
27.3 days is also the average rotation period of a sunspot.
Great Pyramid has Base to Height ratio 440/280 = 11/7 = 1.5714285 which is almost perfect approximation of 1/2 Pi: 3.142857.
In practical terms, such Pi would be possible to produce with high accuracy during construction of GP.
Using this value as Pi the formula for the Royal Egyptian Cubit gives us Petrie’s value exactly:
360*60*60/(2*Pi) = 20.626 * 10,000 and 20.62 inches is value of the Royal Egyptian Cubit “embedded” in the Great Pyramid
Dimensions of the Earth, the Moon and the Sun
The Earth
| Mean radius |
6,371.0 km = 3,958.8 miles |
| Equatorial radius |
6,378.1 km = 3,963.2 miles |
| Polar radius |
6,356.8 km = 3,949.9 miles |
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If we select rounded value for the mean radius of Earth as 3,960 miles, the error would be only 0.03%.
For example, making 100 m track (e.g. for runners) with this accuracy would allow for error (+/-) 3cm.
In imperial system 328.0 feet track would be made with accuracy 1.18 inch.
The Moon
The Moon completes its orbit around the Earth in approximately 27.32 days (a sidereal month). The Earth and Moon orbit about their barycentre (common centre of mass), which lies about 4600 km from Earth’s centre (about three quarters of the Earth’s radius). On average, the Moon is at a distance of about 385000 km from the centre of the Earth, which corresponds to about 60 Earth radii.
Observe the measurements of the Moon:
Equatorial radius 1,738.14 km (0.273 Earths) so
the Moon Diameter is: 3,476.28 km or 2,160 miles.
The Sun
Diameter of The Sun =865,294 miles*.
If we divide 865,294 by 2,160 astonishingly
we get 400.6 …
*The SOHO spacecraft was used to measure the diameter of the Sun by timing transits of Mercury across the surface during 2003 and 2006. The result was a measured radius of 696,342 ± 65 kilometres (432,687 ± 40 miles). Staying within the margin of error, measured radius of the Sun is 432,647 miles (or diameter 865,294 miles).
The Sun has a diameter of about 1,392,000 km, about 109 times that of Earth.
Perfect Earth, Moon and Sun
Perhaps it is just a cosmic “coincidence”, however dimensions in miles of the Earth, our moon and sun are generated by multiplication of consecutive numbers!
Radius of Earth = 3,960 miles = 11 x 360 = 1 x 2 x 3 x 4 x 5 x 6 x (11/2)
Radius of Moon = 1,080 miles = 3 x 360 = 1 x 2 x 3 x 4 x 5 x 6 x (3/2 )
Radius of Sun = 432,720 miles = 1202 x 360 = 1 x 2 x 3 x 4 x 5 x 6 x (1202/2)
Radius of Earth orbit = 92,956,050 miles (semimajor axis) = 258,211.25 x 360
Radius of Moon orbit = 238,606 miles = 662.8 x 360 = 6!x (331.4/2)
Ratio of Earth/moon orbit = 390
“Cosmic unit” derived from 9/3 ration (earth/moon proportion):
1/3 of moon Diameter = 2,160 miles/3 = 720 = 6!
720 miles = 3,801,600 feet = 45619200 inches = 2212376.33 REC
What is even more unbelievable is the fact that ancient designer of the Giza pyramids locked this knowledge into their design.
Note: Although numbers representing dimensions of pyramids depend on units of length, proportions of each pyramid are fractions always independent of the units of measure describing their size.
Proportions of the Giza Pyramids
Here are official dimensions of 3 pyramids at Giza:
- The Great Pyramid: Base =440 Royal Egyptian Cubits,
Height = 280 Royal Egyptian Cubits,
Base to Height ratio = 11/7 (440/280 = 11/7 exactly)
- The Second Pyramid:
Base =411 Royal Egyptian Cubits,
Height = 274 Royal Egyptian Cubits,
Base to Height ratio = 3/2 (411/274 = 3/2 exactly)
- The Third Pyramid:
Base =200 Royal Egyptian Cubits,
Height = 125 Royal Egyptian Cubits,
Base to Height ratio = 8/5 (200/125 = 8/5 exactly)
We can notice the following numerological relationships between 3 pyramids:
11 / 7 = (3 + 8) / (2 + 5)
( we are adding to top value of 2nd and 3rd pyramid ratio to the bottom value of each ratio)
If we add this way all 3 ratios we will get:
(11 + 8 + 3) / (7 + 5 +2) = 22/14 = 11/7
(the ratio of the Great Pyramid and the approximation of “pi” ).
