http://www.geometrycode.com/sg/index.shtml

In nature, we find patterns, designs and structures from the most minuscule particles, to expressions of life discernible by human eyes, to the greater cosmos. These inevitably follow geometrical archetypes, which reveal to us the nature of each form and its vibrational resonances. They are also symbolic of the underlying metaphysical principle of the inseparable relationship of the part to the whole. It is this principle of oneness underlying all geometry that permeates the architecture of all form in its myriad diversity. This principle of interconnectedness, inseparability and union provides us with a continuous reminder of our relationship to the whole, a blueprint for the mind to the sacred foundation of all things created.

Starting with what may be the simplest and most perfect of forms, the sphere is an ultimate expression of unity, completeness, and integrity. There is no point of view given greater or lesser importance, and all points on the surface are equally accessible and regarded by the center from which all originate. Atoms, cells, seeds, planets, and globular star systems all echo the spherical paradigm of total inclusion, acceptance, simultaneous potential and fruition, the macrocosm and microcosm.

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The circle is a two-dimensional shadow of the sphere which is regarded throughout cultural history as an icon of the ineffable oneness; the indivisible fulfillment of the Universe. All other symbols and geometries reflect various aspects of the profound and consummate perfection of the circle, sphere and other higher dimensional forms of these we might imagine.

The ratio of the circumference of a circle to its diameter, Pi, is the original transcendental and irrational number. (Pi equals about 3.14159265358979323846264338327950288419716939937511...) It cannot be expressed in terms of the ratio of two whole numbers, or in the language of sacred symbolism, the essence of the circle exists in a dimension that transcends the linear rationality that it contains. Our holistic perspectives, feelings and intuitions encompass the finite elements of the ideas that are within them, yet have a greater wisdom than can be expressed by those ideas alone.

At the center of a circle or a sphere is always an infinitesimal point. The point needs no dimension, yet embraces all dimension. Transcendence of the illusions of time and space result in the point of here and now, our most primal light of consciousness. The proverbial "light at the end of the tunnel" is being validated by the ever-increasing literature on so-called "near-death experiences". If our essence is truly spiritual omnipresence, then perhaps the "point" of our being "here" is to recognize the oneness we share, validating all "individuals" as equally precious and sacred aspects of that one.

Life itself as we know it is inextricably interwoven with geometric forms, from the angles of atomic bonds in the molecules of the amino acids, to the helical spirals of DNA, to the spherical prototype of the cell, to the first few cells of an organism which assume vesical, tetrahedral, and star (double) tetrahedral forms prior to the diversification of tissues for different physiological functions. Our human bodies on this planet all developed with a common geometric progression from one to two to four to eight primal cells and beyond.

Almost everywhere we look, the mineral intelligence embodied within crystalline structures follows a geometry unfaltering in its exactitude. The lattice patterns of crystals all express the principles of mathematical perfection and repetition of a fundamental essence, each with a characteristic spectrum of resonances defined by the angles, lengths and relational orientations of its atomic components.

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The square root of 2 embodies a profound principle of the whole being more than the sum of its parts. (The square root of two equals about 1.414213562...) The orthogonal dimensions (axes at right angles) form the conjugal union of the horizontal and vertical which give birth to the greater offspring of the hypotenuse. The new generation possesses the capacity for synthesis, growth, integration and reconciliation of polarities by spanning both perspectives equally. The root of two originating from the square leads to a greater unity, a higher expression of its essential truth, faithful to its lineage.

The fact that the root is irrational expresses the concept that our higher dimensional faculties can't always necessarily be expressed in lower order dimensional terms - e.g. "And the light shineth in darkness; and the darkness comprehended it not." (from the Gospel of St. John, Chapter 1, verse 5). By the same token, we have the capacity to surpass the genetically programmed limitations of our ancestors, if we can shift into a new frame of reference (i.e. neutral with respect to prior axes, yet formed from that matrix-seed conjugation. Our dictionary refers to the word matrix both as a womb and an array (or grid lattice). Our language has some wonderful built-in metaphors if we look for them!

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The golden ratio (a.k.a. phi ratio a.k.a. sacred cut a.k.a. golden mean a.k.a. divine proportion) is another fundamental measure that seems to crop up almost everywhere, including crops. (The golden ratio is about 1.618033988749894848204586834365638117720309180...) The golden ratio is the unique ratio such that the ratio of the whole to the larger portion is the same as the ratio of the larger portion to the smaller portion. As such, it symbolically links each new generation to its ancestors, preserving the continuity of relationship as the means for retracing its lineage.

