Le agradezco que en su contrarréplica empiece reconociendo errores y presentando disculpas. En primer lugar, Ud. se refiere al ‘diámetro de la pelota dorada’ que coronaba la Gran Pirámide y que en su primer escrito consideraba en metros, y no en codos reales, con lo cual casi doblaba su medida. Pero permítame un matiz: En geometría, al sólido de superficie curva cuyos puntos equidistan de un punto situado en su interior (el centro) se le llama ‘esfera’, y no ‘pelota’. Como Ud. sabe, la esfera es la forma geométrica que domina el universo, ya que estrellas y planetas son volúmenes esféricos. Es por ello que los pitagóricos hablaban de ‘la música de las esferas’ —y no de ‘la música de las pelotas’— como un componente de la armonía universal.

En segundo lugar, Ud. escribe que de haber recordado el cordial encuentro que tuvimos en Barcelona, el tono de su artículo ‘no hubiera sido tan ácido’. Se lo agradezco. Pero personalmente le diré, Dr. Parra, que conozca o no a mi interlocutor, sea lector mío o no, mi tono siempre es el mismo: El del obligado respeto. ¿Y sabe por qué?… Por educación y por convencimiento. Porque sé que no estoy en posesión de ninguna verdad absoluta, suelo ser comedido.

No obstante, Ud. después de disculparse, añade que ‘las críticas (…) hubieran sido exactamente las mismas’. ¿Cómo puede mantener sus críticas sin haberse informado más?… ¿No ve que sigue hablando sin conocimiento de causa, lo cual descalifica su opinión?

Mire Ud., la Gran Pirámide es el monumento más importante de la Arquitectura del pasado. Y si los arquitectos sabemos de algo, es de Arquitectura. Para hacer proyectos y ejecutar obras aplicamos, cotidianamente, la geometría y las matemáticas que se hallan en nuestro programa de estudios. Por otra parte, la experiencia de proyectar y el estudio de su cultura nos permiten acercarnos a los universos mentales de los arquitectos que concibieron los monumentos investigados, y nos permiten intuir cuales fueron los caminos que pudieron seguir al diseñarlos. El conocimiento de los instrumentos científicos de proyecto usados por la Arquitectura, y la experiencia de la intuición asociada al proceso creativo, nos permiten acercarnos con ciertas garantías a cualquier arquitectura preexistente. Y no lo olvide: La Gran Pirámide es, ante todo, Arquitectura.

Ello no obsta para reconocer la importancia de las otras disciplinas que ayudan a comprender la obra arquitectónica. Así, los estudios y mediciones realizados por otros profesionales han sido básicos para documentar y orientar la reconstrucción del modelo original de la Gran Pirámide.

Es por ello que desde una única disciplina del conocimiento, nadie puede alegar ningún derecho adquirido que le lleve a intentar expulsar a las demás disciplinas de la investigación egiptológica. Lo afirmo porque, a causa de la violencia emocional que su escrito contenía, la impresión que me causó, es que Ud. sentía como si algún extraño que usaba un lenguaje desconocido, invadiera una parcela de su propiedad intelectual. En este contexto, su precisión de que en sus palabras no hay una propuesta de censura cultural, parece una justificación necesaria, porque de su redactado se podía deducir que la Gran Pirámide hubiera de ser un ámbito restringido de lo que Ud. llama ‘especialistas’ a quienes los periodistas habrían de consultar antes de publicar informaciones sobre ella. —Y además, ¿no se da Ud. cuenta que la única profesión auténticamente especialista en Arquitectura es, justamente, la de arquitecto?

Por todo ello, la Gran Pirámide no puede ser un coto cerrado de ninguna profesión: Ni de los arquitectos por el hecho de ser Arquitectura, ni de los historiadores y arqueólogos porque sean ellos quienes más la han estudiado y quienes hasta hoy han hecho las aportaciones más decisivas.

Por eso le proponía colaborar. Y porque tengo la experiencia de haber dirigido durante años un equipo pluridisciplinar para investigar y proteger nuestro patrimonio arquitectónico, en el que participaron historiadores, arqueólogos y abogados. Y le aseguro que no se me ocurrió nunca descalificar a los demás profesionales ni entrometerme en sus trabajos específicos. Es por eso que le sugiero a Ud. que no juzgue el trabajo de un arquitecto si no dispone de la misma preparación disciplinar que él, si no tiene un conocimiento suficiente, por ejemplo, de matemáticas y geometría.

