CUPRINS:

- LightSource Screenshots: images - Metatron Cube - Nuevos aportes a la Geometría Arcana - Sacred Geometry - Sacred Geometry, Crosses and Swastikas - Sacred Geometry in the Quantum Realm - Stones and the Sacred - The Meaning of Numbers - The Platonic Solids - The Thirteen Sacred Geometry Forms - Why Sacred Geometry?

Related Reports - Harmonic Pyramids on Earth and Abroad

Stones of various kinds and sizes have been invested with sacredness from the earliest times. The worship of stones can be found in most ancient cultures, while sacred stones can be found in most of the world's religions.

According to Pausanias (VII, 24. 4) [see BIBLIOGRAPHY], In olden times all the Greeks worshipped unwrought stones instead of images and describes thirty square stones near a spring sacred to Hermes [cf. Water and the Sacred] at Pharae in Greece.

Beginning as early as 5000 BCE, large stones (megaliths - Greek mega, great, and lithos, stone), either unwrought or roughly worked were erected across prehistoric Europe to stand in lines or in circles (such as at Stonehenge in England), or otherwise arranged in conjunction with earthworks usually identified as burial mounds (such as at Newgrange in Ireland). Little is known the purpose or meaning of these megalithic constructions, but it is universally agreed that they mark or embellish a sacred place in the landscape.

Examples of megalithism can also found in countries around the world, such as the Beforo monument near Bouar in the Central African Republic, the Tatetsuki stone circles standing the summit of a tumulus at Okayama in Japan, and the moai statues on ceremonial platforms on Easter Island [see Jean-Pierre Mohen in the BIBLIOGRAPHY].

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The moving and arranging of massive stones into a building or some other configuration in a sacred context also characterizes many early cultures around the globe, from the Inca in South America, to the Egyptians and Mycenaeans.

Smaller individual stones can also become invested with the sacred. The Stone of Scone, also known as the Coronation Stone or the Stone of Destiny, until very recently rested on a shelf beneath the seat of the Coronation Chair in Westminster Abbey in London (it has now been returned to Scotland [see The Stone of Destiny]. It is said that the stone could identify a rightful ruler of the country by emitting a loud cry. Since the 13th century, every British king or queen (except for the first Mary) has been crowned monarch while seated in this chair over this stone. The stone had been brought to London by order of King Edward I from Scotland in 1297. In Scotland the stone had been kept at Scone Palace in Perthshire where 34 successive Scottish kings had been crowned while seated upon it. According to tradition, the stone had been brought to Scotland from Ireland where, up to that time the newly crowned kings of Ireland had been crowned upon it on the Hill of Tara. Legend further explains that the stone had come to Ireland from Judah in the 4th century BCE when the daughter of the last king of Judah married into the Irish royal family. Previously, the stone had been kept in the Temple of Jerusalem (cf Dome of the Rock) when the kings of Judah had been crowned upon it. Traditionally, the stone is believed to be that which Jacob used as a pillow when he had his dream of angels at Bethel.

Another example of a holy stone is the very sacred Black Stone (reddish black, with some red and yellow particles ) inside the holy shrine of the Ka'ba [1. Ka'ba] at Mecca. It is thought that the Black Stone, now in pieces (three large parts, with smaller fragments which are tied together with a silver band), may be a meteor, or a piece of lava, or a piece of basalt. Its original diameter is estimated to have been 30 cm. Besides the Black Stone, built into the western corner of the Ka'ba is less sacred Stone of Good Fortune.

Stones and rocks in Japan were initially seen as symbols of mononoke (supernatural forces which permeate matter and space). Later, an abstract, undifferentiated mononoke was replaced by more definite animistic deities which resided in the stones and rocks. These rock abodes are called iwakura. All over the precinct of the Shrine at Ise are rocks and stones which are venerated as the abodes of deities, such as the subsidiary shrine at the Naiku called Takimatsuri-no-kami. Elsewhere in Japan are many stones and stone arrangements representing the male and female principle, such as the stone circle at Oyu in Akita Prefecture in Northeastern Japan. The emotional attachment to natural stones, originally religion-inspired, has persisted in Japan and is manifest today in the creation of richly symbolic and spiritual stone gardens.

Tiffiney Whitmire "All things throughout our universe seem to follow the same fundamental blueprint or geometric patterns. These geometrical archetypes, which reveal to us the nature of each form and its virational resonances. They are also symbolic of the underlying metaphysical principle of the inseperable relationship of the part to the whole. It is this

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principle of oneness underlying all geometry that permeates the architecture of all inseparability and union provides us with a continous reminder of our relationship to the whole--a blueprint for the mind to the sacred foundation of all things created." We call this blueprint "Sacred Geometry".

Sacred Geometry is a term that is used by archaeologists, anthropologists, and geometricians. It includes the religious, philosophical, and spiritual beliefs that have surrounded geometry in many various cultures throughout history. It covers Pythagorean geometry as well as the relationships between organic curves and logarithmic curves. The "sacred" aspect of geometry has evolved as a result of different cultures. I have provided five different views of how different cultures have made geometry become sacred. Later, I will explain the meaning of certain numbers, as they play an important role in sacred geometry. A few examples of sacred sites will also be provided. These examples will provide you with a real sense of how sacred geometry is used in sacred sites.

Flower of Life

1. The Ancient GreeksThe ancient Greeks used certain geometrically-derived ratios. In this culture the cube traditionally symbolized kingship and earthy foundations. The Golden Section traditionally symbolized philosophy and wisdom. Therefore, if a building was dedicated to a king it would bear traces of cubic geometry and a building dedicated to a heavenly god would be constructed using Golden Section proportions. The term "Golden Proportion" is historically the unique geometric proportion of two terms and it is designated by the 21st letter of the Greek alphabet - phi. Phi was known by cultures much older than the Greek. The three-term proportion is a:b :: b:c. That is, a is related to b as b is related to c. However, within the three-term continuous proportion there is a special sub-set where the third term is equal to the first term plus the second term, a:b :: b:(a+b), so that only two terms, a and b, are found in the three-term proportion. This is called Phi, the Golden Proportion.

• "The fact that it is a three-term proportion constructed from two terms is its first distinguishing characteristic, and is parallel with the first mystery of the Holy Trinity : the Three that are Two." (Lawlor 45)

• "The Golden Proportion represents indisputable proportional evidence of the possibility of a conscious evolution as well as of an evolution of consciousness." (Lawlor 47)

The Golden Proportion is not an ordinary ratio. It is found naturally in nature. Its specific ratio is 1.618. For example, it describes the spiral of seeds in sunflowers and the shape of nautilus shells.

2. The HindusBefore the Hindus erect any type of building, large or small, for religious purposes they first perform a simple geometric construction on the ground. This means that they construct a square from establishing due East and West. It is from this square that they lay out the entire building. The geometric construction is associated by prayers and religious observances.

3. The ChristiansThe cross is used as the major emblem for the Christian religion. In geometrical terms the cross, elaborated in the Medieval period, is the form of an unfolded cube. It was also associated with kingship. Many of the Gothic churches were built by proportions derived from the geometry inherent in the cube or the double-cube. Many Christian churches are still built in this form today.

4. The Ancient EgyptiansThe ancient Egyptians used regular polygons in their construction, but discovered that these polygons could be increased while keeping the ratio of their sides by the addition of a strictly constructed area. This was named the

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"gnomon" by the Greeks. The god Osiris was given the recognition for the concept of the ratio-retaining expansion of a rectangular area. Egyptians also used the square as a symbol of kingship.

5. The Discovery of Jay HambidgeJay Hambidge was an art historian at Yale during the 1920's. He discovered that the spirals on the Ionic column capitals of ancient Greek temples were laid out by the "whirling rectangle" method for creation of a logarithmic spiral. He did not find any "sacred meaning" for the logarithmic spiral form of the Ionic column capital. However, he did find that the Greek architects purposely constructed their temples according to "whirling rectangle" geometric ratios. Click here for image.

"Mathematics, as the basis of all science, is itself a universal symbolism, a language into which all knowledge is eventually translated and rendered communicable. The key to all knowledge is in the science of numbers." (Sepharial 24) OneOne symbolizes manifestation, assertion, the ego, selfhood and isolation. In the philosophical sense, it represents the synthesis and fundamental unity of things. In a religious sense, it represents the lord. In a material sense, it represents the individual. It is the symbol of the Sun.

TwoTwo symbolizes plus and minus, active and passive, male and female, positive and negative and so on. It stands for the dualism of manifested life-God and Nature. It denotes agreement and separation.

ThreeThree symbolizes the trinity of life, substance, and intelligence, of force, matter, and consciousness. The family-father, mother, and child.

FourFour is the number of reality and concretion. It is the cube or the square. It symbolizes the cross, segmentation, partition, order, and classification.

FiveFive represents expansion. It symbolizes inclusiveness, comprehension, understanding, judgment, reason, and logic.

SixSix is the number of cooperation. It symbolizes marriage, a link, and connection. Six is the inner action of the spiritual and material. Six also represents art, music, dancing.

SevenSeven is the number of completion. It represents time, space, duration, and distance. It also represents old age, death, or endurance, and immortality.

EightEight is the number of dissolution. It denotes the law of cyclic evolution, the breaking back of the natural to the spiritual.

NineNine is the number of regeneration. A new birth. It represents spirituality, premonition, and voyaging. It also represents penetration, strife, energy, and anger.

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The superficial equivalents of the sphere, cone and cube are the circle, the triangle, and the square. These figures, used in symbolical thought, represent states of consciousness. These figures are related to the numbers 1, 3, 4, which denote God, Humanity, and Nature. One Being is represented as spirit, soul and body.All geometrical relations are expressions of numerical ratios. "...we give natural assent to the power of numbers on which, in the Pythagorean concept, the universe is founded." (Sepharial 19)

The circles represents the sun and relates the natural aspects with the spiritual. There is only one sun and therefore, one God who is the universal lord. (The number one.)

Numbers are also associated with colors: 1 - White

2 - Yellow or cream

3 - Violet

4 - Orange or ruddy gold

5 - Indigo or dark blue

6 - Pale blue or turquoise

7 - Silver or opalescence

8 - Black or deep brown

9- Red or crimson Examples:

Parthenon

The Parthenon was created by the Greeks. The Greeks believed that everything, form the human body to the entire cosmos, was governed by an order accessible to human reason. The Parthenon was created as a temple for Athena Parthenos. It is located at the top of the Acropolis of Athens. It was built to house a huge gold and ivory statue of the goddess Athena.

The Parthenon is known as a geometrical masterpiece. It is very pleasing to the eye due to the unique architecture. The lines that are perceived as horizontals in fact are curved upward in the middle. The platform upon

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which the columns of the temple stand is slightly curved on all four sides. All of the columns are tilted inward slightly, and are placed closer together toward the corners of the building.

The geometrical aspect of the Parthenon is also very interesting. If you add the number of Columns on the front and then multiply them by 2 and add 1 you will get the number of columns on each side. (8x2 = 16, 16+1 = 17) This is said to be geometrically proportional. It is interesting that the number of columns chosen for the front was eight. Eight also represents the infinity symbol and looks like a spiral. The spiral is important when discussing aspects of the Golden Mean because the spiral helps describe the Golden Mean logarithmic spiral. I have previously given the sunflower as an example. The sunflower has 55 clockwise spirals overlaid onto either 34 or 89 counterclockwise spirals. We recognize these numbers as part of the Fibonacci Series, which is generated by Phi.

Newgrange, Ireland Newgrange was built around 3,200 BCE. It is a circular mound of earth and stone and is about 250 feet in diameter. The interior is solid, but there is a single stone-lined passage that is 62 feet long and 3 feet wide. This passage terminates close to the center of the mound in a main chamber with a corbelled vault 20 feet high and three recessed chambers.