The golden ratio (phi) has some unique properties and makes some interesting appearances:

• phi = phi^2 - 1; therefore 1 + phi = phi^2; phi + phi^2 = phi^3; phi^2 + phi^3= phi^4; ad infinitum.
• phi = (1 + square root(5)) / 2 from quadratic formula, 1 + phi = phi^2.
• phi = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/...)))))
• phi = 1 + square root(1 + square root(1 + square root(1 + square root(1 + square root(1 + ...)))))
• phi = (sec 72)/2 =(csc 18)/2 = 1/(2 cos 72) = 1/(2 sin 18) = 2 sin 54 = 2 cos 36 = 2/(csc 54) = 2/ (sec 36) for all you trigonometry enthusiasts.
• phi = the ratio of segments in a 5-pointed star (pentagram) considered sacred to Plato and Pythagoras in their mystery schools. Note that each larger (or smaller) section is related by the phi ratio, so that a power series of the golden ratio raised to successively higher (or lower) powers is automatically generated: phi, phi^2, phi^3, phi^4, phi^5, etc.
• phi = apothem to bisected base ratio in the Great Pyramid of Giza
• phi = ratio of adjacent terms of the famous Fibonacci Series evaluated at infinity; the Fibonacci Series is a rather ubiquitous set of numbers that begins with one and one and each term thereafter is the sum of the prior two terms, thus: 1,1,2,3,5,8,13,21,34,55,89,144... (interesting that the 12th term is 12 "raised to a higher power", which appears prominently in a vast collection of metaphysical literature)

The mathematician credited with the discovery of this series is Leonardo Pisano Fibonacci and there is a publication devoted to disseminating information about its unique mathematical properties, The Fibonacci Quarterly

Fibonacci ratios appear in the ratio of the number of spiral arms in daisies, in the chronology of rabbit populations, in the sequence of leaf patterns as they twist around a branch, and a myriad of places in nature where self-generating patterns are in effect. The sequence is the rational progression towards the irrational number embodied in the quintessential golden ratio.

This most aesthetically pleasing proportion, phi, has been utilized by numerous artists since (and probably before!) the construction of the Great Pyramid. As scholars and artists of eras gone by discovered (such as Leonardo da Vinci, Plato, and Pythagoras), the intentional use of these natural proportions in art of various forms expands our sense of beauty, balance and harmony to optimal effect. Leonardo da Vinci used the Golden Ratio in his painting of The Last Supper in both the overall composition (three vertical Golden Rectangles, and a decagon (which contains the golden ratio) for alignment of the central figure of Jesus.

The outline of the Parthenon at the Acropolis near Athens, Greece is enclosed by a Golden Rectangle by design.

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The Vesica Piscis is formed by the intersection of two circles or spheres whose centers exactly touch. This symbolic intersection represents the "common ground", "shared vision" or "mutual understanding" between equal individuals. The shape of the human eye itself is a Vesica Piscis. The spiritual significance of "seeing eye to eye" to the "mirror of the soul" was highly regarded by numerous Renaissance artists who used this form extensively in art and architecture. The ratio of the axes of the form is the square root of 3, which alludes to the deepest nature of the triune which cannot be adequately expressed by rational language alone.

View image details

This Hubble telescope snapshot of MyCn18, a young planetary nebula, reveals that the object has an hourglass shape with an intricate pattern of "etchings" in its walls. A planetary nebula is the glowing relic of a dying, Sun-like star.

The results are of great interest because they shed new light on the poorly understood ejection of stellar matter that accompanies the slow death of Sun-like stars. According to one theory on the formation of planetary nebulae, the hourglass shape is produced by the expansion of a fast stellar wind within a slowly expanding cloud, which is denser near its equator than near its poles.

http://hubblesite.org/newscenter/archive/releases/1996/07

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This spiral generated by a recursive nest of Golden Triangles (triangles with relative side lengths of 1, phi and phi) is the classic shape of the Chambered Nautilus shell. The creature building this shell uses the same proportions for each expanded chamber that is added; growth follows a law which is everywhere the same. The outer triangle is the same as one of the five "arms" of the pentagonal graphic above.

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Rotating a circle about a line tangent to it creates a torus, which is similar to a donut shape where the center exactly touches all the "rotated circles." The surface of the torus can be covered with 7 distinct areas, all of which touch each other; an example of the classic "map problem" where one tries to find a map where the least number of unique colors are needed. In this 3-dimensional case, 7 colors are needed, meaning that the torus has a high degree of "communication" across its surface. The image shown is a "birds-eye" view.

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The progression from point (0-dimensional) to line (1-dimensional) to plane (2-dimensional) to space (3-dimensional) and beyond leads us to the question - if mapping from higher order dimensions to lower ones loses vital information (as we can readily observe with optical illusions resulting from third to second dimensional mapping), does our "fixation" with a 3-dimensional space introduce crucial distortions in our view of reality that a higher-dimensional perspective would not lead us to?

There is a wealth of good literature on this subject; it's always fascinating how nature propagates the same essence regardless of the magnitude of its expression...our spirit is spaceless yet can manifest aspects of its individuality at any scale.

The 3/4/5, 5/12/13 and 7/24/25 triangles are examples of right triangles whose sides are whole numbers. The graphic above contains several of each of these triangles. The 3/4/5 triangle is contained within the so-called "King's Chamber" of the Great Pyramid, along with the 2/3/root5 and 5/root5/2root5 triangles, utilizing the various diagonals and sides.