So ratios of all 3 pyramids added this way are equal the ratio of the 1st pyramid.
1732/1417 = 440/360 = 11/9 = 25.2/20.62 = 1.222222
Mystery number 273
2nd pyramid proportions multiplied by 137 generate its dimensions in Royal Egyptian Cubits
This number approximates 273:
273/2 = 136.5 which is nearly 137
One of the recurring numbers in this whole exploration of the underlying mathematics linking the Earth, Moon and Sun is 273, or 0.273.This constant is reached through this simple sum: (4 – pi) / pi = 0.2732
The ratio of moon diameter to Earth diameter (3/11) is 0.273
The ratio of Earth diameter to Moon diameter (11/3) is 3.666
- 366 lunar days (27.32 earth days) = 10,000 earth days.
- 366 is number of earth rotations in 1 year
( there is one extra rotation due to the earth’s revolution around the sun).
- 27.32 earth days in Sidereal period of the moon ( one moon day ).
- 2,730,000 the circumference of the sun in miles.
- 273 days in an average human pregnancy (10 lunar months).
- 27.32 freezing point of water on Kelvin scale (K)
- -273.2 degrees celcius is the temperature of absolute zero.
- Gasses expand by 1/273 of their volume with every degree on the Celcius/centigrade scale.
- If you were to draw a circle inside a square, with the circle’s diameter the same as the square’s length, the area left over that the circle does not cover is 27.32% of the total area of the square.
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Phi and phi
Royal Cubit = 0.5236 m = Pi/6
Pi – Phi2 = 0.5231
phi = 1.61803 39887 49894 84820 45868 34365 63811 77203 09179 80576
phi, 1.618 … is the Golden Ratio in life and the universe.
phi + 1 = phi 2
Phi = 1/phi = 0.618034…
Phi = phi – 1
( 1 + sqrt(5) )/2 = 1.61803 3988…
which is an excellent approximation of Phi
The following formula connects “Pi” (3.14159…) and “phi ” (1.6180…):
(6/5 ) x phi 2 = Pi
or
(12/5) x phi 2 = 2 x Pi
sqrt(phi) nearly equals 4/pi
( 1.272 vs 1.273 )
This Formula is expressed by the numbers describing Pyramids of Giza !!!
Here is how:
Proportions (base to height ratio) of the 1st Pyramid: 11/7
Proportions (base to height ratio) of the 2nd Pyramid: 3/2
Proportions (base to height ratio) of the 3rd Pyramid: 8:/5
(24/10) x phi2 = 2 x Pi
the same formula written with ratios of 3 pyramids:
2 x [ 2 x (11/7)] = (3/2) x (8/5) x phi2
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The closest distance between Earth and Sun is 147 x 106 km, which converted to Royal Egyptian Cubits is 280 x 109 ( 280 cubits is the height of the Great Pyramid).
3960/360 = 11 miles
11 miles = 58080 feet
58080/365.24 = 159.02 feet
Circumference 159.02 *2 * Pi = 1000 |
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A Geometer's Washington D.C. Notebook
A Frame-by-Frame Look at Geometric Aspects of the Design of Washington D.C.
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Updated June 16 - Images open in new windows so that you can look at as many at once as you need to. This will be added to and revised as time permits.
Geometry
If you were new to the idea, and did a search for the term "sacred geometry", you might get the sense that the subject was a sub-set of geometry, restricted to figures like Metatron's Cube and the Flower of Life, and notions like pi and phi. The truth is that Philosophers have, for centuries, considered all of Geometry to be sacred; and some, like Plato and Pythagoras, consider it to be the 'corner stone' of their system of study.
Plato wrote above the entrance to his academy, "Let none ignorant of geometry enter here", meaning that no one could understand his philosophy without knowing geometry, because geometry contained the fundamental secrets of all the ancient sciences. This viewpoint is shared by Masonry.