Pero es que además, cuando me discute las medidas generales de la Gran Pirámide, entra en contradicción con Ud. mismo, ya que en sus libros da iguales medidas de la base (440 cr, pág. 49 de ‘Las Pirámides’ y pág. 190 de la ‘Historia de las Pirámides de Egipto’), y de la altura (280 cr en la misma pág. 190 del segundo de ellos).  Y le añadiré que el promedio de las medidas de los cuatro lados de la base de la Gran Pirámide es 230,364 m, sólo 2,3 cm inferior a los 440 cr, por lo que el error medio sería de 1/10.000ª, es decir, que por cada 100 m habrían acumulado 1 cm de diferencia. —Si Ud. hubiera construido algún edificio, sabría la dificultad de evitar, en la obra, pequeñas desviaciones respecto del proyecto.

Por todo ello, la única reconstrucción informática posible será la del modelo original de la Gran Pirámide, la de la forma proyectada. Porque los arquitectos, Dr. Parra, solemos trabajar sobre ideas, sobre modelos geométricos y matemáticos que representan concepciones intelectuales expresadas en las medidas y las proporciones que las representan. Y el modelo original de la Gran Pirámide es el que contendrá información sobre el saber de los sacerdotes-arquitectos que la proyectaron.
Si seguimos con sus observaciones, le diré que confunde Ud. el perímetro de la base de la pirámide de 1.760 cr, con el perímetro del monumento, que incorpora todas las aristas incluso las del zócalo y las apotemas. Es por ello que suma 8.388 cr. Además, no es cierto que yo haya escrito ‘que un codo real son 0,5235 m’, que es la medida que recoge Ud. en sus libros, sino que es 0,5236 m como está mayoritariamente documentado, o para ser más exactos 0,523606797 m, longitud que corresponde a la 5ª parte del cuadrado de la Proporción Áurea (Φ = 1,618033989).

En cuanto a lo que Ud. llama ‘uno de mis grandes ‘descubrimientos’’ refiriéndose al uso de coordenadas geográficas asociadas al Monte Everest, le sugiero que evite sus comillas irónicas hasta que no consiga demostrar que no son ciertos. Créame, es de sabios rectificar, pero es de más sabios no errar.

No obstante, si que acierta al afirmar que ‘creo no equivocarme si considero que el uso del Everest como referencia geográfica se debió a que es la montaña más alta del planeta’. Pero a partir de ahí se explica a Ud. mismo un largo chiste sobre los egipcios viajando por la Tierra y midiendo todos los montes del planeta. Al respecto, le haré una reflexión: Si consideramos que nuestra civilización ha tardado 6 milenios en desarrollarse y que el ‘homo sapiens’ tiene una antigüedad de por lo menos 40.000 años, ¿no le parecería lógico preguntarse si en los 34.000 años restantes pudo haber evolucionado el conocimiento humano en algún lugar del planeta hasta un nivel similar al que encontramos en la Gran Pirámide?… ¿No le parece que hay suficientes enigmas distribuidos por toda la Tierra como para abrir la puerta a esa posibilidad?

En cuanto al Diluvio, Ud. me pregunta: ‘¿Realmente considera que el Génesis describe acontecimientos históricos?’… En general, la única respuesta posible es no. Pero a su vez, le interrogo: ¿No se ha preguntado Ud. por qué razón diversas civilizaciones del Mediterráneo Oriental y de Oriente Medio hablan del Diluvio?… ¿No se ha preguntado Ud. por qué el mito del génesis egipcio —común a las cosmogonías de Heliópolis y de Hermópolis Magna, entre otras— nos habla del Nun, del Océano Primigenio que cubría toda la Tierra?… ¿No se ha preguntado Ud. si los mitos podían contener información que configurara alguna forma de protohistoria?… ¿No sabe Ud. que Schliemann se basó en la mitología griega, en la Ilíada, para descubrir Troya?
En cuanto a que la Gran Pirámide conmemora el Milenario del Diluvio, si aceptamos que las pirámides fueron tumbas, ¿no se ha preguntado Ud. por qué Snefru, el padre de Keops, construyó tres pirámides para un solo cadáver, el suyo, con un volumen conjunto bastante superior al de la Gran Pirámide?… ¿No le parece que una respuesta posible es que tenía una fecha fija en el horizonte, una cita con la historia?