The entrance of Newgrange incorporates a "roof box" that allows the sun, at sunrise on the morning of the winter solstice on December 21, to enter the interior. The sun penetrates the full length of the interior passage all the way to the main chamber.

It is interesting to me that Newgrange was choosen to be a circle and that the sun plays a very important role in its architecture. As I have stated previously, The circle represents the sun and relates the natural aspects with the spiritual. There is only one sun and therefore, one God who is the universal lord. This also represents the number one.

(top) photograph showing sunlight shining through the "roof box"

(right) photograph showing sunlight entering the main chamber

Bibliography: • Sepharial,The Kabala of Numbers,California: Newcastle Publishing Co. Inc.,1974. • Lawlor, Robert,Sacred Geometry, New York: Crossroad, 1982. • Schimmel, Annemarie, The Mystery of Numbers, New York: Oxford University Press, 1993.

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Each lightSource image is fully animated and utilizes 6000 colors. At normal speed (suitable for meditation) it takes about ten minutes for an image to unfold its full range of colors.

These thumbnails and screenshots are instant snapshots of the images captured in a single moment, and each is displayed here in only 256 colors.

The Sri Yantra

Icosidodecahedron and Pentagonal

Star

Golden Ratio Spirals

Tree of Life superimposed with

Seed of Life

Harmonics of Music with 13 Strand DNA

Flower of Life with 2nd Harmonic Overlay

Electromagnetic Field of the Human Merkaba

The Endless Knot

Torus

Metatron's Cube

Ankhs (ansate cross) and the Seed

of Life

Sacred Heart

Vesica Piscis

Sacred Geometry is the blueprint of Creation and the genesis of all form. It is an ancient science that explores and explains the energy patterns that create and unify all things and reveals the precise way that the energy of Creation organizes itself. On every scale, every natural pattern of growth or movement conforms inevitably to one or more geometric shapes.

As you enter the world of Sacred Geometry you begin to see as never before the wonderfully patterned beauty of Creation. The molecules of our DNA, the cornea of our eye, snow flakes, pine cones, flower petals, diamond crystals, the branching of trees, a nautilus shell, the star we spin around, the galaxy we spiral within, the air we breathe, and all life forms as we know them emerge out of timeless geometric codes. Viewing and contemplating

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these codes allow us to gaze directly at the lines on the face of deep wisdom and offers up a glimpse into the inner workings of the Universal Mind and the Universe itself.

The ancients believed that the experience of Sacred Geometry was essential to the education of the soul. They knew that these patterns and codes were symbolic of our own inner realm and the subtle structure of awareness. To them the “sacred” had particular significance involving consciousness and the profound mystery of awareness … the ultimate sacred wonder. Sacred Geometry takes on another whole level of significance when grounded in the experience of self-awareness.

The gift of lightSource is that it actually allows you to experience that essential self within the designs of pure Source energy. As the blueprints literally come to life before your eyes, you are propelled into ecstatic play with the very the heart of Creation.

Each of the thirteen images featured represents a complex melding of sacred geometric elements with a state-of-the-art media realization into complex, flowingly animated art. Exponential combinations of color palettes, images and unlimited choices of music and sound create unique, unparalleled experiences.

Embedded in these experiences are the properties associated with each geometry. Also, there is always an experiential and emotional aspect associated with every sacred geometrical form. These particular aspects become more apparent over time. In the end, keep only what your personal experience validates.

Sacred Geometry Forms Properties Associated with the Form

1. Torus

The first shape to emerge out of the genesis pattern. It governs many aspects of life including the human heart with its seven muscles that form a torus. The torus is literally around all life forms, all atoms, and all cosmic bodies such as planets, stars and galaxies. It is the primary shape in existence.

2. Vesica Piscis

The crucible of the creating process. An opening to the womb from which all geometric forms are born. A symbol of the fusion of opposites and a passageway through the world’s apparent polarities. The geometric image through which light was born. Also the geometry for the human eye.

3. Flower of Life

The geometric power symbol, which activates energy coding in the mind, helping one to access their “light body.” It is the primal language of the universe—pure shape and proportion. This interlocking circle design has the ability to

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unlock memories that are deep within our being because it is a primary energy/language pattern that has a resonance with all things within us and around us. Shown here with a harmonic overlay.

4. Tree of Life and Seed of Life

The Tree of Life is one of the most ancient and profound teachings of the awareness of Universal life force energies and the light body. Along with the Seed of Life it is part of the geometry that parallels the cycle of the fruit tree. When these two forms are superimposed upon each other that relationship becomes apparent. The Tree of Life is most widely recognized as the geometry that is the basis for the Kabalah, the ancient system of mystical Judaism.

5. Seed of Life and Ankh Cross

Geometry of seven interconnected circles, the Seed of Life is considered to be the basic unit of information necessary for the formation of all material substance. In this rendition, the Seed of Life is superimposed over the geometry of an Ankh or Ansate cross, an ancient Egyptian hieroglyph signifying life, health and happiness. This cross has been extensively used in the symbolism of the Coptic Christian church.

6. Electro Magnetic Field of the Human

Merkaba

The Star Tetrahedron (a three dimensional Star of David) is the sacred geometry at the center of this form and is the pattern of the etheric light grid that surrounds each human being. This grid is called the Merkaba and it is an interdimensional vehicle used initially to incarnate spirit into human bodily form. The Universal energy of Love is the fuel for this vehicle.

7. Metatron’s Cube

One of the most important informational systems in the universe and one of the basic creation patterns for all of existence. Within it are found all five of the Platonic Solids, the ”building blocks” of creation.

8. Decagon with a Pentagonal Star

The Decagon emerges from the pentagon and shares its self-generating divine proportion, the golden mean. At the center of this design is the Pentagonal Star, a powerful psychological icon symbolizing excellence, authority and uprightness.

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9. Golden Mean Spiral

The Golden Mean Spiral is the ideal and correlates to Source. It is the symbol of life’s unfolding mysteries. With each revolution the spiral reveals a complete cycle of evolution. It offers a wiser and more all-encompassing perspective gleaned from growing by “learning all angles” of each experience. With their continuous curves, spirals are feminine in nature. Logarithmic spirals, like cochlea of the inner ear, reveal the intimate relationship between the harmonics of sound and geometry.

10. Harmonics of Music

and Thirteen Chakras

Like the Golden Mean Spiral, this geometric progression has no beginning and no end. It is from the Harmonics of Music that all the laws of physics can be derived, reveling the potent nature of this form. Music is a powerful tool for opening the charkas. This geometry artistically symbolizes this relationship, and as such, may be a particularly good focus for meditation when listening to Enos Dream.

11. Endless Knot

One of the eight sacred emblems of Tibetan Buddhism, this geometry forms ten enclosures and symbolizes the endless cycle of death and rebirth until illumination. (The core Buddhist insight underlying this symbol is: addiction and aversion lead to delusion, which is the ongoing source of all suffering.)

12. Sacred Heart

Is said to be primary source of spiritual intuition, and the seat of true wisdom. The purpose of which is to illuminate, inspire and lead the mind, rather than be controlled by the mind.

13. Sri Yantra

A geometric power symbol. The ancient yogis of India considered it to be the most powerful of all known geometric power symbols. Represents the geometric structure of the sound of creation—OM.

Meditation on the Sri Yantra will bring enlightenment and that all the secrets of the universe will be revealed to the person who meditates on it until its image is engraved in the mind. This form also has the ability to focus, balance

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and increase the level of life force energy. The key is experiencing Sri Yantra as a “star gate” to the Zero Point of Source from which all manifestation ultimately comes.

by IDTimeTravellerfrom 3rdDimensionOnLine Website

Metatron's Cube

The image you see above is the correct version of "Metatron’s Cube", or the fruit of life with the 5 platonic solids. I made it with a 3D program and what you see are the actual edges of the platonic solids.

The dodecahedron and icosahedron actually have their "inner" corner points touching the star tetrahedron that fits in a circle that is = 1/Ø x the circle connecting the corners of the outer cube.

Where Ø ("phi") = 1.618 033 988 749 594 ...

The way to figure out drawing this is by beginning with the normal flower of life "grid" (of 5 non-intersecting inner circles, or in this case: 7 intersecting full circles - left image):

Then draw a circle that is equal to 1/Ø x the outer circle.

For this, put the point of a compass on the middle of the vertical radius (in the centre of the second "flower" from the top along the vertical axis) and draw a circle from where the horizontal axis (through the middle of the circle) cuts the outer circle (see below);The circle you can draw when you put one point of the compass in the centre of the grid, and draw a circle from

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where the other circle cuts the vertical axis (through the middle of the circle), is a circle Ø times smaller than the outer circle:

After this, draw the appropriate startetrahedron(s) and you have found all the points necessary to draw the other platonic solids.

Here are all the platonic solids the way they fit in Metatron’s cube:

Tetrahedron Star tetrahedron

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Cube Octahedron

Dodecahedron Icosahedron

All platonic solids

Not all solids can be (fully) seen, as some lines are hidden behind others.

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All solids as in metatron’s cube, seen from side

Here are all the solids of Metatron’s cube. This is what you see in Metatron’s cube from the top, but here it is seen from the (right) side.

Classic representation of dodecahdron in tetrahedron

This is a correct version of a dodecahdron in a startetrahedron. It’s a classic representation that is commonly done in a way that is incorrect.

The corners of the dodecahedron are found by drawing lines from the corners of the big startetrahedron to those of a startetrahedron that is Ø

times smaller. .

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from Sangraal Website

Drawing by Drunvalo Melchizedek

Perhaps you can see the rectangle with the triad on top and bottom. It is part of the cube nested within a cube.

Metatron’s Cube is the incubator of 3D. It represents a box within a box or a cube nested within a cube. The Tesseract represents a process in which one might peer into the fourth dimension. The drawings of the Dodecahedron - Eve’s Grid and the Tesseract are basically the same geometry except that the Tesseract is tilted so you might better define the six sections.

Outlined in red is one of the six sections. The idea is to go into the outlined area and see it as a cube. Once you have visualized being inside the cube, it represents the cube of 4D. Click on the Tesseract to get a larger image

The Tesseract Drawing comes from a book published in

1928 titled "Theosophy and the Fourth Dimension" by Alexander Horne.

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for visualization.

It often takes a student several tries to actually get inside the 4D cube. The larger image works much better than the small one. If you have difficulty after a couple of days, perhaps stop for a few days and try again. It took me several attempts to see it the first time.

Seeing the cube within a cube dimensionally leads one to consider the nature of the Holographic model. It has the nature of being exactly the same structure if you were to tear off a piece from the edge. The integrity of the geometry would be maintained infinitely. The image below could be that of the corner you just ripped off the edge.

Above, we see that the Tree of Life is contained in Metatron’s Cube/Grid. The view above comes from the Seed of Life, therefore

metaphorically, the Tree is contained within the seed, and is a fractal property from the

beginning.

Drawing by Drunvalo Melchizedek

When considering the Flower of life Geometries, keep in mind that curved lines represent female characteristics and straight lines represent male characteristics. The drawing depicts the holographic nature of the male and female character of the grid work and a deeper, more "within" nature, of Metatron’s Cube.

Merkaba Field

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Introducción La Geometría está presente por doquier en toda la naturaleza, está en el basamento de la estructura de todas las cosas desde las moléculas hasta las galaxias, desde los ínfimos virus hasta los grandes elefantes. A pesar de nuestra actual separación del mundo natural, nosotros seres humanos seguimos ligados a las leyes naturales del universo.

El término Geometría significa literalmente "medida o medición de la tierra".

Es una herramienta fundamental que está estrechamente ligada a todo aquello que sea hecho por las manos del hombre y desde tiempos antiguos a todo lo que significan las mediciones, que en esos tiempos eran consideradas como pertenecientes a una de las ramas de la Magia . En la antigüedad la magia, la ciencia y la religión eran de echo inseparables, constituyendo el fundamento del conocimiento de los sacerdotes.