The 5 Platonic solids (Tetrahedron, Cube or (Hexahedron), Octahedron, Dodecahedron and Icosahedron) are ideal, primal models of crystal patterns that occur throughout the world of minerals in countless variations. These are the only five regular polyhedra, that is, the only five solids made from the same equilateral, equiangular polygons. To the Greeks, these solids symbolized fire, earth, air, spirit (or ether) and water respectively. The cube and octahedron are duals, meaning that one can be created by connecting the midpoints of the faces of the other. The icosahedron and dodecahedron are also duals of each other, and three mutually perpendicular, mutually bisecting golden rectangles can be drawn connecting their vertices and midpoints, respectively. The tetrahedron is a dual to itself.

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Indelibly etched on the walls of temple of the Osirion at Abydos, Egypt, the Flower of Life contains a vast Akashic system of information, including templates for the five Platonic Solids.

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Thank You Donna..

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I think I found one of these on the sidewalk downtown yesterday... bizarre...

There are 13 Archimedean solids, each of which are composed of two or more different regular polygons. Interestingly, 5 (Platonic) and 13 (Archimedean) are both Fibonacci numbers, and 5, 12 and 13 form a perfect right triangle.

Here are fold-up patterns for the Archimedean Solids.

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Metatron's Cube contains 2-dimensional images of the Platonic Solids (as shown above) and many other primal forms

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http://www.youtube.com/watch?v=6KCEMZWRf4o

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http://www.youtube.com/watch?v=admrfA1IkMs

as you know, enormous work done on the subject of sacred geometry and the goddess/god/allthatis.  mounds and mounds and mounds of work.

bb, ani 

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This is a stellation of a dodecahedron where each pentagonal face is capped with a pentagonal pyramid composed of 5 golden triangles, a sort of 3-dimensional 5-pointed star.

Click here for more images of polyhedra (Platonic and Archimedean Solids.)

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http://www.world-mysteries.com/sar_sage1.htm

The "Flower of Life" can be found in all major religions of the world.
It contains the patterns of creation as they emerged from the "Great Void". Everything is made from the Creator's thought.
After the creation of the Seed of Life the same vortex's motion was continued, creating the next structure known as the Egg of Life.
This structure forms the basis for music, as the distances between the spheres is identical to the distances between the tones and the half tones in music. It is also identical to the cellular structure of the third embryonic division (The first cell divides into two cells, then to four cells then to eight). Thus this same structure as it is further developed, creates the human body and all of the energy systems including the ones used to create the Merkaba. If we continue creating more and more spheres we will end up with the structure called the Flower of Life.

 

The Flower of Life (left) and the Seed of Life (right).

The flower of life holds a secret symbol created by drawing 13 circles out of the Flower of Life. By doing this, one can discover the most important and sacred pattern in the universe. This is the source of all that exists; it's called the Fruit of Life. It contains 13 informational systems. Each one explains another aspect of reality. Thus these systems are able to give us access to everything ranging from the human body to the galaxies. In the first system, for example, it's possible to create any molecular structure and any living cellular structure that exists in the universe. In short every living creature.

The most common form of the "Flower of Life" is hexagonal pattern (where the center of each circle is on the circumference of six surrounding circles of the same diameter), made up of 19 complete circles and 36 partial circular arcs, enclosed by a large circle.

The "Seed of Life" is formed from seven circles being placed with sixfold symmetry, forming a pattern of circles and lenses, which acts as a basic component of the Flower of Life's design.

The Temple of Osiris at Abydos, Egypt contains the oldest to date example. it is carved in granite and may possibly represent the Eye of Ra a symbol of the authority of the pharaoh. Other examples can be found in Phoenician, Assyrian, Indian, Asian, Middle Eastern, and medieval art.

Flower of Life - Turkey

Flower of Life - Amistar, India

Flower of Life - Amistar, India (close up)

Leonardo da Vinci has studied the Flower of Life's form and its mathematical properties. He has drawn the Flower of Life itself, as well as components therein, such as the Seed of Life. He has drawn geometric figures representing shapes such as the platonic solids, a sphere, a torus, etc., and has also used the golden ratio of phi in his artwork; all of which may be derived from the Flower of Life design.

Flower of life made of intersecting spheres instead of circles.

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Merkaba, also spelled Merkabah, is the divine light vehicle allegedly used by ascended masters to connect with and reach those in tune with the higher realms. "Mer" means Light. "Ka" means Spirit. "Ba" means Body. Mer-Ka-Ba means the spirit/body surrounded by counter-rotating fields of light, (wheels within wheels), spirals of energy as in DNA, which transports spirit/body from one dimension to another.

Sacred Geometry

Star Tetrahedron

In modern esoteric teachings, it is taught that the MerKaBa is an interdimensional vehicle consisting of two equally sized, interlocked tetrahedra of light with a common center, where one tetrahedron points up and the other down. This point symmetric form is called a stella octangula or stellated octahedron which can also be obtained by extending the faces of a regular octahedron until they intersect again.