You will please note that the notion of the sacredness of mathematics and geometry is inconsistent with the idea that some numbers and some geometric figure are inherently evil. Here is something from John Mitchell's "View Over Atlantis" that sums up this viewpoint:
"It is inconsistent to relate moral principles to numbers, for numerical relationships are precise and unalterable while morals are neither, being simply mores, customs adapted by general consent in reponse to the circumstances at a particular time and place. No number, in itself is exclusively representative of a moral quality, whether negative or positive, for every natural principle has it's own rightful place in the Universe. A true cosmology must encompass every created element."
. . .
Symmetry, the Triangle and the Rhombus
see fig. 1 - The Washington DC map features two axes of symmetry - 16th Street runs north-south through the White House and Scott Circle, and East Capitol Street runs east-west through the Capitol Building and Lincoln Square. The central segment of Pennsylvania Avenue connects those two buildings to form a triangle. It is this triangle that David Ovason focuses on in Secret Architecture while ignoring the fact that Pennsylvania and Maryland Aves are symmetrical to one another. Ovason also focuses on the August sunset along Penn Ave without ever mentioning the May sunset there, or the sunsets along Maryland Ave in Feb and Nov.
This is the pair of streets that people liken to the compass in the map. The Jefferson Memorial is symmetrical to the WH seen from the CB. (In the image above looking west the Wash Mmt is directly ahead, the WH is down Penn Ave to the right, and the Jeff Mm, is to the left down Maryland Avenue.)
Maryland and New York Avenues help form similar triangles around the point intended for a monument to George Washington 1 2, located where those axes cross (marked 'A'). These three (Penn, NY and Maryland) provide all but one side of a rhombus around the monument location.
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The Stonehenge and Cross Quarter Days
see shng2_2.jpg The shortened hexagram from the DC map looks like this on the Stonehenge. The corners of the rectangle match the Station Stones. One of the diagonals of this rectangle at the Stonehenge aligns with the cross-quarter sunset just like the northwest segment of Penn Ave.
Norman Lockyer, a naturalist, suggests that ancient astronomical monuments like the Stonehenge were originally sighted according to what he called the May-November year instead of to the solstices and equinoxes. The May and November dates correspond to what are known as cross quarter days that are half way between the solstices and equinoxes; the other two are in February and August. Since the sun moves more quickly through the solar arc near the equinoxes, it moves 71% of 23.5 degrees (16.6 degrees) between the equinoxes and cross quarter days at the equator.
At the equator the cross quarter sunrises and sunsets occur 16.6 degrees north and south of due east and west. At the latitude of DC they occur at 23+ degrees. At the Stonehenge it's 28+ degrees. The pyramid of the sun in Mexico is aligned to the Aug 13 sunset which is very close. see sunpyr.gif
. . .
52 Degrees
These next images show how the vesica piscis can be used to generate both the equilateral and the 52 degree triangles. Here both triangles are equal in height but if we were to scale the 52 degree triangle so that it had the same base as the equilateral triangle it would be shorter than that.
The 60 degree triangle represents the cathedral
while the 52 degree triangle represents the map.
see Animation2.gif The derivation of the Tree of Life, Metatron's Cube and the cathedral plan from the original vesica shows that while the cross centers on the rhombus, the center of the triangle (where the diagonals cross) lies at Daath's location. A static version of that looks like this: see 60.jpg.
This image shows just the upright rhombus plus the 52 degree triangle that we see above. see rhombus52.jpg The diagonals of the equilateral triangle form 30 degree angles, in the 52 degree triangle they are 23+ degrees. see vesica52b.jpg
see Animation3.gif The derivation of the grid upon which DC is based looks like this . All the elements are the same height as in the 60 degree model, they are just wider. Here is a simplified version of that: see grid52a.jpg
Ad Quadratum and Ad Triangulum
The center circle of the cathedral plan shows an inscribed triangle, hexagon and square. The triangle and hexagon represent the ad triangulum while the square represent the ad quadratum. The DC boundary is shaped like this oblique square and represents the quadratum.