La armonía inherente a la geometría fue comprendida como una de las expresiones del plan divino que basamenta al universo, un patrón metafísico que determina lo físico. La realidad interna, trascendente a las formas externas, ha permanecido a través de la historia como la base de las estructuras sagradas. Hoy día es tan valido construir un edificio moderno de acuerdo a los principios de la geometría sagrada como lo fue en el pasado en estilos como el egipcio, griego, románico, islámico, gótico o renacentista.

La proporción y la armonía se hallan íntimamente ligadas a la geometría sagrada, porque ella a su vez está ligada metafísicamente a la estructura íntima de la materia.

Los principios de la Geometría Sagrada

Los principios que basamentan disciplinas tales como la geometría sagrada, la magia o aún la electrónica están ligados a la naturaleza del universo. Las variaciones en la forma externa pueden estar influidas por consideraciones religiosas o aún políticas, mas los fundamentos operativos permanecen constantes. Un ejemplo lo encontramos en una analogía eléctrica. Para poder iluminar con una lámpara eléctrica es necesario cumplir con una serie de condiciones. Es necesario hacer circular por dicha lámpara una corriente eléctrica de determinada intensidad, para lo cual hay que aplicar una tensión eléctrica por medio del circuito y las conexiones adecuadas. Estas condiciones no son negociables, si algo se realiza incorrectamente la lámpara no ha de iluminar o se quemará. Todo aquél que realice tales tareas debe adherir a estos principios fundamentales o fallará en su intento. Tales principios son independientes de toda consideración política o sectaria, el circuito ha de funcionar ya sea bajo un régimen dictatorial como bajo uno democrático.

De manera análoga, los principios fundantes de la geometría arcana trascienden las consideraciones religiosas sectarias. Como una ciencia que lleva a la reintegración de la humanidad con el todo cósmico, ella ha de obrar, como en el caso de la electricidad, sobre todo aquél que reúna los criterios fundamentales, sin importar de quién se trate. La aplicación universal de idénticos principios de geometría arcana en lugares separados por vastos espacios de tiempo, lugar y creencia atestigua su naturaleza trascendental. Fue aplicada a las pirámides y templos del Antiguo Egipto, los templos mayas, los tabernáculos de Jehová, los zigurat babilonios, las mezquitas islámicas y las catedrales cristianas. Como un hilo invisible los principios inmutables conectan estas estructuras sagradas.

Uno de los principios de la geometría sagrada lo encontramos en la máxima hermética "como es arriba, así es abajo" y también en "aquello que se halla en el pequeño mundo, el microcosmos, refleja lo que se halla en el gran mundo o macrocosmos". Este principio de correspondencia se halla en la base de todas las ciencias arcanas, donde las formas del universo manifestado se reflejan en el cuerpo y constitución del hombre.

En la concepción bíblica el hombre ha sido creado a imagen y semejanza de Dios, siendo él un templo dispuesto por el Creador para albergar al espíritu que eleva al hombre por encima del reino animal. Por ello, la geometría sagrada no trata únicamente sobre las figuras geométricas obtenidas a la manera clásica con compás y escuadra, sino también de las relaciones armónicas del cuerpo humano, de la estructura de los animales y las plantas, de las formas de los cristales y de todas las manifestaciones de las formas en el universo.

Desde tiempos remotos la geometría ha sido inseparable de la magia. Aún las arcaicas inscripciones en las rocas siguen formas geométricas. Debido a que las complejidades y abstractas verdades expresadas por las formas geométricas solamente pueden ser explicadas como reflexiones de las más profundas verdades , fueron consideradas como misterios sagrados del mayor nivel y fueron puestas fuera de los ojos profanos. Estos profundos conocimientos pudieron ser transmitidos de un iniciado a otro por medio de símbolos geométricos sin

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que los ignorantes de ello siquiera tomaran nota que se efectuaba dicha comunicación.

Cada forma geométrica está investida de un significado simbólico y psicológico. De esta manera todo aquello hecho por la mano del hombre que incorpore dichos símbolos deviene un vehículo para las ideas y conceptos incorporados en su geometría. A través de las edades las geometrías simbólicas han sido las bases para la arquitectura sagrada y aún profana. Algunas subsisten todavía como potentes arquetipos de fe: el hexagrama como símbolo del Judaísmo, la cruz en el Cristianismo.

Las formas y figuras geométricas Unas pocas formas geométricas constituyen la base de toda la diversidad de la estructura del universo.

Todas estas formas geométricas básicas pueden ser fácilmente realizadas por medio de dos herramientas que los geómetras han usado desde los albores de la historia: la escuadra y el compás. Como figuras universales, su construcción no requiere de ninguna medida, ellas se dan también a través de formaciones naturales en el reino orgánico como en el inorgánico.

- El círculo

El círculo ha sido seguramente uno de los primeros símbolos dibujados por el hombre. Es simple de dibujar, es una forma visible cotidianamente en la naturaleza, visto en el cielo como los discos del sol y la luna, en las formas de animales y plantas y en las estructuras geológicas. Muchas construcciones antiguas adoptaron esta forma, los tipi americanos y los yurt mongoles son los sobrevivientes de estas formas universales. Desde los círculos neolíticos británicos y a través de las formas megalíticas de piedra circulares de los templos, la forma circular ha imitado la redondez del horizonte visible, haciendo de cada construcción un pequeño mundo en sí mismo.

El círculo representa la completura y la totalidad. En un antiguo tratado alquímico se lee: "Haz un círculo del hombre y la mujer, y dibuja fuera de él un cuadrado, y fuera del cuadrado un triángulo. Haz un círculo y tendrás la piedra de los filósofos". El círculo ha sido empleado como símbolo de la Eternidad y de la Unidad.

Como eternidad porque no tiene principio ni fin y siempre retorna al mismo punto. También por esta razón simboliza el Universo, no hay punto donde comience ni punto donde tenga fin, entonces todo lo contiene y no hay nada fuera de él, por ello también es símbolo de la Unidad, especialmente cuando en él se hace presente el centro como símbolo de la primera manifestación.

También simboliza el Destino, Hado o Necesidad y la ley cíclica porque a medida que la rueda de la vida gira los ciclos retornan marcando en la naturaleza la repetición y renovación de los ciclos de vida y en la historia humana el eterno retorno de los arquetipos.

- El cuadrado

Muchos templos antiguos fueron realizados bajo una forma cuadrada. Representando el microcosmos y con ello la estabilidad del mundo, esta es una característica saliente de las llamadas montañas del mundo, los zigurat, las pirámides y los stupas. Estas estructuras simbolizan el punto de transición entre el cielo y la tierra, centradas idealmente en el omphalos, el punto axial en el centro del mundo, su ombligo.

Puede ser dividido en cuatro cuadrados haciendo una cruz que automáticamente define su centro. Orientado hacia los cuatro puntos cardinales, en el caso de las pirámides egipcias con excepcional precisión, puede ser además biseccionado además por diagonales, dividiéndolo en ocho triángulos. Estas ocho líneas, radiando del centro, forman los ejes hacia las cuatro direcciones del espacio, y los cuatro rincones del mundo, la división octuple del espacio. Esta división del espacio está emblematizada en el octuple sendero del Buddhismo y en

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los cuatro caminos reales de Bretaña, señaladas en la Historia de los Reyes de Bretaña. Cada una de las ocho direcciones en Tibet, están bajo la guarda simbólica de una familia, una tradición similar a la de las ocho nobles familias de Bretaña.

- La Vesica Piscis

La vesica piscis es la figura producida cuando dos círculos de igual tamaño son dibujados hasta el centro del otro. Ha representado el vientre de la Diosa Madre, el punto de surgimiento de la vida. Ha tenido una posición de primacía en la fundación de construcciones sagradas. Desde los antiguos templos y círculos de piedra hasta las grandes catedrales medievales, el acto inicial de fundación ha estado relacionado a la salida del sol en un día predeterminado. Este nacimiento simbólico del templo con el nuevo sol es un tema universal, relacionado con la también con la vesica piscis. La geometría de los templos hindúes, así como los de Asia Menor, norte de África y Europa, tal como ha sido registrado, derivan directamente de la sombra de un gnomón. Hay un antiguo texto sánscrito referido a la fundación de templos, el Manasara Shilna Shastra, que detalla el plan para su orientación.

El sitio ha de ser elegido por un practicante de la geomancia, clavándose allí un gnomón, alrededor del cual se traza un círculo. Este procedimiento fija el eje este-oeste. Desde cada extremo de este eje se trazan arcos, produciendo una vesica piscis, la que a su vez determina el eje norte-sur. De esta vesica inicial, se dibuja otra en ángulo recto y de esta un círculo central y entonces un cuadrado dirigido a los cuatro cuartos de la tierra. El sistema utilizado por los romanos para la fundación de sus ciudades descrito en los libros de Vitruvio se muestra idéntico al sistema hindú aquí descrito.

- El número de oro

El número de oro, o sección de oro, es una relación que ha sido usada en la arquitectura sagrada y el arte ya desde el período del antiguo Egipto.

Las construcciones y los objetos sagrados de egipcios y griegos tienen geometrías basadas en la división del espacio obtenida por rectángulos raíz y sus derivados. Los rectángulos raíz son producidos directamente a partir de un cuadrado por el simple dibujo con compás, entrando así a la categoría de la geometría clásica, producida sin mediciones.

Existe una serie de rectángulos raíz que se hallan interconectados. El primero de ellos es un cuadrado, el segundo es raíz de 2, el tercero es raíz de 3, el cuarto es el doble cuadrado y el quinto es raíz de 5. Si bien los lados de dichos rectángulos no son medibles en términos numéricos, los griegos decían que no eran realmente irracionales porque eran medibles en términos de cuadrados producidos de ellos. La posibilidad de medición en términos de área en lugar de longitud ha sido uno de los grandes secretos de los griegos.

Esto nos lleva a otro factor fundamental en diseño de arquitectura sagrada: la proporción y la conmensurabilidad. La música lo demuestra admirablemente en sus armonías, y de hecho de ella se ha dicho que es geometría convertida en sonido. La conmensurabilidad asegura completa armonía a través de una construcción u obra de arte, es una integración de todas las proporciones de las partes de tal manera que cada una de ellas tiene una forma y tamaño fijos. Nada puede ser añadido o removido sin alterar la armonía del todo. Ciertos rectángulos que son punto de partida de figuras geométricas relacionadas constituyen las bases para tales estructuras armonizadoras.

Los rectángulos con relaciones entre lados de 3:2, 5:4, 8:5, 13:6, etc. en los cuales las relaciones están expresadas en números enteros se los ha llamado rectángulos estáticos, mientras que rectángulos tales como los rectángulos raíz son llamados rectángulos dinámicos. Hay unos pocos rectángulos que combinan las propiedades de lo estático y lo dinámico: el cuadrado y el doble cuadrado. La diagonal de este es seguramente la forma más favorecida en las construcciones sagradas y es raíz de 5, lo cual se halla directamente relacionado a la proporción de oro.

Esta importante razón, llamada por los griegos la Sección , la Divina Proporción por Luca Paccioli (1509), y

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bautizada por Leonardo da Vinci y sus seguidores la Sección Dorada o Número de Oro , tiene propiedades únicas que han cautivado a los geómetras desde tiempos egipcios.

Esta relación existe entre dos objetos o cantidades cuando la razón entre la mayor y la menor es igual a la existente entre la suma de las dos (la totalidad) y la mayor.

Es simbolizada por la letra Phi, en honor a Fidias. Numéricamente posee propiedades excepcionales, tanto algebraicas como geométricas, Phi=1,618, 1/Phi=0,618 y Phi al cuadrado=2,618. En toda progresión o serie de términos que tenga a Phi como la razón entre sus términos sucesivos cada término es igual a la suma de los dos que lo preceden.