In his books, researcher and physicist Drunvalo Melchizedek describes this figure as a "Star Tetrahedron", since it can be viewed as a three dimensional Star of David. By imagining two superimposed "Star Tetrahedrons" as counterrotating, along with specific "prana" breathing techniques, certain eye movements and mudras, it is taught that one can activate a non-visible 'saucer' shaped energy field around the human body that is anchored at the base of the spine.

This looks like a UFO

Depending on the height of the person doing the exercise, this field is about 55 feet across. Once activated, this 'saucer' shaped field is capable of carrying ones consciousness directly to higher dimensions.

http://www.crystalinks.com/merkaba.html

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One plant in particular shows the Fibonacci numbers in the number of "growing points" that it has. Suppose that when a plant puts out a new shoot, that shoot has to grow two months before it is strong enough to support branching. If it branches every month after that at the growing point, we get the picture shown here.

A plant that grows very much like this is the "sneezewort": Achillea ptarmica.

On many plants, the number of petals is a Fibonacci number:
buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters have 21 whereas daisies can be found with 34, 55 or even 89 petals.
The links here are to various flower and plant catalogues:

• the Dutch Flowerweb's searchable index called Flowerbase.
• The US Department of Agriculture's Plants Database containing over 1000 images, plant information and searchable database.

Fuchsia
Pinks
Lily
Daisies
available as a
poster at AllPosters.com3 petals: lily, iris
      Mark Taylor (Australia), a grower of Hemerocallis and Liliums (lilies) points out that although these appear to have 6 petals as shown above, 3 are in fact sepals and 3 are petals. Sepals form the outer protection of the flower when in bud. Mark's Barossa Daylilies web site (opens in a new window) contains many flower pictures where the difference between sepals and petals is clearly visible.
4 petals Very few plants show 4 petals (or sepals) but some, such as the fuchsia above, do. 4 is not a Fibonacci number! We return to this point near the bottom of this page.
5 petals: buttercup, wild rose, larkspur, columbine (aquilegia), pinks (shown above)
      The humble buttercup has been bred into a multi-petalled form.
8 petals: delphiniums
13 petals: ragwort, corn marigold, cineraria, some daisies
21 petals: aster, black-eyed susan, chicory
34 petals: plantain, pyrethrum
55, 89 petals: michaelmas daisies, the asteraceae family.
Some species are very precise about the number of petals they have - eg buttercups, but others have petals that are very near those above, with the average being a Fibonacci number.

Here is a passion flower (passiflora incarnata) from the back and front: Back view:
the 3 sepals that protected the bud are outermost,
then 5 outer green petals followed by an inner layer of 5 more paler green petals Front view:
the two sets of 5 green petals are outermost,
with an array of purple-and-white stamens (how many?);
in the centre are 5 greenish stamens (T-shaped) and
uppermost in the centre are 3 deep brown carpels and style branches)

Fibonacci numbers can also be seen in the arrangement of seeds on flower heads. The picture here is Tim Stone's beautiful photograph of a Coneflower, used here by kind permission of Tim. The part of the flower in the picture is about 2 cm across. It is a member of the daisy family with the scientific name Echinacea purpura and native to the Illinois prairie where he lives.

You can have a look at some more of Tim's wonderful photographs on the web.

You can see that the orange "petals" seem to form spirals curving both to the left and to the right. At the edge of the picture, if you count those spiralling to the right as you go outwards, there are 55 spirals. A little further towards the centre and you can count 34 spirals. How many spirals go the other way at these places? You will see that the pair of numbers (counting spirals in curing left and curving right) are neighbours in the Fibonacci series. Click on the picture on the right to see it in more detail in a separate window.  [ send green star]

Here is a sunflower with the same arrangement: This is a larger sunflower with 89 and 55 spirals at the edge:


Sunflower 

Here are some more wonderful pictures from All Posters (which you can buy for your classroom or wall at home). Click on each to enlarge it in a new window. Sunflower

The same happens in many seed and flower heads in nature. The reason seems to be that this arrangement forms an optimal packing of the seeds so that, no matter how large the seed head, they are uniformly packed at any stage, all the seeds being the same size, no crowding in the centre and not too sparse at the edges.

So the number of spirals we see, in either direction, is different for larger flower heads than for small. On a large flower head, we see more spirals further out than we do near the centre. The numbers of spirals in each direction are (almost always) neighbouring Fibonacci numbers! Click on these links for some more diagrams of 500, 1000 and 5000 seeds.

Click on the image on the right for a Quicktime animation of 120 seeds appearing from a single central growing point. Each new seed is just phi (0·618) of a turn from the last one (or, equivalently, there are Phi (1·618) seeds per turn). The animation shows that, no matter how big the seed head gets, the seeds are always equally spaced. At all stages the Fibonacci Spirals can be seen.

The same pattern shown by these dots (seeds) is followed if the dots then develop into leaves or branches or petals. Each dot only moves out directly from the central stem in a straight line.