Taking the bottom of the square and the top of the triangle gives us the Masonic Compass and Square, representing the triangulum and quadratum. The compass indicates the rhombus and the square the cross.
This is the ideal (triangulum) template for the map which was shortened. It is basically Metatron's Cube, although you can also see the yin/yang symbol there among others. Letters and numbers as well. 1, 2, 3, 4 ...
[Note that the sides of the triangle form the upright rhombus and the diagonals form the horizontal rhombus and the cube. Extending the top sides of the hexagon locate the top points of the pentagram.]
The Upright Rhombus and Tree of Life
Can Be Found Within Metatron's Cube
John Mitchell readers will recognize this image as the source of his St. Mary's Chapel at Glastonbury and Stonehenge images. It is also the source of David Fideler's 'Three Worlds' image. Metatron's Cube is probably the source for the story in Rev 21 about the cubic city with twelve gates. Neither Mitchell or Fideler mention Metatron's Cube. The geometry on the 1935 version of the Great Seal that we find on the dollar bill relates to this template as well.
 
In an equilateral triangle lines that bisect the corner angles also bisect the opposite sides. These three lines cross at the 'center' of the triangle. Reducing the height of the triangle so that the base angles are 52 degrees produces diagonals of 23 degrees like we see in the map. see sixpoints.jpg
Close enough to mimic the passages in the pyramid (which are at 26+ degrees).
Note the pentagonal fractals
Coincidently
If we inscribe a hexagram in a circle, the points touch the circle at 30 degrees north and south; the same angles of the lines that bisect the corners and sides of the equilateral triangle. The Great Pyramid is located just south of 30 degrees north latitude. In Washington DC, the solar arc is just over 30 degrees north and south, so that a hexagram could be used to lay out a sun wheel there. At the equator (or a lodge) the hexagram can serve to determine the arc of all of the planets, including Mercury the most eratic. That is to say, at the equator none of the planetary bodies strays outside of a 62 degree arc, while at DC this is the arc of the sun itself.
At the equator the solar arc is 23.5 degrees and the sun moves from 23+ degrees north of the eqiuator to 23+ degrees south of there. At the equator you need 47 degrees of free space in order to watch the sun rise or set each day. Since the moon's orbit varies 5 degrees beyond that of the sun as seen from the earth, we would need 57 degrees to see it too there.
Mercury varies 7.5 degrees above and below the sun, so to see it we need 62 degrees of space on the horizon. This means that no planet is overhead further north than 31 degrees. Bromwell points out that we can depict this 60+ degree band 360 degrees wide as a rectangle that is 1:6 without much distortion to the map.
The Pyramid lies just below 30 degrees north latitude but neither it's faces nor it's cross-section is an equilateral triangle. The faces are 58 degrees and the cross section is ~52 degrees. The map illustrates that if we ruduce the equilateral traingle to 52 degrees, the 30 degree diagonals become 23.5 degrees like the tropics. The passages in the pyramid run at 26.5 degrees (about half of 52).
The upright rhombus image above has a ratio of 26:15 for the long to the short axis (52:30), and as was pointed out, this ratio was altered three times in the map. It was also pointed out that the triangle base angles were altered from 60 to 52 degrees.
If the triangle in the vesica images above is 481+ feet tall, the diameter of the circle is 555+ feet (or 6660+ inches); that is, 555+ foot diameter circles produce a vesica 481+ feet tall. The Great Pyramid is 481+ feet tall and the Washington Monument is 555+ feet tall. In Greek leters were also numbers and the word 'rhombus' totals to 482
More about Geometry
Geometric Design Principles , or how the templates were applied to the DC map, ties esoteric geometry to design theory
DC's Isometric Map Grid , the ideal template for the map confirms the straight-line hypothesis that the Capitol was displaced
Doubling the Circle A drawing exercise that uses vesicas was used to design the Great Seal and much more
The Map and the Milan Cathedral Plan both derive from the doubling the circle images
Contemplating the Hexagon
Occult Symbolism: As American as Baseball Nine men per side, nine innings, three strikes, three outs, four balls, four bases (including home) 90 feet etc
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Sabemos que Vesica Piscis esta en funcion al a los 153 peces de Juan 21:11.