En términos numéricos esta serie fue primeramente conocida en Europa por Leonardo Fibonacci, nacido en 1179. Viajó con su padre a Argelia donde los geómetras árabes le enseñaron los secretos de la serie, pudiendo también introducir los números arábicos, revolucionando las matemáticas europeas.

Esta serie ha sido reconocida como el principio de la estructura de los organismos vivientes y de la estructura del mundo.

El número de oro ha sido honrado a través de la historia. Platón en su Timeo lo considera como la clave de la física del cosmos y hasta el moderno arquitecto Le Corbusier, padre de los edificios torre, diseñó un sistema modular basado en dicha proporción.

by Richard Hawkins(es necesario tener instalado QuickTime Player)

"click" en las fotos y espere 2 minutos aprox. para que cargue el archivo.

TENGA PACIENCIA!!!

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Sacred Geometry, Crosses and Swastikas

by Jiri Mruzekfrom PrehistoricScienceArt Website

While looking at the golden grid of the glyphic square from the inscription, I began pondering the crosses and swastikas, which can be isolated in this grid. The swastikas looked to me markantly unlike the nazi symbols. Searching the web then produced confirmation for this impression.

Unlike the swastikas we see here, the official swastika of the Third Reich was built from seventeen identical squares in a grid of 25 such squares.

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The Abydos Helicopter inscription emphasizes the golden grid of a square - a field of Golden Rectangles, and corresponding squares.

The swastikas, as well as the crosses you see here conform to the Divine Proportion. I would not be surprised, if the dimensions of the cross, on which Jesus was crucified, had just happened to conform to the Divine Proportion for the sake of the divine presence, and it may have looked much like the cross on the left, below.

The cross on the right is also made out of Golden Rectangles. Crosses, and swastikas are among the essential sacred symbols, but their actual construction may vary between sacred, and ordinary.

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The above swastikas from circa 1907 postcards seem to be constructed by the olden Section. They are the only such old swastikas I found on the net. Similarly, a Google search for the keywords ’swastika’ and ’golden section’ produces only one complete hit - this page. It seems unbelievable that no one else has ever raised this important subject.

copyright 1907 by E. Phillips, a U.S. card publisher

The text on the card back reads: GOOD LUCK EMBLEM

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"The Swastika" is the oldest cross and emblem in the world. It forms a combination of four "L’s" standing for Luck, Light, Love and Life. It has been found in ancient Rome, excavations in Grecian cities, on Buddhist idols, on Chinese coins dated 315 B.C., and our own Southwest Indians use it as an amulet.

It is claimed that the Mound Builders and Cliff Dwellers of Mexico, Central America consider "The Swastika" a charm to drive away evil and bring good luck, long life and prosperity to the possessor. The above swastika from probably the same series misses its mark, as a good luck charm, no doubt. It certainly did not help the nazis any. This is the one swastika, which shall for ever be tarnished as the symbol of Evil. Just look at the 2/3 ratios on its sides.

2/3 = .666.. Need I say more? This is no divine life-giving proportion. This is no sacred swastika. Were its proportions the main factor in Hitler’s blessings for it as the official symbol of his state?

So, there is a difference between the 666 Swastika adopted by Hitler , and the 1.618 swastika composed upon the Divine Proportion and selected from the golden grid of a square. It was not in Hitler’s power to undo the sacred fundamental nature of this symbol, just like it was not in Stalin’s power to diminish the sacred nature of the 5-pointed star.

Some interesting related reading on Fulcanelli

q t T tsh nb

3.1 ATLANTEAN SECRETS REVISITED

As illustrated in our previous volume, a majority of the unified cosmological picture that we have been describing in this book is provided in exquisite detail throughout the Vedic scriptures, which date themselves as being 18,000 years old. It is highly likely that the entire cosmology that we are discussing was well known by both the Atlanteans and the Ramans during ancient times. Then, roughly 12,000 years ago, a worldwide cataclysm caused the destruction of both civilizations. As the years passed, those who inherited the scientific knowledge would have more and more difficulty seeing “the big picture.”

Almost all sacred traditions, including those of the Vedas, insisted that there was a hidden order that unified all aspects of the Universe, and that with sufficient study and visualization of the underlying geometric forms of this order, the mind of the Initiate could be connected with the Oneness of the Universe, enabling great feats of consciousness and mind-over-matter capability to occur. Some of these visualizations took the form of studying mandalas, such as the Sri Yantra formation. Others preferred to engage in dances where the movements and music were in tune with these geometric patterns. Still others preferred to assemble, sculpt and / or draw these forms with a compass and straightedge, hence the importance of the main symbol of the Masonic fraternity, which has the letter “G”, symbolizing “God,” “Geometry” and the “Great Architect of the Universe,” surrounded by a compass above it and a straightedge below it. Pre-Masonic groups such as the Knight Templars chose to encode these geometric relationships into their sacred structures, such as the stained-glass windows in cathedrals.

3.2 SACRED GEOMETRY AND THE PLATONIC SOLIDS

Hence, the cornerstone of knowledge for secret mystery schools regarding this hidden order in the Universe has always been sacred geometry. We have written extensively on this subject in both of our previous books, and the reader is encouraged to refer back to them for greater understanding. In short, sacred geometry is simply another form of vibration, or “crystallized music.” Consider the following example: First, we vibrate a guitar string. This creates “standing waves,” meaning waves that do not move back and forth across the string but remain stable in one place. We will see some areas where there is an extreme of vertical movement, representing the top and bottom of the wave, and other areas where there is no vertical movement,

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known as nodes. The nodes that are formed in any type of standing wave will always be spaced evenly apart from each other, and the speed of the vibration will determine how many nodes will appear. This means that the higher the vibration rises, the more nodes we will see. In two dimensions, we can either use an oscilloscope or vibrate a flat circular “Chladni plate” and see nodes develop that will form common geometric forms such as the square, triangle and hexagon when connected together. This work has been repeated many times by Dr. Hans Jenny, Gerald Hawkins and others. - If the circle has three equally spaced nodes, then they can connect to form a triangle- If the circle has four equally spaced nodes, it can form a square- If it has five nodes, it forms a pentagon- Six nodes form a hexagon, et ceteraThough this is a very simple concept in terms of wave mechanics, Gerald Hawkins was the first to establish mathematically that such geometries inscribed within circles were indeed musical relationships. We may be surprised to realize that he was led to this discovery by analyzing various geometric crop formations that would appear overnight in the fields of the British countryside. This has been covered in both of our previous volumes.

The deepest, most revered forms of sacred geometry are three-dimensional, and are known as the Platonic solids. There are only five formations in existence that follow all the needed rules to qualify, and these are the eight-sided octahedron, four-sided tetrahedron, six-sided cube, twelve-sided dodecahedron and twenty-sided icosahedron. Here, the tetrahedron is shown as a “star tetrahedron” or interlaced tetrahedron, meaning that you have two tetrahedra that are joined together in perfect symmetry:

Figure 3.1 – The five basic Platonic Solids.

Here are some of the main rules for these geometric solids: - Each formation will have the same shape on every side:

• equilateral triangle faces on the octahedron, tetrahedron and icosahedron • square faces on the cube • pentagonal faces on the dodecahedron

- Every line on each of the formations will be exactly the same length. - Every internal angle on each of the formations will also be the same. And most importantly, - Each shape will fit perfectly inside of a sphere, all the points touching the edges of the sphere with no overlaps. Similar to the two-dimensional cases involving the triangle, square, pentagon and hexagon inside the circle, the Platonic Solids are simply representations of waveforms in three dimensions. This point cannot be stressed strongly enough. Each tip or vertex of the Platonic Solids touches the surface of a sphere in an area where the vibrations have canceled out to form a node. Thus, what we are seeing is a three-dimensional geometric image of vibration / pulsation.

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Both the students of Buckminster Fuller and his protégé Dr. Hans Jenny devised clever experiments that showed how the Platonic Solids would form within a vibrating / pulsating sphere. In the experiment conducted by Fuller’s students, a spherical balloon was dipped in dye and pulsed with “pure” sound frequencies, known as the “Diatonic” sound ratios. A small number of evenly-distanced nodes would form across the surface of the sphere, as well as thin lines that connected them to each other. If you have four evenly spaced nodes, you will see a tetrahedron. Six evenly spaced nodes form an octahedron. Eight evenly spaced nodes form a cube. Twenty evenly spaced nodes form the dodecahedron, and twelve evenly spaced nodes form the icosahedron. The straight lines that we see on these geometric objects simply represent the stresses that are created by the “closest distance between two points” for each of the nodes as they distribute themselves across the entire surface of the sphere.

Figure 3.2 – Dr. Hans Jenny’s Platonic Solid formation in spherical vibrating fluid.

Dr. Hans Jenny conducted a similar experiment, a small part of which is pictured here in Figure 3.2, wherein a droplet of water contained a very fine suspension of light-colored particles, known as a “colloidal suspension.” When this roughly spherical droplet of particle-filled water was vibrated at various “Diatonic” musical frequencies, the Platonic Solids would appear inside, surrounded by elliptical curving lines that would connect their nodes together, as we see in the picture, where it is clear that there are two tetrahedrons in the central area. If the droplet were a perfect sphere instead of a flattened sphere, then the formations would be even more clearly visible.

3.3 PLATONIC SOLIDS AND “SYMMETRY” IN PHYSICS

The mystery and significance of the Platonic Solids has not been completely lost to modern science, as these forms fit all the necessary criteria for creating “symmetry” in physics in many different ways. For this reason, they are often seen in theories that deal with multi-dimensionality, where many “planes” need to intersect in symmetrical ways so that they can be rotated in a number of ways and always remain in the same positions relative to each other. These multi-dimensional theories include “group theory,” also known as “gauge theory,” which consistently features various Platonic models for “infolded” hyperdimensional space.

These same “modular functions” are considered to be the most advanced mathematical tools available for the study and understanding of “higher dimensions,” and the “Superstring” theory is entirely built off of them. In short, the Platonic Solids are already known to be the master key to unlock the world of “higher dimensions.” Remember that we have only briefly mentioned the above points, as they have been well-addressed in our previous volumes, and the key is symmetry. When we keep in mind the symmetrical quality of the Solids as we have indicated, Dr. Wolff’s words from Chapter 5 entitled On the Importance of Living in Three Dimensions should make good sense to us: Pg. 71 – As your advisor in exploration, I can tell you, “Whenever you see a situation of symmetry in a physical problem, stop and think! Because you will nearly always find an easier way to solve the problem by using the

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symmetry property.” This is one of the rewards of playing around with symmetry. The ideas are neat…

In mathematics and geometry, there is a need to be precise; so there symmetry is defined to mean that a function or a geometric figure remains the same, despite: 1) a rotation of coordinates, 2) movement along an axis, or 3) an interchange of variables. In physical science, which is our main concern, the existence of a symmetry usually means that a law of Nature does not change, despite: 1) a rotation of coordinates in space, 2) movement along an axis through space, 3) changing the past into the future such that t becomes –t, 4) an interchange of two coordinates such as exchanging x with y, z with –z, etc. or, 5) the change of any given variable. [emphasis added]The Platonic Solids have the greatest geometric symmetry of any shapes in existence, though Dr. Wolff does not call them by name here. In the next excerpt from Dr. Aspden, he refers to the Platonic Solid forms in the aether as “fluid crystals,” and explains how they can have an effect similar to a solid, even while they are appearing in a fluidlike medium: …19th century physicists were puzzled by the aether because it exhibits some properties telling us it is a fluid and some telling us it is a solid. That was the perception from a time when little if anything was known about ‘fluid crystals’. The displays in many pocket calculators use electrical signals and rely on the properties of a substance that, like the aether, exhibits properties characteristic of both the liquid state and the solid state as a function of electric field disturbances. [emphasis added]This gives us a “solid” explanation for why Tesla said that the aether “behaves as a liquid for matter, and as a solid for light and heat". The Platonic Solids actually do act as if they were structural frameworks within the aether, organizing the energy flows into specific patterns.