This process models what happens in nature when the "growing tip" produces seeds in a spiral fashion. The only active area is the growing tip - the seeds only get bigger once they have appeared.

[This animation was produced by Maple. If there are N seeds in one frame, then the newest seed appears nearest the central dot, at 0·618 of a turn from the angle at which the last appeared. A seed which is i frames "old" still keeps its original angle from the exact centre but will have moved out to a distance which is the square-root of i.]

Note that you will not always find the Fibonacci numbers in the number of petals or spirals on seed heads etc., although they often come close to the Fibonacci numbers.

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Metatron (from Greek Meta+Tron meaning Beyond+Matrix.). Metatron is an angel in Judaism, some branches of Christianity and Islamic tradition Witchcraft. However, there are no references to him in the Jewish Tanakh (Old Testament), the Christian Scriptures (New Testament) or any Islamic source.

There is no consensus as to his genesis or the role that he plays in the hierarchy of Heaven and Hell. A mysterious figure, Metatron is identified with the term, "lesser YHVH" which is the Lesser Tetragrammaton - in a Talmudic version read by the Karaite scholar Kirkisani.

The word 'Metatron' is numerically equivalent to Shaddai according to Hebrew gematria, therefore he is said to have a "Name like his Master".

The Talmud records an incident with Elisha ben Abuya, also called Aher ("another"), who is said to have entered Paradise, and saw Metatron sitting down (an action in heaven that is permissible only to God Himself). Elisha ben Abuya therefore looked to Metatron as a Deity, and is reported to have said, "There are indeed two powers in heaven!"

The rabbis explain that Metatron was allowed to sit because of his function as the Heavenly Scribe, writing down the deeds of Israel, mush as Thoth was the Egyptian scribe.

According to one school of thought Enoch was taken by God and transformed into Metatron, explaining the mysterious passage "Enoch walked with God; then he was no more, because God took him away (Genesis 5:24 NIV). However, this viewpoint is not shared by many Talmudic authorities.

There may be two Metatrons, one spelled with six letters, and one spelled with seven. The former may be the transformed Enoch, while the latter is the Primordial Metatron.

The Zohar calls Metatron "the Youth", identifies him as the angel that led the people of Israel through the wilderness after their exodus from Egypt, and describes him as a heavenly priest.

Metatron is also mentioned in the Pseudepigrapha, most prominently in the Hebrew Book of Enoch (also called Third Enoch), in which his grand title, "the lesser YHVH" resurfaces. According to Johann Eisenmenger, Metatron transmits the daily orders of God to the angels Gabriel and Sammael. Metatron is often identified as being the twin brother to Sandalphon, who is said to have been the prophet Elijah.

Metatron's Cube

Sacred Geometry

The Flower of Life has thirteen circles. [13=4=time] If each circle's center is considered a "node", and each node is connected to each other node with a single line, a total of seventy-eight lines are created. Within this cube, many other shapes can be found, including two-dimensionally flattened versions of the five platonic solids. In early kabbalist scriptures, Metatron supposedly forms the cube from his soul.

This Cube can later be seen in Christian art, where it appears on his chest or floating behind him. Metatron's cube is also considered a holy glyph, and was often drawn around an object or person to ward off demons and satanic powers.

This idea is also present in alchemy, in which the cube was favored as a containment circle or creation circle.

The simplest means of constructing Metatron's Cube is to begin with a cube flattened along a diagonal that passes through its center, such that it becomes a 2D figure, equivalent to a regular hexagon divided via its own diagonals into six equilateral triangles. The vertices of this 2D figure are then connected with additional lines. Several steps later, the full Metatron's Cube figure is formed.

One must understand the metaphors of this geometry to understand Metatron and the electromagnetic nature of the creational of our reality. Metatron's Latin name is 'Metator' - A guide or measurer As in 'Creational Geometry' - or 'Metaphor'. Some say he is an Archangel as in 'Arcs or Angles of Geometry.

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This was also attributed to Thoth.

The Metatron is a reference to the highest archangel of the Kabbalah at Kether or the crown. Metatron is also sometimes equated with Thoth or Hermes, author of the Emerald Tablets of Thoth- As is Above, So is Below - the merge of polarities at Zero Point. More properly, it should be associated with the supreme Egyptian god Ptah, also known as the Opener.

The wheel you refer to combines the symbology of Kabbalah with the Tarot cards and the 22 paths in the Tree of Life. The image is of an 8-spoked wheel with the secret vowels of the Tetragammaton (name of god) and the letters ROTA, which means Wheel - however if you transpose the letters it spells "TARO". There are other esoteric symbols relating to the elements and processes involved. You should be able to find this image in books or websites dealing with the Tarot. The connections between Alchemy and the Qabbalahare among the deepest mysteries, and are gone into a later stage in the course.