Por otra parte, la Gran Pirámide presenta diversas pruebas de que sus arquitectos conocían las medidas de la Tierra. Y si su ubicación de acuerdo con un sistema de coordenadas geográficas referido al ecuador y a un meridiano 0 situado en el Monte Everest es hoy una evidencia irrefutable matemáticamente, todavía es una evidencia inexplicada. Al respecto, le diré que hay descubrimientos de la ciencia que durante mucho tiempo han sido evidencias inexplicadas, auténticos enigmas. Así, hasta hace poco más de cinco siglos se creía que la Tierra era plana. Entonces era inexplicable que la torre del vigía fuera lo último que se veía de los barcos antes de desaparecer por el horizonte. Pero este enigma tuvo una solución lógica: La superficie terrestre era curva y la Tierra se asemejaba a una esfera. Pues mire Ud., ¡eso ya lo sabían los antiguos egipcios!… Porque si a la Gran Pirámide le dieron como nombre oficial ‘el Horizonte de Khufu’ fue a causa de la medida y del área del horizonte de visión generado al situar un ojo en el centro de la esfera de coronación, que simbolizaría el Udyat  u Ojo de Horus y que como está documentado, se halla asociado a seis fracciones matemáticas: 1/2, 1/4, 1/8, 1/16, 1/32 y 1/64.

Al referirse al conocimiento del Everest por parte de los arquitectos de la Gran Pirámide, Ud. afirma que ‘requiere repensar toda la historia del mundo Antiguo.’… ¿Y si ello fuera necesario?… La ciencia evoluciona siempre, Dr. Parra. Lo que hoy se da por cierto, mañana está en duda. Recuerde a Ortega y Gasset: ‘La ciencia consiste en sustituir el saber que parecía seguro por una teoría, o sea, por algo problemático.’

Pero ante el vértigo de lo desconocido, Ud. escribe: ‘De ahí la crítica a su doctorado. Teniendo en cuenta las importantes implicaciones históricas de sus conclusiones matemáticas, me pregunto si hubo, no ya un egiptólogo, sino algún historiador entre los miembros de su tribunal.’ Y a pesar de que en él he investigado el monumento más importante de la Arquitectura de la Antigüedad, Ud. añade: ‘Porque dadas sus conclusiones, su presencia era imprescindible para valorar su trabajo adecuadamente y de forma objetiva’. Es decir, según Ud. un historiador es imprescindible para valorar objetivamente el trabajo de investigación de un arquitecto. Perdone, Dr. Parra, el programa de sus estudios universitarios, ¿cuántas asignaturas de geometría y matemáticas contiene?… ¿No le parece que otra vez sobrevalora su especialidad como una forma de sobrevalorarse a Ud. mismo?
Por todo ello, le agradecería que deje en paz mi doctorado. Porque a pesar de que Ud. incumple un principio del método científico —el estudio previo— y un principio ético —no descalificar y no juzgar sin conocer—, ni aún así entraré a valorar si merece Ud. el título de doctor por sus méritos científicos. Ya tuvo Ud. su tribunal universitario. Y no se me ocurriría nunca dudar de su competencia.

Finalmente añadiré que coincido con su propuesta final: No perdamos más el tiempo con textos estériles. Para mí esta cuestión queda zanjada. Yo tengo su e-mail, y les solicito a los editores de la revista ‘La aventura de la Historia’ —a quienes agradezco la publicación de mis dos escritos— que le proporcionen el mío. Hágamelo saber cuando venga a Barcelona. Yo haré lo mismo cuando me desplace a Madrid. Y en nuestro primer encuentro me comprometo a demostrarle que la referencia a un meridiano 0 situado en el Monte Everest es un enigma que —como Ud. afirma— nos obliga a replantearnos algunos principios sobre nuestros orígenes.

Mientras tanto, reciba un cordial saludo.