Hence, the Platonic Solids are the simple geometric forms of “crystallized music” that will naturally form themselves in the aether when it pulsates. Another important point to remember is that as the hierarchy of Platonic Solids “grow” into each other, the movement will always occur along spiral pathways, predominantly rooted in the classic “phi” ratio. Torsion waves have been seen to follow the “phi” pattern as well, which shall be more fully explored when we discuss the under-appreciated “pyramid power” phenomenon and the “cavity structural effect” pioneered by Dr. Victor Grebennikov in Chapter Seven.

3.4 MICROCLUSTER PHYSICS

Just as we were finishing up the first half of this book, a new associate alerted us to the burgeoning new field of “microcluster physics,” which changes our entire view of the quantum world by presenting us with a whole new phase of matter that does not obey the conventionally accepted “rules.” Microclusters are tiny “particles” that present clear and straightforward evidence that atoms are vortexes in the aether that naturally assemble into Platonic Solid formations by their vibration / pulsation. Furthermore, these new discoveries pose quite a challenge for those who still believe that there must be single electrons orbiting a nucleus instead of standing-wave electron clouds of aetheric energy that assemble into geometric patterns. The story of “microclusters” first broke into the mainstream world in the December 1989 issue of Scientific American, in an article by Michael A. Duncan and Dennis H. Rouvray: Divide and subdivide a solid and the traits of its solidity fade away one by one, like the features of the Cheshire Cat, to be replaced by characteristics that are not those of liquids or gases. They belong instead to a new phase of matter, the micro cluster… They pose questions that lie at the heart of solid-state physics and chemistry, and the related field of material science. How small must an aggregate of particles become before the character of the substance they once formed is lost? How might the atoms reconfigure if freed from the influence of the matter that surrounds them? If the substance is a metal, how small must this cluster of atoms be to avoid the characteristic sharing of free electrons that underlies conductivity? [emphasis added]Less than two years after this story broke in the mainstream, the science of microcluster physics was realized in its own graduate-school textbook authored by Satoru Sugano and Hiroyasu Koizumi. Microcluster Physics was published by the respectable, mainstream Springer-Verlag corporation as volume 21 in a series of texts in the field of materials science. All of the quotes from this text that we shall use are from its revised second edition, which was released in 1998. In Sugano and Koizumi’s text, we are told that with the new discoveries of microclusters, we can now arrange groupings of atoms into four basic categories of size, each with different properties:

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- Molecules: 1-10 atoms- Microclusters: 10-1000 atoms- Fine Particles: 1000-100,000 atoms- Bulk: 100,000+ atomsWhen we study the above list, we would initially expect that microclusters would have traits in common with molecules and with fine particles both, but in fact they have properties that neither display, as Sugano et al. explain here: Microclusters consisting of 10 to 10^3 atoms exhibit neither the properties of the corresponding bulk nor those of the corresponding molecule of a few atoms. The microclusters may be considered to form a new phase of materials lying between macroscopic solids and microscopic particles such as atoms and molecules, showing both macroscopic and microscopic features. However, research into such a new phase has been left untouched until recent years by the development of the quantum theory of matter. [emphasis added]As we continue reading, we learn that microclusters do not form randomly from any group of 10-1000 atoms; only certain “magic numbers” of atoms will gather together to form microclusters. The next quote describes how this was first discovered, and when we read it we should remember that the “mass spectrum” being mentioned describes spectroscope analysis, which we covered in the last chapter. When “cluster beams” are being discussed, this means that atoms (such as Na, or sodium) are being blasted through a tiny nozzle to form into a “beam” that is then analyzed. Most importantly, as the atoms blast out of the nozzle, some of them spontaneously gather into microclusters, which demonstrate anomalous properties: The microscopic features of microclusters were first revealed by observing anomalies of the mass spectrum of a Na [sodium] cluster beam at specific sizes, called magic numbers. Then it was experimentally confirmed that the magic numbers come from the shell structure of valence electrons. Being stimulated by these epoch-making findings in metal microclusters and aided by progress of the experimental techniques producing relatively dense, non-interacting microclusters of various sizes in the form of microcluster beams, the research field of microclusters has developed rapidly in these 5 to 7 years [since the first 1991 edition of the book.] The progress is also due to the improvement of computers and computational techniques…

The field of microclusters is attracting the attention of many physicists and chemists (and even biologists!) working in both pure and applied research, as it is interesting not only from the fundamental point of view but also from the viewpoint of applications in electronics, catalysis, ion engineering, carbon-chemical engineering, photography and so on. At this stage of development, it is felt that an introductory book is required for beginners in this field, clarifying fundamental physical concepts important for the study of microclusters. This book is designed to satisfy such a requirement. It is based on series of lectures given to graduate students (mainly in physics) of the University of Tokyo, Kyoto University, Tokyo Metropolitan University, Tokyo Institute of Technology and Kyushu University in the period of 1987-1990. [emphasis added]Our next quote comes from the first area in Sugano and Koizumi’s book where specific details are given regarding the highly anomalous physical properties of microclusters. Though they are only slightly smaller than fine particles in terms of the number of atoms, they are much more stable. Here, the greater stability refers to the fact that microclusters burn at a much higher temperature than molecules or fine particles of the same elements. According to David Hudson, (whom we shall discuss later,) Russian scientists were the first to discover that microclusters must be burned for more than 200 seconds to reveal a color spectrum to be analyzed, whereas all other known molecular compounds burn up in a maximum of about 70 seconds: When we arrive at the fragment called microcluster with a radius of the order of 10 angstroms by further dividing fine particles, we see that we have to use physics different from that for fine particles. The essential difference is derived from the theoretical postulate, partly supported by experiments, that microclusters of a given shape and size can, in principle, be extracted and their properties can be measured, even though this kind of measurement is impossible for fine particles. This postulate may be justified by considering the fact that clusters of a given regular shape are very stable as compared with those of the other shapes, the number of which is rather small. In contrast to this fact, fine particles of different shapes and a fixed size forming a big ensemble to allow a statistical treatment are nearly degenerate in energy. This makes impossible the extraction of fine particles of a given shape.

Clear-cut evidence has been obtained such that microclusters of alkali [1.8] and noble [1.9] metal elements in the form of a cluster beam have a nearly spherical shape at the size of the so-called magic numbers. A magic number means a specific size N [i.e. the number of atoms in the cluster] where anomalies of abundance in the mass spectra are found. This indicates that microclusters of those sizes are relatively stable as compared with those of neighboring sizes. [emphasis added]The “nearly spherical” shapes that are described above will be seen in later quotes as the Platonic Solids and related geometries. Our next passage is probably too technical for most readers and can be skipped over, but it is a clear-cut description of how the “cluster beams” are being made and analyzed and what specific “magic

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numbers” of atoms emerged. Furthermore, we should note that the clusters that are formed become electrically neutral, which is another anomalous and unexpected result: As an example, we show the mass spectrum of the Na cluster beam in Fig. 1.5. The beam is produced by the adiabatic expansion of a heated Na and Ar gas mixture through a nozzle. The Na clusters in the beam are photoionized, mass analyzed by a quadrupole mass analyzer, and finally detected by an ion-detection system. Detailed examinations of the experiment verify that the mass spectrum thus observed reflects that of [electrically] neutral clusters originally produced by the jet expansion. The anomalies of abundance of the size N, being 8, 20, 40, 58 and 93 (Fig. 1.5), are regarded as the magic numbers of neutral Na clusters. [emphasis added]Now pay very close attention to the next sentence, as its significance can easily be missed: In what follows, we shall show that these magic numbers are associated with the shell structure of valence electrons moving independently in a spherically symmetric effective potential… [emphasis added]What this is telling us is that the hypothetical “electrons” are no longer bound to their individual atoms in microclusters, but rather move independently throughout the entire cluster itself! Remember that in our new quantum model, there are no electrons, only clouds of aetheric energy that are flowing in towards the nucleus via the Biefield-Brown effect. In this case, the microcluster acts as one single atom, with the center of the cluster becoming akin to the positively-charged atomic nucleus where the negatively-charged energy is flowing in. Interestingly, in keeping with the fluidlike behaviors of the aether, the next passage suggests that the microclusters can have properties similar to a fluid as well as a solid: [The symmetry of] metal microclusters seems to reveal that microclusters belong to the microscopic world like atoms and molecules, whereas fine particles belong to the macroscopic world. This is true in some aspects, but not so in every aspect. In Chap. 2 we shall discuss that, at finite internal temperatures, microclusters may reveal the liquid phase as encountered in the macroscopic world... [emphasis added]The next excerpt comes from a completely different study by Besley et al., referenced at the end of this chapter, entitled Theoretical Study of the Structures and Stabilities of Iron Clusters. Obviously, their work builds directly off of Sugano and Koizumi’s textbook and the findings that went into its production. Here, the key is that Besley et al.’s research points to anomalous electrical and magnetic properties possessed by microclusters that are not seen either in molecules or in condensed matter: Clusters are also of interest in their own right, since for small clusters there is the possibility of finite size effects leading to electronic, magnetic or other properties which are quite different from those of molecules or condensed matter. There has also been a considerable research effort into understanding the geometries, stabilities and reactivities of gas phase bare metal clusters from a theoretical viewpoint. [emphasis added]And now, as we skip ahead to page 11 of Sugano et al.’s microcluster physics textbook, we come to section 1.3.1 entitled Fundamental Polyhedra. This is where the connection between microclusters and the geometry of Johnson’s physics becomes readily apparent: Recently, it has been discussed [1.12] that stable shapes of microclusters are given by Plato’s five polyhedra; the tetrahedron, cube, octahedron, pentagonal dodecahedron, icosahedron, [i.e., the Platonic Solids]; and Keplers’ two polyhedra of rhombic faces; the rhombic dodecahedron and rhombic triacontahedron…

It is very important to note that tetrahedra are not space-filling, as shown in Fig. 1.9, and icosahedra, trigonal decahedra and pentagonal dodecahedra with five-fold rotational symmetry are non-crystalline structures: they do not grow into the periodic structure of the bulk. If the polyhedron is a non-crystalline structure, then the microcluster has to undergo a phase transition to a crystalline structure on the way of growing into the bulk. [emphasis added]For one who has studied sacred geometry for many years, it is amazing to consider that at a level far too tiny for the naked eye, atoms are grouping together into perfect Platonic Solid formations. It is also interesting to consider that some of these microclusters also have fluidlike qualities, allowing them to flow from one type of geometric structure into another. In their text, Sugano and Koizumi have assumed that certain polyhedra such as the icosahedron and dodecahedron are non-crystalline, and must therefore undergo a phase change before they could become a larger crystallized object. However, later in this chapter we will present hard, irrefutable evidence that the entire model of crystallography is flawed, and that under certain circumstances, formations very similar to microclusters can be formed at larger levels of size, from two or more atomic elements grouped together.

Importantly, as the reader thumbs through the rest of Sugano et al.’s textbook, scores of diagrams of atoms grouped into Platonic Solids are seen. We learn that the “magic number” groupings of atoms will, in every case, form into one of the geometric structures mentioned above. If we took a tetrahedron, for example, and constructed it out of a certain number of marbles that all had an equal width, then we would need an exact “magic” number of marbles to construct a tetrahedron of a given size. This is the same as Buckminster Fuller’s model of “close-packed spheres,” and in its simplest form is expressed by seeing that if you put three marbles together into a triangle and then place a fourth marble above it in the middle, you will see a tetrahedron form.