List Of Alternate Names Wikipedia

http://www.crystalinks.com/metatron.html

11:11 - Working With Metatronic Numbers

Metatron's Cube - Sacred Geometry - Mandalas - by Gilchrist

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Metatron's Cube (an incomplete version that does not contain valid coordinates for the dodecahedron or icosahedron)

The Fruit of Life (a component of the Flower of Life) has thirteen circles. If each circle's center is considered a "node", and each node is connected to each other node with a single line, a total of seventy-eight lines are created. Within this cube, many other shapes can be found, including two-dimensionally flattened versions of the five Platonic solids. The true Metatron's Cube will include all five Platonic solids in such a way that the solids, existing in volumetric 3D space, have had their z-coordinates set to zero but their x- and y-coordinates retained, such that they are orthogonally flattened.

In early kabbalist scriptures, Metatron supposedly forms the cube from his soul. This cube can later be seen in Christian art, where it appears on his chest or floating behind him. Metatron's cube is also considered a holy glyph, and was often drawn around an object or person to ward off demons and satanic powers. This idea is also present in alchemy, in which the cube was favoured as a containment circle or creation circle.

The simplest means of constructing Metatron's Cube is to begin with a cube flattened along a space diagonal, such that it becomes a 2D figure, equivalent to a regular hexagon divided via its own diagonals into six equilateral triangles. The vertices of this 2D figure are then connected with additional lines. Several steps later, the full Metatron's Cube figure is formed.^[23] This method requires dividing vertices according to the golden ratio. There is also a method of construction from the Flower of Life.^[24] The cube resembles the fourth dimensional analog of the cube, or the Tesseract.

http://en.wikipedia.org/wiki/Metatron

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12 Around 1

The universe, our reality, is created by thought consciousness which manifests in physical reality through a geometric blueprint that we call Sacred Geometry. It repeats in cycles giving the illusion of linear time so we can experience emotions. The term "sacred geometry" is used by archaeologists, anthropologists, and geometricians to encompass the religious, philosophical, and spiritual beliefs that have sprung up around geometry in various cultures during the course of human history. It is a catch-all term covering Pythagorean geometry and neo-Platonic geometry, as well as the perceived relationships between organic and logarithmic curves.

Reality is a consciousness insert, created by sound, light, and color frequencies that repeat in patterns, or time. Sound wave patterns will soon be proven to be universal, through harmonics brought forth from our planetary grids and those in space. Harmonic sound waves emanating from regions in space are based on this universal design. Harmonics create a cymatic effect on Saturn -- A Mysterious Hexagonal Cloud System on Saturn. The tones will prove to be the same as those that create all of reality.

Milky Way Galaxy

Sacred Geometry is abbreviated SG referencing Stargate, the wheel of Time or Karma through which we experience and evolve. We are soul sparks of light having a physical experience, our consciousness spiral down through the patterns of the golden ratio the (slinky effect) about to reverse the spiral (spin) and return to source consciousness. The program is about to evolve. There is no going back. Watch for clues in Earth changes, science and technology mirroring the patterns of programmed realities to allow you to understand ... your behavior patterns and the consciousness patterns of the reality. Step outside the box and observe reality through its patterns rather than your emotional body.

12 Spiraling Cones Around 1 - Creation

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I am in awe of all this information. I thought I had much on Sacred Geometry, but you add much more here to understand and enjoy. Thank you very much.

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About This Video

http://www.thegatheringofone.com/

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There is one maybe two words that can describe what was read and seen. One word is interesting and the other word would have to be enjoyable. Both for the knowledge gained.

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Proportion refers the size relationship of visual elements to each other and to the whole picture. One of the reasons proportion is often considered important in composition is that viewers respond to it emotionally. Proportion in art has been examined for hundreds of years, long before photography was invented. One proportion that is often cited as occurring frequently in design is the Golden mean or Golden ratio.

Golden Ratio: 1, 1, 2, 3, 5, 8, 13, 21, 34 etc. Each succeeding number after 1 is equal to the sum of the two preceding numbers. The Ratio formed 1:1.618 is called the golden mean - the ratio of bc to ab is the same as ab to ac. If you divide each smaller window again with the same ratio and joing their corners you end up with a logarithmic spiral. This spiral is a motif found frequently throughout nature in shells, horns and flowers (and my Science & Art logo).

The Golden Mean or Phi occurs frequently in nature and it may be that humans are genetically programmed to recognize the ratio as being pleasing. Studies of top fashion models revealed that their faces have an abundance of the 1.618 ratio.

tlc.discovery.com/convergence/humanface/articles/mask.html

Many photographers and artists are aware of the rule of thirds, where a picture is divided into three sections vertically and horizontally and lines and points of intersection represent places to position important visual elements. The golden ratio and its application are similar although the golden ratio is not as well known and its' points of intersection are closer together. Moving a horizon in a landscape to the position of one third is often more effective than placing it in the middle, but it could also be placed near the bottom one quarter or sixth. There is nothing obligatory about applying the rule of thirds. In placing visual elements for effective composition, one must assess many factors including color, dominance, size and balance together with proportion. Often a certain amount of imbalance or tension can make an image more effective. This is where we come to the artists' intuition and feelings about their subject. Each of us is unique and we should strive to preserve those feelings and impressions about our chosen subject that are different.