Miquel PÉREZ-SÁNCHEZ

Phi, The Golden Ratio, and the Fibonacci Sequence

 

                              

Here is a list of what phi is:

 

1. The 21st letter of the Greek Alphabet
2. The Golden Ratio (in Mathematics, Art, and Architecture)
3. Electric Potential (in Physics)
4. The Work Function (in Electronics)
5. A Representation of Groups of Atoms in Molecules (in Organic Chemistry)
6. The Fugacity Coefficient (in Thermodynamics)
7. Navigation and Latitude (in Cartography/Map Making)
8. The Equivalence Ratio (in Combustion Engineering)
9. Representation of a Sentence (in Symbolic Logic)
10. Porosity (in Geology and Hydrology)
11. Strength (in Structural Engineering)
12. The Roll Angle (in Flight Dynamics)
13. A Generic Act (in Philosophy)
14. Magnetic and Electric Flux (in Physics)
15. The Cumulative Distribution Function (in Mathematics and Statistics)
16. The Number of Phases in a Power System (in Electrical Engineering)

So, as you can see, we have many uses for Phi.

 

THE GOLDEN RATIO

QUOTED FROM WIKIPEDIA:

"In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant that is approximately 1.61803398874989 (but goes on infinitely never repeating itself). Other names frequently used for the golden ratio are the golden section (Latin: sectio aurea) and golden mean.Other terms encountered include extreme and mean ratio,^[5] medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut,^[6] golden number, and mean of Phidias.In this article the golden ratio is denoted by the Greek lowercase letter phi (), while its reciprocal,  or , is denoted by the uppercase variant Phi ().

The figure below illustrates the geometric relationship that defines this constant. Expressed algebraically:

This equation has one positive solution in the set of algebraic irrational numbers:

 ^[1]

At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties. The golden ratio is also used in the analysis of financial markets, in strategies such as Fibonacci retracement.

 

 

The 9 edge-transitive convex polyhedra: 

ALL OF THE FOLLOWING CONTAIN WITHIN THEM THE GOLDEN RATIO OF PHI

AT EVERY EDGE; THEY CANNOT BE FORMED CORRECTLY WITHOUT PHI

 

1. Tetrahedron (Fire)
2. Hexahedron (Earth)
3. Octahedron (Air)
4. Icosahedron (Water)
5. Dodecahedron (Ether/Universe/Consciousness)
6. Cuboctahedron (see image below)
7. Rhombic Dodecahedron (see image below)
8. Icosidodecahedron (see image below)
9. Rhombic Triacontahedron (see image below)

 
 

Cuboctahedron: an Archemedian Solid;

It is one of nine edge-transitive convex polyhedra. 

Edge-transitive means that there is only one type of edge to the object; 

given two edges, whatever happens on one edge will be translated or reflected onto every other edge, 

without changing the original region.

Formed by merging the Cube (Hexahedron) and the Octahedron.

 

Rhombic Dodecahedron: This is formed by merging two Cuboctohedrons; It is how the bee's honeycomb is formed

ICOSIDODECAHEDRON: This is the closest we can come to the shape of the earth geometrically. Looking back at the Earth's Electro-Magnetic Field, and the maps I have provided, (under the title "Earth")  this is where those shapes (our conscious electro-magnetic field and ley lines) come from.

 

Icosidodecahedron

Please click here to see how the golden ratio represents the geometric relation between all ancient sites on the planet.

Rhombic Triacontahedron: This is the duality of the Icosidodecahedron

Johannes Kepler:

"Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first, we may compare to a measure of gold; the second, we may name a precious jewel" (Johannes Kepler)

 

Kepler's Model of the Solar System:

THE GREAT PYRAMID:

 

Vesica Piscis:

The Vesica Piscis from the Seed of Life & The Golden Ratio:

 

 

 

 

The Egyptians Knew This Stuff!

The Eye of Horus:

 

THE FIBONACCI SPIRAL:

This is the representation of PHI

This is the Fibonacci Sequence:

 

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 

233, 377, 610, 987, 1597, 2584, 4181, 6765, 

10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ...

 

The 2 is found by adding the two numbers before it (1+1);

The 3 is found by adding the two numbers before it (1+2);

And the 5 is found by adding the numbers before it (2+3);

this can go on forever in either direction (negative numbers).

 

 

Here is Pascal's triangle, which is very closely related to the Fibonacci sequence; 

you'll see this later on.