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Even more interestingly, on page 18 of the Microcluster Physics textbook, Sugano et al. have a photograph of a gold cluster consisting of “about 460” atoms, where we can clearly see the close-packed sphere structure of the atoms inside, forming unmistakable geometry. These images are taken by a scanning electron microscope at very high magnification, and the structure of the cuboctahedron geometry [Fig. 3.3, L] is clearly visible in a series of different angles. Interestingly, the cluster is seen to undergo different geometric changes from the cuboctahedron to other forms in its structure from image to image, again suggesting a fluidlike quality, and unseen “stresses” in the aether at work. Figure 3.3 is an artist-rendered diagram of how the “magic number” of 459 spherical atoms will pack together to form a cuboctahedron-shaped cluster, whereas 561 atoms will cluster into the form of an icosahedron.

Figure 3.3 - Cuboctahedral cluster of 459 atoms (L) and Icosahedral cluster of 561 atoms (R)

Our next quote comes from section 3 of Besley et al.’s study, which discusses the “jellium” model and makes it very clear that the individual nature of the atoms in a microcluster is lost in favor of a group behavior. Again we will see the mentioning of magic numbers and of electrons moving through the entire structure instead of just through their parent atom; we also see the hypothesis that “geometric shells” of electrons are somehow formed in the microcluster.

For small clusters of simple metals, such as the alkali metals, mass spectroscopic studies have indicated the presence of preferred nuclearities or “magic numbers” corresponding to particularly intense peaks. These experiments led to the development of the (spherical) jellium model, wherein the actual cluster geometry (i.e. the nuclear coordinates) are unknown and unimportant (perhaps because the clusters are molten or rapidly fluxional) and the cluster valence electrons are assumed to move in a spherically average central potential. The jellium model therefore explains cluster magic numbers in terms of the filling of cluster electronic shells, which are analogous to the electronic shells in atoms. For somewhat larger nuclearities (N ~ 100-1500 [total atoms in the cluster,]) there are periodic oscillations in mass spectral peak intensities which have been attributed to the bunching together of electronic shells into supershells.

The observation of long period oscillations in the intensities of peaks in the mass spectra of very large metal clusters (with up to 10^5 atoms) has led to the conclusion that such clusters grow via the formation of 3-dimensional geometric shells of atoms and that for these nuclearities it is the filling of geometric rather than electronic shells that imparts extra cluster stability.

Certainly, the idea of “supershells” of electrons suggests a fluidlike blending together of atoms in the quantum realm. Again, it appears that the entire idea of electrons is flawed, since the next passage from Besley et al., tells us that the “jellium” model where “particle” electrons fill up into “geometric shells” does not work for what are known as transition metals. Since there can be no individual electrons at this point, Besley et al. hypothesize the existence of “explicit angular-dependent many-body forces.” In short, a “fluid crystal” aetheric quantum model is essentially required to explain the forces that create microclusters: For transition metals there is no clear evidence that the jellium model holds, even for low nuclearities… we would hope that a model which introduces explicit angular-dependent many-body forces (as in the MM [Murrell-Mottram] model that we have adopted) will fare better at explaining cluster structure preferences. As we think through the results of these microcluster studies, we must not forget that the Platonic Solids are very easily formed by vibrating a spherical area of fluid. It is quite surprising that the microcluster researchers do

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not appear to have noticed this connection. The prevailing view of quantum mechanics as a particle phenomenon has such a strong hold on the minds of scientific researchers that elaborate explanations involving “geometric shells” of electrons must be invoked. The key question that must be addressed is how and why this geometry would form – and the idea of a vibrating, fluidlike quantum medium is by far the simplest answer. A microcluster is simply a larger “aetheric atom” in a perfect geometric form.

3.5 DAVID HUDSON AND “ORMUS ELEMENTS”

KNOWN ORMUS ELEMENTS

Element

Atomic Number

Cobalt 27Nickel 28Copper 29Ruthenium 44Rhodium 45Palladium 46Silver 47Osmium 76Iridium 77Platinum 78Gold 79Mercury 80

Table 3.1 – Known Metallic Microclusters or “Ormus” Elements in David Hudson’s patent.

Next, we introduce the work of David Hudson, who discovered a substance that turned out to contain microclusters in a goldmine on his property in the late 1970s. He spent several million dollars having these mysterious materials analyzed and tested in various ways, and in 1989 Hudson patented his microcluster discovery by naming them Orbitally Rearranged Monatomic Elements, or “ORMEs.” [The name is usually changed to “Ormus” or “M-state” elements when discussed online so as not to interfere with Hudson’s copyrights.] Hudson displays a broad knowledge of microcluster physics in his published lectures from the early 1990s, but his findings are more controversial than what we find in Sugano et al.’s textbook or other published mainstream sources. Hudson’s patent focuses on the microcluster structures he found in the following precious metal elements. (We should note here that Sugano and Koizumi have established that microclusters have been found in non-metallic elements as well.)

Hudson found that all of the above microcluster metals exist plentifully in sea water. Even more surprisingly, Hudson discovered that these elements in the microcluster state may be up to 10,000 times more abundant on Earth than in their common metallic state. Hudson’s research demonstrated that these metallic microclusters are found throughout many different biological systems, including many different plants, and that they form up to 5% of the material in a calf’s brain by weight. Furthermore,

• they act as room-temperature superconductors, • have superfluid qualities and • levitate in the presence of magnetic fields, since no magnetic energy is able to penetrate through

their outer shells. Their physical qualities match the descriptions of various materials in alchemical traditions from China, India, Persia and Europe. Various people have volunteered to ingest gold microclusters or “monatomic gold,” and have reported experiencing the same psychic effects as the kundalini changes noted in the Vedic scriptures of ancient India.

Even more controversial are Hudson’s patented discoveries surrounding the heating of iridium microclusters. As the material is heated, its weight is seen to increase by 300 percent or more. Even more surprisingly, as microcluster iridium is heated to 850 degrees Celsius, the material disappears from physical view and loses all of its weight. However, when the temperature is again reduced, the microcluster iridium will reappear and regain most of its former weight. In Hudson’s patent, he has a chart that was generated by thermo-gravimetric analysis that shows this effect in action.

The idea of a material gaining weight, then spontaneously losing weight and disappearing from all physical view is

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no longer out of place when we combine Kozyrev’s findings with Ginzburg’s changes to conventional relativity equations and Mishin and Aspden’s discoveries of multiple densities of aether. In the first chapter, Kozyrev showed how the heating or cooling of an object can affect its weight in subtle but measurable ways. We also saw that these weight increases and decreases occur in sudden “quantized” bursts, not in a smooth, flowing fashion. Dr. Vladimir Ginzburg suggested that an object’s mass is converted into pure field as it approaches the speed of light, and Mishin and Aspden’s data suggests that the mass is actually moving into a higher density of aetheric energy.

Thus, Hudson’s observed and patented effects with microcluster iridium provide the first major proof in this volume for the idea that an object can be completely displaced into a higher density of aetheric energy. In the case of microcluster iridium, it would seem that the geometric structure of the microcluster allows for heat energy to be harnessed much more efficiently. This harnessing of the vibrations of heat then creates extreme resonance at a lower relative temperature, bringing the internal vibrations of the iridium past the speed of light. (These internal vibrations may already be relatively close to the speed of light before such added resonance is introduced, due to the speed at which aether flows through the atomic “vortex” of negative electron clouds and the positive nucleus.) Then, when the threshold point of light-speed is finally reached, the aetheric energy of the iridium is displaced into a higher density, thus causing it to disappear from measurable view. When the temperature is reduced, the iridium again displaces back down into our own density, since the pressure that was holding it in the higher density has now been eliminated.

3.6 ANOMALIES OF CRYSTAL FORMATION

Now that we have covered the anomalous area of microclusters, we are ready to tackle the more conventionally understood problems of crystal formation. Common table salt is a perfect example of how two different elements, sodium and chloride, can bond together and form a Platonic Solid geometry, in this case the cube. Two hydrogen atoms and one oxygen atom form together in the shape of a tetrahedron to create the water molecule, (which is not a crystal in the liquid state but has a tetrahedral molecule,) and fluorite crystals form the octahedron. Crystals that form with these properties will maintain the same orientation throughout themselves, and are symmetrical. A more technical description is that crystals are “solids which have flat surfaces (facets) that intersect at characteristic angles, and are ordered at a microscopic level.” Our key question to remember here would be, “Why do spherical energy vortexes end up joining together in these characteristic geometric angles and patterns?” The answer, of course, shall be found in our understanding of the Platonic Solids as “harmonic” energy structures in the aether.

Glusker & Trueblood’s classical definition for how crystals are formed is that they are produced by: …a regularly repeating arrangement of atoms. Any crystal may be regarded as being built up by the continuing three-dimensional translational repetition of some basic structural pattern. [emphasis added]The term “translation” means that we rotate a specific object by an exact number of degrees, such as 180, which would form a “two-fold” crystal since there are two such translations in a 360-degree circle. Thus, “translational repetition” means that that the basic structural element (atom or molecular group of atoms) making up a crystal can be rotated again and again in the same way to form the repeated pattern. The technical term for such a regular arrangement of atoms is periodicity, which means that a crystal is made up of “some basic structural unit which repeats itself infinitely in all directions, filling up all of space” within itself. The same structure (atom or group of atoms) keeps repeating in the same, periodic way, hence the term periodicity.

In this classical theory of “periodic” crystal formation, each atom retains its original size and shape and does not affect any of the other atoms except for those it is directly bonded to.

It is important to realize that the model of periodicity worked very well in crystallography. Any type of crystal that had been discovered could be analyzed with this method, and the angles between all of the facets could be predicted based on simple geometric principles. Then in 1912, Max von Laue discovered a way to use X-rays to illuminate the inner structure of crystals, creating what is known as a “diffraction diagram.” The diagram appears as an arrangement of single points of light on a black background. This led to a whole science of X-ray crystallography that was formalized by William H. and William L. Bragg, where the points of light are analyzed geometrically in relation to each other in order to determine what the structure of the true crystal actually is. For seventy years after this technology was developed, every diffraction diagram that had ever been observed by mainstream scientists fit the periodicity model perfectly, which led to the inevitable and apparently quite simple conclusion that all crystals were an arrangement of single atoms as structural units.

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One of the periodicity model’s most straightforward mathematical rules is that a crystal can only have 2-, 3-, 4-, and 6-fold rotations (translations.) In this model, if you have a crystal that is indeed made of single atoms or molecules in a repeating, periodic structure, the crystal cannot have a five-fold rotation or any rotation higher than 6. Atoms are “supposed” to retain their own individual point-like identities and not merge with other atoms into a larger whole. Nevertheless, in terms of pure geometry, the dodecahedron has 5-fold symmetry and the icosahedron has 5- and 10-fold symmetry. These Platonic Solids fit all the requirements for symmetry as outlined by Dr. Wolff earlier in this chapter, but you simply cannot pack single atoms together to make either of these shapes. So again, the dodecahedron and icosahedron have symmetry, but they do not have periodicity as crystal formations. Therefore, there was no provision in science to believe that either of these forms would appear as a molecular, crystalline structure – it was “impossible.” Or so they thought…

Now enter the infamous Roswell crash. According to former Groom Lake / Area 51 employee Edgar Fouche, molecular structures were found on the recovered hardware that did not fit the conventional model of crystalline periodicity. These became known as “quasi-crystals,” short for “quasi-periodic crystals.” Both the icosahedron and dodecahedron have appeared in these unique alloys. Similar to microclusters but on a larger level of size, these quasi-crystals were discovered to have many strange properties, such as extreme strength, extreme resistance to heat and being non-conductive to electricity, even if the metals involved in their creation would normally act as conductors! (This will be explained as we progress.) Unlike microclusters, which only appear to be able to be formed individually from “cluster beams”, quasi-crystals can be grouped together into usable alloys. Fouche states the following on his website, with our added emphasis: I’ve held positions within the USAF that required me to have Top Secret and ‘Q’ Clearances and Top Secret-Crypto access clearances…

In the mess hall at [the top-secret] Groom [Lake facility,] I heard words like Lorentz Forces, pulse detonation, cyclotron radiation, quantum flux transduction field generators, quasi-crystal energy lens and EPR quantum receivers. I was told that quasi-crystals were the key to a whole new field of propulsion and communication technologies.