Aqui tenemos a Pi - la circunferencia del toro y la vesica piscis 256/153 equivalente a la raiz cuadrada de 3
En el hipercubo las coordinadas binarias de Piscis son decimal 3 y binario 11
153 los pescados de Jesus en la biblia
Por ello Pi-c-is, o sea Pi es C que es la letra numero 3¿Cúal es la conexión toroide-rombododecaedro-vesica-piscis?
-¿rombo-dodecahedro que es la representación en planta 2D del hipercubo en el momento actual que vivimos? o es una plano genérico?
Tiene algo que ver Torus con Horus, supongo
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Hay una obvia conexion DE VESICA PISCIS CON EL TOROIDE.
No se que entiendo la relacion 4/3, con que arco ? con que fin dicha relacion ?
La relacion de la vesica piscis es 256/153, lo mismo el rombo que esta comprendido en ella.
Aunque esta todo conectado, vamos a no mezclar la actividad gaseosa en el centro de la galaxia con el movimiento del hipercubo sobre su eje en espiral que es lo que en definitiva forma la vesica piscis en la forma del Toro geometrico de la galaxia, no el Universo.
Todo esto ya lo explique varias veces desde diferentes angulos, te recomiendo revises mis posts anteriores, si es a lo que se referian lo Mayas, seguramente.
La relacion del Toro al hipercubo es la misma que la del circulo al cuadrado y la vesica piscis al rombo, digamos que a traves del cubismo es mas facil interpretar la realidad pero el Toro es la verdadera forma geometrica de la galaxia, tiene 4 dimensiones por lo tanto su forma varia en el tiempo, si la vesica piscis se forma al finalizar un ciclo de tiempo, cuando el espiral o la serpiente se come la cola, para dar comienzo a otro a traves de la regeneracion explosiva en el centro de la galaxia la cual invierte los cubos dando lugar a un nuevo ciclo de tiempo.
El pan de cristo, la levadura y la fermentacion, el murecillo, el roscon, etc, todo fue explicado, no quiero repetir siempre lo mismo.
Los tioles mercaptores, codigo del mercurio, y los enlaces S-S, gases combustibles en el centro de la galaxia que se activaran el fuego cosmico al chocar los cubos del hipercubo en el 9-6 del rombo dodecahedro.
Torus es la definicion del Toro en Ingles, seguramente se inspiraron en Horus, el Cristo Egipcio, pero la clave del nombre es el toro Egipcio Apis - Venus en los cuernos del Tauro, o sea Isis.
Evidentemente la VIA LACTEA, al igual que LOS MOTORES, LOS OSCILADORES, LA CORRIENTE ALTERNA, EL MOTOR ELECTRICO, LA DINAMO, ETC,ETC, TIENE EL MISMO PATRON DE LA OSCILACION EN EL CUAL EL PUNTO DE INFLEXION (CUANDO LA SERPIENTE SE MUERDE LA COLA) ES VESICA PISCIS. EL ESTUDIO DE LA TORA CON ALTA PROFUNDIDAD, PARA GLORIA DE YHWH ES SINONIMO DE CIENCIA.
Vesica Piscis tiene fuerte relacion ESOTERICA CON LA RESURRECCION y con el NUMERO 8=INFINITO=VIDA ETERNA.
LA SERPIENTE SE MUERDE LA COLA (VESICA PISCIS)
LA ESTRELLA DE 8 PUNTAS/ISHTAR/ESTRELLA DEL ORIENTE/LLAVE DE SOLOMON/ORION
LA SERPIENTE SE MUERDE LA COLA=LA LLAVE DE SALOMON
Si observamos esta grafica de la PRECESION DE LOS EQUINOCCIOS, notamos que el justo el punto PISCIS/ACUARIO es un PUNTO DE CAMBIO DE SENTIDO. Aparentemente VESICA PISCIS TIENE ESTA REFERENCIA. Concretamente DETRAS DE VESICA PISCIS ESTA EL COMIENZO DE LA ERA DE ACUARIO. VESICA PISCIS TIENE FUERTE NEXO CON EL SEXO FEMENINO EN EL CONTEXTO AL NACIMIENTO DE UN BEBE. EL TOROIDE/TAURO TIENE FUERTE RELACION CON EL UTERO FEMENINO.