 

 

 

It is found in the Yin-Yang:

 

 

 

 

Here, the spiral represents FEMALE ENERGY; and the straight lines, turning at the corners, represent MALE ENERGY. At every 90 degree angle, the MALE and FEMALE energy meet.

MALE AND FEMALE ENERGY:

SOURCE

"First I would like to say something about the nature of the male and the female. These energies are two aspects of the One. They therefore are not really opposed or dualistic, they are one; they are two faces of one energy.

 

The male energy is the aspect that is outwardly focused. It is that part of God or Spirit that drives outward manifestation, that makes Spirit materialize and take form. The male energy therefore knows a strong creative force. It is natural to the male energy to be highly focused and goal-oriented. In this manner the male energy creates individuality. The male energy allows you to separate yourself from the One, from the Whole and to stand alone and be a specific individual.

 

The female energy is the energy of Home. It is the energy of the Primal Source, the flowing Light, pure Being. It is the energy that has not yet manifested, the inner aspect of things. The female energy is all encompassing and oceanic; it does not differentiate or individualize.

 

Now, imagine the energy of the female becoming aware of a certain movement inside of her, a slight restlessness, a desire for… reaching out, outside of her boundaries, moving outside of herself to attain experience. There is a longing for something new, for adventure! And then an energy comes to her that answers that longing. It is the male energy that wants to be of service and help her manifest in matter, in form. The male energy defines and shapes the female energy and by their cooperation the total sum of energies can take a completely new direction. A new reality can be created in which everything can be explored and experienced, in ever changing forms of manifestation.

 

The dance of the male and the female brings forth the fluctuating spectacle of created reality, of your creation. This is a spectacle of great beauty wherein the male and female energy worship each other and celebrate their cooperation and playful joining. And this is as it should be. The male and female energy belong together, they are two aspects of the One and together they celebrate the joyful manifestation that Creation is supposed to be.

 

It has been said that in the final realization of who you are, the only truth that matters is: I AM. And in this mystical mantra, precisely those two aspects merge. In the I is the male energy, in the AM is the female energy. The I is constricting, differentiating. It gives focus, it gives direction, it individuates: I, not the other, I. And then AM. AM is oceanic, all encompassing. It reflects the ocean of Home, the female energy, the inexhaustible source that knows no bounds, no differentiation. The flowing and joining aspect is the core of the female energy. In the I AM, the male and female come together and blissfully join their energies."
[FOR A CONTINUATION OF THIS QUOTE, CLICK HERE]

 

 

CLICK HERE TO SEE EXAMPLES OF PHI IN NATURE

It can be found everywhere; from humans, to plants, to animals, to galaxies. It is the mathematical sequence of the seed of life. It is representative of a never-ending holographic universe we just so happen to live inside of. Everything is one. Everything is eternal.

CLICK HERE IF YOU WANT TO LEARN 

EVEN MORE ABOUT THE GOLDEN RATIO

^^(This is a great site.)^^

 

audreythoreau.blogspot...
THE GREAT PYRAMID: Vesica
389 × 387 - 68k - bmp

Squaring the Circle - The Earth & the Moon

The Math:
 

Article by Ralph Miller

Since I wrote the first article about the DaVinci Code, I have received emails from readers who have suggested that there is more information contained within Leonardo DaVinci's drawing "Proportions of the Human Figure". I have continued researching the subject myself as well. In order to give some more of the information, I decided to write this second installment. I would also like to thank those who have sent me these ideas.

There seems to be a connection between all things. In other words, the nature of reality itself, or at least what we would consider consensual reality or 3D, seems to be holographic in nature. Each part of nature contains clues that unlock the puzzle of all the rest of reality, or to the whole of creation. DaVinci's drawing contains incredible information that shows the connection between humans and all of reality. There is a geometry hidden within the human body that reflects the geometry in everything else.

During an Ayahuasca journey, many people experience a perception of everything as part of an extraordinary mathematical equation. They see themselves in mathematical form. From nature around them to even their thoughts and emotions, everything is somehow represented as part of a beautiful mathematical geometry. Ayahuasca unlocks or awakens the visionary brain. The visionary brain completes the human ability to perceive. It unlocks the capacity of a greater seat of understanding that is located in the heart.