To this day I’d be hard pressed to explain to you the unique electrical, optical and physical properties of quasi-crystals and why so much of the research is classified…

Fourteen years of quasi-crystal research has established the existence of a wealth of stable and meta-stable quasi-crystals with five-, eight-, ten- and twelve-fold symmetry, with strange structures [such as the dodecahedron and icosahedron] and interesting properties. New tools had to be developed for the study and description of these extraordinary materials.

I’ve discovered that the classified research has shown that quasi-crystals are promising candidates for high energy storage materials, metal matrix components, thermal barriers, exotic coatings, infrared sensors, high power laser applications and electro-magnetics. Some high strength alloys and surgical tools are already on the market. [Note: Wilcock was personally told in 1993 that Teflon and Kevlar are both reverse-engineered.]

One of the stories I was told more than once was that one of the crystal pairs used in the propulsion of the Roswell crash was a Hydrogen Crystal. Until recently, creating a Hydrogen crystal was beyond the reach of our scientific capabilities. That has now changed. In one Top Secret Black Program, under the DOE, a method to produce hydrogen crystals was discovered, [and] then manufacturing began in 1994.

The lattice of hydrogen quasi-crystals, and another material not named, formed the basis for the plasma shield propulsion of the Roswell craft and was an integral part of the bio-chemically engineered vehicle. A myriad of advanced crystallography undreamed of by scientists were discovered by the scientists and engineers who evaluated, analyzed and attempted to reverse engineer the technology presented with the Roswell vehicle and eight more vehicles which have crashed since then. Arguably after 35 years of secret research on the Roswell hardware, those who had recovered these technologies still had hundreds if not thousands of unanswered questions about what they had found, and it was deemed “safe” to quietly introduce “quasi-crystals” to the non-initiated scientific world. There are now literally thousands of different references to quasi-crystals on the Internet, completely separate from any mention of microclusters. (Not a single scientific study that we have been able to find online mentions both microclusters and quasi-crystals in the same document.) Many of the quasi-crystal references are from companies that are government contractors, and it is very easy to see that they are being studied with widespread intensity. However, they are almost never mentioned in the general media, even though they present such a unique challenge to our prevailing theories of quantum physics. The research goes on, but it is with a very subdued excitement.

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Dan Schechtman was given the honor / duty of having “discovered” (or being allowed to re-discover) quasi-crystals on April 8, 1982 with an Aluminum-Manganese alloy (Al6Mn) that began in a molten liquid state and was then cooled off very quickly. Crystals in the shape of an icosahedron were produced, as determined by the X-ray diffraction diagram that was seen, similar to the image below. Schechtman’s data was not even published until November 1984! In the image to the right of Figure 3.4, we can clearly see a number of pentagons, indicating the five-fold symmetry of the icosahedron:

"click" image to see multimedia Figure 3.4 – The Icosahedron (L) and its X-ray diffraction diagram from a quasi-crystal formation (R).

As we said, with the advent of quasi-crystals, both the dodecahedron and icosahedron appear, along with other unusual geometric forms, completing the appearance of all five of the Platonic Solids in the molecular realm in some way. Both the dodecahedron and icosahedron possess elements of five-fold symmetry with their pentagonal structures. Figure 3.5, from An Pang Tsai of NRIM in Tsukuba, Japan, shows an Aluminum-Copper-Iron quasi-crystal alloy in the shape of a dodecahedron and an Aluminum-Nickel-Cobalt alloy in the shape of a decagonal (10-sided) prism:

Figure 3.5 – Dodecahedral (L) and decagonal prism (R) quasi-crystals created by An Pang Tsai of NRIM.

The problem here is that you cannot create such crystals by using single atoms bound together, yet as we can see in the photographs, they are very real. The key problem for scientists, then, is how to explain and define the process by which these crystals are forming. According to A.L. Mackay, one of the ways to include five-fold symmetry in a crystallographic definition is “Abandonment of Atomicity:” Fractal structures with five-fold axes everywhere require that atoms of finite size be abandoned. This is not a rational assumption to the crystallographers of the world, but the mathematicians are free to explore it. [emphasis added]What this suggests is that similar to microclusters, quasi-crystals appear to not have individual atoms anymore, but rather that the atoms have merged into a unity throughout the entire crystal. While this may seem impossible for crystallographers to believe, it is actually among the simplest of A.L. Mackay’s four potential solutions to the problem, as it involves simple three-dimensional geometry and correlates with our microcluster observations. Again, since the crystals are very real, the only major hurdle to cross is our fixation on the belief that atoms are made of particles.

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Another related example is seen with the Bose-Einstein Condensate, which was first theorized in 1925 by Albert Einstein and Satyendranath Bose, and was first demonstrated in a gas in 1995. In short, a Bose-Einstein Condensate is a large group of atoms that behaves as if it were one single “particle,” with each constituent atom appearing to simultaneously occupy all of space and all of time throughout the entire structure. All the atoms are measured to vibrate at the exact same frequency and travel at the same speed, and all appear to be located in the same area of space. Rigorously, the various parts of the system act as a unified whole, losing all signs of individuality. It is this very property that is required for a “superconductor” to exist. (A superconductor is a substance that conducts electricity with no loss of current.)

Typically, the Bose-Einstein condensate is only able to be formed at extremely low temperatures. However, we seem to be observing a similar process occurring in microclusters and quasi-crystals, where there is no longer a sense of individual atomic identity. Interestingly, yet another similar process is at work with laser light, known as “coherent” light. In the case of the laser, the entire light beam behaves as if it were one single “photon” in space and time – there is no way to differentiate individual photons in the laser beam. It is interesting to note that lasers, superconductors and quasi-crystals were all found in recovered ET technologies since the 1940s.

This obviously introduces a whole new world of quantum physics to the discussion table. In time, it appears that quasi-crystals and Bose-Einstein condensates will be much more widely used and understood as examples of how we had gone astray in our “particle”-based quantum thinking. Furthermore, British physicist Herbert Froehlich proposed in the late 1960’s that living systems frequently behave as Bose-Einstein condensates, suggesting a larger-scale order that is at work. We will discuss this in later chapters that will deal with aetheric biology.

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Figure 3.6 – Dan Winter’s reprint of Sir William Crookes’ geometric Table of the Elements.

Our next question concerns the “electron clouds” that have been seen in the atom. Both Rod Johnson and Dan Winter have noted that the teardrop-shaped “electron clouds” in the atom will all fit perfectly together with the faces of the Platonic Solids. Winter refers to the electron clouds as “vortex cones,” and Figure 3.6 is an unfortunately illegible copy of the Periodic Table of the Elements as originally devised by Sir William Crookes, a well-known and highly respected scientist from the early 20th century who later became an investigator into the field of parapsychology. At the bottom of the image, we see an illustration of how the “vortex cones” fit on each face of the Platonic Solids.

(It appears that a more legible copy of Figure 3.5 may exist in one of Winter’s earlier books. Some of the element names can be made out when viewing the image at full size, and the others can be inferred by their position relative to the known Periodic Table of the Elements. The chart is obviously read from the top down, and the first element that is written out below the two circles in the center is Helium, and the line then moves to each successive element. The scale to the left is a series of degree measurements, beginning with 0 at the top line and counting by units of 10° for each line. The degree numbers written in on the scale are 50, 100, 150, 200, 250, 300, 350 and 400. This appears to indicate that Sir Crookes’ theory involved set angular rotations or translations of the

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elements in terms of their geometry as we move from one element to the next. We can see that the wave is mostly straight, but at times there are “dips” in the line that appear to correspond to larger angular rotations that must be made.)

If we think back to what Dr. Aspden wrote about Platonic Solids in the aether, he stated that they act as “fluid crystals,” meaning that they can behave as a solid and as a liquid at the same time. Thus, once we understand that electron clouds are all being positioned by invisible Platonic Solids, it becomes much easier to see how crystals are being formed and even how quasi-crystals could be made. There are “nests” of Platonic Solids in the atom, one solid for each major sphere in the “nest”, just as there are “nests” of electron clouds at different levels of valence that all co-exist. The Platonic Solids form an energetic structure and framework that the aetheric energy must flow through as it rushes towards the low-pressure positive center of the atom. Thus, we see each face of the Solids acting as a funnel that the flowing energy must pass through, creating what Winter called “vortex cones.”

With the necessary context in place, Johnson’s concepts of Platonic symmetry within the structure of atoms and molecules in the next chapter should not seem as strange to us now as they would to most people. Given what we have seen with the comprehensive research that has gone on, especially with quasi-crystal engineering, it appears that this information is already in use by humanity in certain circles.

REFERENCES: 1. Aspden, Harold. Energy Science Tutorial #5. 1997. URL: http://www.energyscience.co.uk/tu/tu05.htm

2. Crane, Oliver et al. Central Oscillator and Space-Time Quanta Medium. Universal Expert Publishers, June 2000, English Edition. ISBN 3-9521259-2-X

3. Duncan, Michael A. and Rouvray, Dennis H. Microclusters. Scientific American Magazine, December 1989.

4. Fouche, Edgar. Secret Government Technology. Fouche Media Associates, Copyright 1998/99. URL: http://fouchemedia.com/arap/speech.htm

5. Hudson, David. (ORMUS Elements) URL: http://www.subtleenergies.com

6. Kooiman, John. TR-3B Antigravity Physics Explained. 2000. URL:http://www.fouchemedia.com/Kooiman.htm

7. Mishin, A.M. (Levels of aetheric density) URL: http://alexfrolov.narod.ru/chernetsky.htm

8. Winter, Dan. Braiding DNA: Is Emotion the Weaver? 1999. URL: http://soulinvitation.com/braidingDNA/BraidingDNA.html

9. Wolff, Milo. Exploring the Physics of the Unknown Universe. Technotran Press, Manhattan Beach, CA, 1990. ISBN 0-9627787-0-2. URL: http://members.tripod.com/mwolff

from Mid-Atlantic Geomancy

If we want to talk with God/dess, experience has shown that it helps to be in the right environment. Spiritual seekers from Mayans through Christians, Native Americans, Egyptians and Hindus to the Neolithic builders of the stone rings in Britain and Ireland (and many more) found that by constructing their sacred places using certain geometrical ratios - just a small handful of them - they could more easily connect with their Maker.

Yes, it is possible to speak with our Creator anytime. However, sacred geometry makes this easier, and different ratios make different connections easier. The ratios have to do with different spiritual activities like healing, foretelling the future, long-distance communication, levitation and, most important, heightened ability to communicate with our Maker. These ratios help us to vibrate at the appropriate frequency to aid us in accomplishing the particular spiritual activity we have in mind.

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Nearly every ancient archaeological site predating recorded history, from the Pyramids of Egypt and Mexico, to Stonehenge and beyond, employs mysterious mathematical alignments throughout their design.

These architectural formulas, rarely used today, are considered sacred and have also been found in the way they're arranged relation to each other and, most inexplicably, in the Monuments of Cydonia, and the Face on Mars.

When one looks at sacred enclosures globally, there is a group of five mathematical ratios that are found all over the world from Japan's pagodas to Mayan temples in the Yucatan, and from Stonehenge to the Great Pyramid. These ratios are:

• Square Root of Two = 1.414... • Square Root of Three = 1.732... • Square Root of Five = 2.236... • Phi = 1.618...

Phi is the Golden Section of the Greeks. It was said to be the first section in which the One became many.

• Pi = 3.1416... Pi is found in any circle. If the diameter is 1, the circumference is 3.1416 (C = D).

These are all irrational numbers. Pi can be taken to 1500 decimal places with no discernable pattern to it (is that Chaos?). Let's take a closer look at each of these special numbers, and see how we can find them in the sacred geometry used by geomancers around the world. All five of these numbers gain their meaning only when beaten against the One. They are all ratios of x:1. The One is where it begins .