On analyzing some of my favorite photographs by laying down grids (thirds or golden ratio in Adobe Photoshop) I find that some of my images do indeed seem to correspond to the rule of thirds and to a lesser extent the golden ratio, however many do not. I suspect an analysis of other photographers' images would have similar results. There are a few web sites and references to scientific studies that have studied proportion in art and photography but I have not come across any systematic studies that quantified their results- maybe I just need to look harder (see link for more information about the use of the golden ratio: http://photoinf.com/Golden_Mean/).

In summary, proportion is an element of design you should always be aware of but you must also realize that other design factors along with your own unique sensitivity about the subject dictates where you should place items in the viewfinder. Understanding proportion and various elements of design are guidelines only and you should always follow your instincts combined with your knowledge. Never be afraid to experiment and try something drastically different, and learn from both your successes and failures. Also try to be open minded about new ways of taking pictures, new techniques, ideas - surround yourself with others that share an open mind and enthusiasm and you will improve your compositional skills quickly.

The above segment is part of the article COMPOSITION & the ELEMENTS of VISUAL DESIGN by Robert Berdan 

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http://www.youtube.com/watch?v=PwRqIAK1tu8

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The template

http://www.youtube.com/watch?v=SvKP0SERi6c

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http://www.youtube.com/watch?v=Cq6QPTop5CE

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http://www.youtube.com/watch?v=X420jMORYe8

The Gaiadon Heart Introduction Video
www.gaiadonheart.com
email: saranya@gaiadonheart.com

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http://www.youtube.com/watch?v=CiM1lH_qLJw

Sacred geometry is geometry used in the design of sacred architecture and sacred art. The basic belief is that geometry and mathematical ratios, harmonics and proportion are also found in music, light, cosmology. This value system is seen as widespread even in prehistory, a cultural universal of the human condition. It is considered foundational to building sacred structures such as temples, mosques, megaliths, monuments and churches; sacred spaces such as altars, temenoi and tabernacles; meeting places such as sacred groves, village greens and holy wells and the creation of religious art, iconography and using "divine" proportions. Alternatively, sacred geometry based arts may be ephemeral, such as visualization, sandpainting and medicine wheels.

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and science in general.

The inherent connection between philosophy, sacred geometry, and numbers is manifested in numerous ways.  There is the Geometry of Alphabets, i.e. the Hebrew, Greek, and Arabic alphabets being sacred and the first five books of the Bible being representations of sacred geometry.  Much of this understanding was contained in the Ha Qabala, an aspect of Jewish and Christian mysticism which is worthy of prolonged and concentrated study.

(6/1/05) It has also been said that "Sacred Geometry exists beyond religion, belief or nationality. It unites us all in the belief of the one. By understanding the concept of the one each of us can take control over our own lives and break free of the circle of chaos in the material world which Judaism calls the world of lies." [quoted from ka-gold's Age of Aquarius article] This is significant stuff!

For just an inkling of what Sacred Geometry is all about, consider just one facet of it, the Golden Mean or Golden Number. The latter website provides a wealth of information in a very nicely designed web-package.

The idea that philosophy is inherently mathematical might not be construed as good news for mathematically uninclined philosophers.  But as pointed out in A Non-Mathematical Digression, it might be a good idea to momentarily address this potential obstacle.

Given that disclaimer, the amazing phenomenon of Fibonacci Numbers (complete with “bunnies”, the Golden Mean (a very rewarding subject), Golden Mean Mathematics (for those so unwise or so inclined), The Great Pyramids (a really big subject), Nines (e.g. cloud addresses), Transcendental Numbers (for those who really want to get above the crowd), Cycles, Music, and the Harmony of the Spheres (harmonies of all kinds being a good thing)...  All of these glories await your click of the mouse.

For the more sophisticated mathematicians, an excellent beginning commentary can be found at <http://mathworld.wolfram.com/GoldenRatio.html>.  As an initial example, the referenced website describes the Golden Mean (Ratio) as “A number often encountered when taking the ratios of distances in simple geometric figures such as the pentagram, decagon and dodecagon. It is denoted f, or sometimes t (which is an abbreviation of the Greek “tome,” meaning “to cut”.

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is also known as the divine proportion, golden mean, and golden section and is a Pisot-Vijayaraghavan constant. It has surprising connections with continued fractions and the Euclidean algorithm for computing the greatest common divisor of two integers.” Wow.