This expanded perception of reality cannot be simply intellectualized. We are used to conceptualizing ideas with our 'thinking' minds, and this is far too elaborate and complicated to grasp at that level. There is however, an expanded state of consciousness that elicits a 'knowing'. Knowing is quite different from 'understanding.' This knowing relies on a perception and trust that comes from the heart. It is very strange, because as soon as you trust … is as quick as you know.

Somehow 'knowing' is the feminine counterpart of masculine 'understanding'. We have had generations of conditioning around understanding, to the point where much of the art of knowing has gone dormant. This is all changing now. We are moving through a transition as humans. We are moving back to remembering our feminine selves.

The first DaVinci Code article showed step-by-step how a perfect six-pointed star could be constructed within the human figure. Some suggest that the six-pointed star also represents two three-dimensional tetrahedrons. A tetrahedron is a four-sided solid, where each side is an equilateral triangle. The two interlocking tetrahedrons together form a solid called a star tetrahedron.

Click on the image below to launch a slideshow explaining the concepts here. Once in the slideshow, you can hover over the right side of the image and click to navigate to the next image.

The star tetrahedron also represents what some believe to be the human energy field, also called the Merkaba. I don't think any of us can be certain that the human energy field looks like this, but there are some very synchronistic relationships that are revealed.

If you place a star tetrahedron inside of a sphere, with one of the apexes of the tetrahedron at the 'North' pole and one at the 'South' pole of the sphere, then the other six apexes of the star will touch or intersect the sphere at 19.47° above and below the "equator" of the sphere.

Consider the fact that the earth is a thin solid crust that is rotating at great speed around what is basically a liquid magma center. The result is an upwelling of great force that occurs at 19.47° North and South, that seemingly comes from nowhere. In any case the result is that a large amount of volcanic activity occurs at those latitudes. It is theorized that these forces are hyper-dimensional in nature and cascade into three-dimensional reality resulting in volcanoes.

Many of the sacred sites of ancient civilizations are also located at or very near to 19.47° North or South of the earth's equator including the Pyramid of the Sun at Teotihuacan, Mexico (19°, 36' N of equator).

Further, volcanic activity is pronounced at 19.47° on other bodies in our solar system, including:

Another synchronicity that occurs in DaVinci's drawing is that you can take the two-dimensional six-pointed 'Star of David' and if you interpret it as a view of a three-dimensional object it is a perfect dipyramid. The pyramids that were constructed by the Egyptians were not 3-sided tetrahedrons but were 4-sided pyramids, because they had a square base, plus four triangular sides. A dipyramid is simply two pyramids stuck together at their base.

If you rotate the dipyramid represented by the Star of David in DaVinci's drawing, by an amount equal to 36.26° (90° minus 19.47° divided by 2) the dipyramid will move into a perfect right-angle, two-dimensional view. The pyramids of Egypt were not quite perfect pyramids, as they were constructed slightly squatty. But even so, there is definitely a connection. Remember they are located at 19.5° North latitude!

Click on the image below to launch a slideshow explaining the concepts here. Once in the slideshow, you can hover over the right side of the image and click to navigate to the next image.

The ayahuasca journeys unfold reality into an extraordinary fractal mathematical representation. There is such a vast amount of information that is encoded into us already; it is simply a matter of unlocking the brain in order to perceive it. Somehow there is a connection between the dimensions of the human body to the earth; to the location of volcanoes; to the location of sacred sites; and to even to the pyramids themselves.

Incredible! To review, you have a perfect six-pointed Star of David in DaVinci's drawing, which can be extended into a three-dimensional star tetrahedron, unfolding a story about unknown hyper-dimensional physical forces occurring at 19.47° North and South. The two-dimensional Star of David can also be represented as a three-dimensional dipyramid, that when rotated by 35.26° which happens to be a mathematical factor of 19.47°, will return back to a two-dimensional representation of a dipyramid. Half of the dipyramid is a perfect equilateral pyramid.

The divine nature of man is hidden inside of reality itself, and the true nature of reality is hidden within humans. In our modern world we have developed myopia to such a degree, that we have collectively distorted our perception of where we really are and who we really are. But, many are making the journey back. A journey of remembering.

© Ralph Miller 2004

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.

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.

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.

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.