Pi - 3.1416 : 1 - the Circle

Pi (3.1416 : 1) is found in any circle. In sacred geometry, the circle represents the spiritual realms. A circle, because of that transcendental number pi, cannot be described with the same degree of accuracy as the physical square. The circle is yin.

It is a good shape to do all kinds of spiritual activities in. It is good for groups to work in circles. There are many examples of sacred spaces that are circular.

The Circle: Radius (CD) = 1

Diameter (AB) = 2 Circumference = pi (3.1416) x

Diameter

Ring of Brodgar, Mainland Orkney.

Most stone rings in the British isles are not actually circular. Dr Alexander Thom proved this with his pioneering work in the sixties. Some of the true circles are Merry Maidens in Cornwall, Stonehenge and the Ring of Brodgar.

Square Root of Two - 1.414 : 1 - the Square

In sacred geometry, the square represents the physical world. It can be defined totally. If its side is one, its perimeter is exactly four, and its area is one square - exactly. The Square is yang. The Square Side (AB) = 1

Diagonal (AC) = Square Root of Two, 1.414

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The Square Side (AB) = 1 Diagonal (AC) = Square Root of Two, 1.414

The square was found was in the Holy of Holies (the back room) of Solomon's Temple (G,H,F,E). This was where the Hebrews kept the Ark of the Covenant and other most sacred treasures. (The dimensions here are taken from the first part of the Ezekiel Chapter 41.)

On top of Glastonbury Tor sits an impressive stone tower. The Tor and its tower dominate the Somerset Levels. This is a view taken from inside the tower looking upward.

Square Root of Three - 1.732 : 1 - Vesica Pisces

The Vesica Pisces is created by two identical intersecting circles, the circumference of one intersecting the center of the other. The vulva-shaped space thus created is called the Vesica Pisces.

The Vesica Pisces: Two Circles share a common radius (AB). Radius AB = 1 The intersecting circles create a Vesica Pisces. The minor axis of this Vesica Pisces (AB) = 1, The major axis (CD) = the square root of three, 1.732

CB = AB = 1 ..... Therefore:

a² + b² = c²

.5² + x² = 1²

x² = .75

2 = .75

x = .8660 = CE

CE is 1/2 of the major axis CD

2 CE = CD

.8660 * 2 = CD

CD = 1.7320 = 3

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This is the lid of the Chalice Well designed by Bligh Bond in the early part of this century. It covers one of the most powerful Holy Wells in Britain. The Chalice Well has numerous examples of vesicas.

Gothic arch on the tower on the Glastonbury Tor. This site was a hermitage and retreat

for early Christian monks

Gothic arch in Gallilee of Glastonbury Abbey. Note circular Romanesque arches

behind in the Mary Chapel.

The top half of the Vesica Pisces is the Gothic Arch - see Chartres Cathedral. It is the sacred geometric shape of the Piscean Age.

Square Root of Five - 2.236 : 1 - the Double Square

The Double Square is found in some of the best known sacred spaces in the world, from the King's Chamber in the Great Pyramid and Solomon's Temple in the Bible to the interior of Calendar II, an important underground stone chamber in Vermont, USA.

The diagonal of a double square is to the shorter side as the square root of five is to one. The square root of five = .618 + 1 + .618.

The Double Square: Short Side = 1

Longer Side = 2 Diagonal = Square Root of Five, 2.236

(ABCD) Double Square in Solomons Temple

Solomons temple provides numerous examples of sacred geometry. The holy place (EFCD) is the place where good Jews who had been properly cleansed could go. This space measures twenty cubits by forty cubits.

Another place where a double square is found is the Calendar II underground chamber site in central Vermont in the USA. It measures ten feet by twenty feet.

.Calendar II, a drystone walled underground stone

chamber in central Vermont, USA.

The interior of the chamber is 20 feet long by 10 feet wide , or 2 to 1. The chamber is oriented towards the

Winter Solstice Sunrise.

Phi - 1.618:1 - Ø - the Phi Rectangle

The Golden Section, Phi, 1.618: The shorter section on the right = 3

In the Beginning was the One. In order to observe itself, it cut part of itself away to make 'Other'. This Golden Section is in beautiful proportion. As the subdividing continued away from the One, they continued in this phi ratio. This can be used to go back to the One as well. It is in this sense that three is farther away from the One than two is.

Have you ever noticed that it is easier mathematically to go away

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The longer section = 5

The shorter is to the longer as the longer is to the whole

3:5 : : 5:8

from One than to go towards it? In other words, it is easier to add and multiply than it is to subtract and divide.

3:5 : : 5:8. This ratio indicates that it is part of this series: 1 . 2 . 3 . 5 . 8 . 13 . 21 . 34 . 55 . 89, and so on. This is called the Fibonacci Series. Start anywhere in the series, add the number below, and you get the next number (for example, 21 + 13 = 34). As one ascends up the series, any number in the series, when divided into the next one up, gets closer and closer to (but never hits exactly) 1.618, phi, the Golden Section.

On a line create square(ABCD) where AB = 1

Divide lines (AD) and (BC) in half at (F) and (E). (BC) = 1, (EC) = .5

Double square (ECDF) is thus created with a diameter of (ED).

Using (ED) as a radius swing arc from (D) downwards to 0 intersect the initial base line at (G).

Extend line (AFD), and create a perpendicular to line (BECG) at (G)

so that it intersects line (AFD) at (H), thus creating phi rectangle (ABGH).

The formula that shows this is:

Phi = ( 1 + square root of 5 ) divided by 2

(BE) = 1/2 (ED) = 5/2

.5 + 1.118 = 1.618

Extend arc (DG) through (A) to (I). Note the clear relationship between

phi and the square root of five.

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Solomons Temple also contains phi. The Vestibule (DCBA) measures twelve cubits by twenty cubits. 12 to 20 can be reduced to 6 to 10 and further to 3 to 5. Three and five are two numbers in the fibonacci series. 3/5 = 1.6, a close approximation to 1.618, or phi.

Calendar I was measured very carefully by the NEARA/ASD Earth Mysteries Group in the early 80's. Three measurements of the length were taken and averaged. The same was done with the width. Upon dividing the length by the width, the resultant ratio was 1.619 to 1. Phi (Ø) = 1.618 to 1.

The Parthenon is the Queen of Greek Temples, and personifies their interest in Sacred Geometry. If the height of the Parthenon is 1, its width is phi (Ø) 1.618, and its length is root of 5= 2.236. And 1.618 + .618 = 2.236.

These are the 5 sacred geometrical ratios - Pi, (2),(3),(5) and Phi. They are found in sacred spaces all over the world. Remember, sacred geometry is basically simple. You must do it with your hands, if you want to really know sacred geometry.

Squaring the Circle - The Great Pyramid The square represents the physical. The circle represents the spiritual. All sacred geometers have attempted the impossible: to square the circle (create a square who's perimeter is equal to the circumference of a circle.) Here is the first of two valiant attempts: This squaring of the circle works with a right triangle that represents the apothem (ZY) - (a line drawn from the base of the center of one of the sides to top of the pyramid), down to the center of the base (ZE), and out to the point where the apothem touches the Earth (EY).

The Great Pyramid of Egypt (Sphinx in foreground)

Now let's look at this in 2D, from directly above.

For the purpose of this exercise, the side (AB) of the base equals 2.

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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.

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

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).

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.

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

Construct two 3 . 4 . 5 right triangles, with the 4 . 5 angles at (A) and (D).

Connect the 5 . 3 angles creating square (abcd) with side (ab) = 3

{4 + 3 + 4 = 11, or side (AD) of square (ABCD)}

Create diagonals (ac) and (bd) centering at (e)

Create a circle that is tangent to square (abcd) at four places.

Draw line (Ee) which intersects side (AD) at (F)

(EF) = the radius of the larger circle and (eF) = the radius of the smaller circle

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

With your compass point at (E), create a circle with radius (Ee)

This creates a circle whose circumference is equal to the perimeter of square (ABCD)!

The Math:

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

2In 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.

3(EF) = 5.5 (F e) = 1.5

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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!)

Sacred Geometry Geomancers are interested in sacred geometry because this is the study of the way that spirit integrates into matter - by echoing and amplifying the geometry of nature and planetary movements, we help to align the resonance of body/mind/spirit with the harmonic frequencies of the above and the below.

Geomancers are interested in sacred geometry because it has been found that certain spaces, with particular ratios, enable the participant to resonate or vibrate at the appropriate rate that maximizes the possibility of connection to the One.

A violin isn't built out of a cigar box! It is built with the proper wood with the proper shape and ratios, so that it resonates correctly for the notes/frequencies it is expected to produce. These same principles are applied to sacred spaces to maximize the possibility that whatever is being done there on spiritual levels will succeed.

Definitions

Two Dimensions I've been a student of sacred geometry for over twenty-five years. While there has been recent interest in three-dimensional sacred geometry based on the Platonic Solids and in sacred sites themselves, most sacred geometrical documents I've read talk in only two dimensions - height and width.

Obviously there is a fourth dimension and others beyond it that are much more complex and sophisticated. But why does the record left to us from geomancers of the past come primarily in two dimensions?

Two is closer to the One than three is. It's less complex. I think one of the biggest mistakes Western geomancers have made was to take something that is very simple and make it much more complex. The Chartres Labyrinth strikes me as being an example of this. This stuff is simple. If you really gnow (that is, know both rationally and intuitively) a handful of irrational ratios - pi ( ), phi (Ø) and the square roots of two, three and five, you've basically got it all.

Three-dimensional sacred geometry just builds on this basic handful.

Numbers One aspect of Sacred Geometry is that it works with irrational numbers. To go to the spiritual, one must go beyond the rational, and it appears that some of these ratios and numbers can lead us there. By being inside a sacred space that has been constructed using one of a handful of these sacred geometrical ratios, the resonance that has been set up can enhance the possibility of your making the spiritual connection you want to make.

So, what are these irrational numbers? Let's begin with the rational.

Rational Numbers A rational number is a number which can be expressed as the ratio of two integers (whole numbers), such as 1/3 or 37/22. All numbers which, when represented in decimal notation, either stop after a finite number of digits or fall into a repeating pattern, are rational numbers.

Irrational Numbers An irrational number is one that cannot be represented as a ratio of any two whole-number integers, and consequently it does not fall into a repeating pattern of any sort when written in decimal notation.

All of the Sacred Geometry ratios we will be working with, the square roots of two (1.414), three (1.732) and five (2.238), phi (1.618) and pi (3.1416), are all irrational numbers.

Transcendental NumbersThere are certain kinds of irrational numbers that are called transcendental numbers. Just like irrational numbers, they are defined by what they are not (they aren't rational numbers), yet transcendental numbers are so identified because they are not another sort of number, known as an algebraic number.

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Any number which is a solution to a polynomial equation is an algebraic number. A polynomial equation is a sum of one or more terms involving the same variable raised to various powers, for example:

7 (x5) + 5 (x3) + x = 137

Any X for which any such equation is true is an algebraic number. Because the square root of two is a solution to the polynomial equation,

x2 = 2

it is an algebraic number.

A transcendental number requires an infinite number of terms to be defined exactly. That's one way of thinking of God/dess. There are special equations to derive transcendental numbers where the terms get smaller and smaller as you go along, so you can keep adding them together to reach any level of accuracy you need, but the true number cannot be reached exactly . That is the beauty of transcendental numbers!

Pi ( = 3.1416...) is such a transcendental number. It is the only one we will be using here with Sacred Geometry. One infinite equation which relates to the value of pi ( ) is this:

Pi / 4 = 1 - (1/3) + (1/5) - (1/7) + (1/9) - (1/11) + (1/13) - (1/15) + ...and so on into infinity.

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