Aqui en estas graficas observamos que justamente en el comienzo de la ERA DE ACUARIO LA LUZ/ESPADA DE ORION va a estar justo en el SOLSTICIO. Esto explica por lo menos de un punto de vista cientifico la relacion de TAURO/ORION CON VESICA PISCIS(OJOS DE GATO)/JUAN 21:11. En este enlace se lo puede ver directamente.
Este es el SECRETO DE LA SEÑAL DE JONAS. Por eso NUESTRO SEÑOR INTERRELACIONA LA CONSTELACION "OJOS DE GATO", DRACO, ORION Y TAURO.
A.F: En su libro El legado perdido de María Magdalena, usted afirma que la unión entre Jesús y su esposa es la piedra angular de la primera comunidad cristiana. ¿Qué motivos la han llevado a esta afirmación?
M.S: Una de las parábolas de los evangelios nos dice que cierto rey ofreció un banquete de bodas para su hijo, pero que todos los invitados declinaron la invitación. Creo que este es el escenario exacto que se presentó en el siglo I. Jesús ofreció a su comunidad un «banquete de matrimonio» que celebrase la unión de amor entre el marido y su mujer. Jesús utiliza este banquete como una metáfora del «Reino de Dios». Creo que el círculo de personas más próximo a ellos reconocía la simbiosis arquetípica del «Esposo» y de su «Hermana-esposa» evocada en el Cantar de los cantares. Su «unión» está confirmada por la Gematria cabalística de algunas frases del evangelio. Si añadimos el valor de las letras griegas presentes en el título honorífico «la Magdalena», la suma será igual a 153, el número de los «peces» que se menciona en Juan 21. Este pasaje es una metáfora. Los peces son los iniciados. El número 153 está asociado también a la forma geométrica llamada Vesica piscis, que en la geometría sagrada de los pitagóricos correspondía a las antiguas diosas del amor y de la fertilidad: la matriz, el regazo, la puerta hacia la vida, el Sancta Sanctorum. Jesús era representado como «Pez» por los primeros cristianos y a Magdalena se le había conferido un título que la asociaba con el «Recipiente de los peces». Ambos son el Señor y la Señora de los «Peces» y de la Edad de los peces (la Era de Piscis).
Hechos 12:12: Y habiendo considerado esto, llegó a casa de María la madre de Juan, el que tenía por sobrenombre MARCOS, donde muchos estaban reunidos orando.
Observamos los dos tipos de flujos, el horario y el antihorario, al igual que EL SOL Y LA LUNA. Fuerte interrelacion con CANCER/SHAVUOT/PENTECOSTES. El mismo planeta tierra esta diseñado en funcion a la UNION ENTRE EL HOMBRE Y LA MUJER, INSISTO, EL SOL Y LA LUNA. GENESIS 1:19
OBSERVEN EL FUNCIONAMIENTO DE LA DINAMO en funcion a una maquina externa adentro de un campo magnetico fijo DE UN ANILLO (REVOLU-SION=NUMERO PI=3.14).
El anillo que tiene connotacion con SATURNO/SATURDAY/SABADO/SEPTIMO DIA tambien es un TOROIDE/TAURO/PLEYADES. EL FLUJO MAGNETICO ES ORION. LA ROTACION DEL ANILLO QUE PRODUCE LA LUZ/ILUMINACION TIENE FUERTE INTERRELACION INSISTO CON EL CIRCULO. ESTA TODO CODIFICADO. LA LUZ GENERADA SIMBOLIZA A LA LUZ DE ISTAR/ORION/ESTATUA DE LA LIBERTAD. LA DINAMO FUNCIONA EN FUNCION A SHAVUOT/PENTECOSTES. LA ENERGIA ELECTRICA GENERADA TIPIFICA EL GRIAL.
LA MISMA PALABRA REVOLU-SION ES UNA REFERENCIA AL NUMERO PI (LONGITUD DE LA CIRCUNFERENCIA ES IGUAL A PI X DIAMETRO.)
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ESCALERA DE JACOB
SABIDURIA/SABADO/ SOPHIA/PHI=1.618033
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La gran piramide vista desde arriba sin la piedra angular
interesante:
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