Sacred Mathematics Magic Squares Nines

Fibonacci Numbers Modified Fibonacci Series

Pythagorean Theorem Vesica Pisces

http://www.halexandria.org/dward095.htm

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Essentially the intersection of two, overlapping spheres, the Vesica Pisces (including the interior portion of it, and/or the more common two dimensional version) represents, among other things:  

7)  The formative power of polygons,

3)  Virtually every medieval church in Europe uses as a standard motif, the Vesica Pisces in two dimensions. The fact many of these churches were dedicated to the Virgin Mary or to Mary Madagalene (aka the goddess) is simply part of the understanding.  Several of the churches in northern France are even located in such a manner that their points of light recreate the “lights” of the constellation Virgo.  In Glastonbury, England, the site normally attributed to Avalon (the island of the Goddess), is also wh

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4)  The goddess of any and all religions which recognize her power and significance invariably use the Vesica Pisces to identify her.  From the overlapping pools of water and the chalice well cover in the goddess’s garden in Glastonbury (aka Avalon) to any number of representations of the Tree of Life, the goddess and her ability to create and birth life are celebrated.

7)  Robert Lawlor, in one of the best books available on Sacred Geometry [Thames and Hudson, 1982] notes that the Ö3 contained within the Vesica Pisces is “the formative power giving rise to the polygonal ‘world’.”

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 hourglass), and a similar configuration is:  

http://hubblesite.org/newscenter/archive/  ,,,

1966/07/image/a 

http://hubblesite.org/news/archive/1966/07/image/b

In general, the Hubble website is worth visiting, if only

 because of the fascinating pictures which the universe

has so thoughtfully provided for our entertainment.  

(**)  http://www.nationalgeographic.com

    There is a recent book showing some of the more stunning

    photographs from the Hubble Space Telescope, entitled

    The Hand of God, edited by Michael Reagan, Templeton

    Foundation Press, Philadelphia and London, 1999.

    But in any and all cases, come back to visit ialexandriah

 and discover (or remind yourself of) yet more.

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http://www.youtube.com/watch?v=QbRlfPG1_2k
Vesica Piscis - We All Know the Name Unspoken

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http://www.youtube.com/watch?v=Kynzemkv86c

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June 12, 2002

When I awoke this morning I was dreaming that I was talking to Osiris, an Egyptian God who wore a conical shaped hat. His partner was Isis. As a watched him, his headdress suddenly started to spiral from the top of his head. It became a pyramid of light energy then changed into the flame of creation into which he disappeared. The top of Osiris' headdress is torus shaped. This is a reference to creation by consciousness.

The Tube Torus is derived from the basic study of the Flower of Life. By using a simple compass one can create the Flower of life very easily. There are seven basic steps in the composition of the Seed of Life which, if continued to its conclusion, yields the study of the vortex through the Flower of Life. This goes to spiraling consciousness, coiling (DNA) back to source.

Views of the Tube Torus as the

polar grid in other positions.

Golden Ratio/Mean Spiral

from two different calculations

Looking at the Golden Mean

from the side.
Zero Point
As is Above, So is Below

Harmonics of Sound

View of the polar grid derived from the Flower of Life containing the same Golden Mean Spiral. As you contemplate this image, the beginning of the study of Character Math seems to appear. This is a one dimensional look at the polar grid which is actually 3 dimensional. The study of music and how it pertains to the Flower of Life and the polar grid, yields harmonic calculations which describe other proportional properties in Sacred Geometry. Phi Harmonics research continues at San Graal School of Sacred Geometry. There are links on the front page to other articles and downloadable music files which are pertinent to the study of The Language of Light, according to Phi and the Vibration of our Universe.

Calculating the polar grid from a different perspective we get the harmonics of music equaling the twelfth root of two, which is the standard for tuning harmonics as we know them.

Quetzalcoatl wears a conical cap as wind god Ehecatl. He brought love into the world by mating with the maid Mayahuel as a single tree with flowering branch.

Pharaoh Akhenaten, from a statue in the library of the British Museum. The Pharaoh is equally a priest and a ruler, and wears the crown of the two halves (upperworld and underworld) of his dominion. the lower crown denotes the upperworld, the high conical hat the lower.

They also wore conical hats

• Traditional Vietnamese conical hats or 'Non La'
  

• Certain religous figures in the church

• Witches - Warlocks - Magicians Mysterious gold cones 'hats of ancient wizards - Telegraph.com - Ju

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• 
  Wizards really did wear tall pointed hats, but not the crumpled cloth kind donned by such fictional characters as Harry Potter, Gandalf and Merlin. The wizards of early Europe wore hats of gold intricately embellished with astrological symbols that helped them to predict the movement of the sun and stars. This is the conclusion of German archaeologists and historians who claim to have solved the mystery behind a series of strange yet beautiful golden cone-shaped objects discovered at Bronze Age sites across Europe.

  Four of the elaborately decorated cones have been uncovered at sites in Switzerland, Germany and France over the past 167 years. Their original purpose has baffled archaeologists for decades. Some concluded that they were parts of Bronze Age suits of armour; others assumed that they served as ceremonial vases. A third theory, which had gained widespread acceptance until now, was that the cones functioned as decorative caps that were placed on top of wooden stakes that surrounded Bronze Age sites of worship.

  Historians at Berlin's Museum for Pre- and Early History, however, claim to have established with near certainty that the mysterious cones were originally worn as ceremonial hats by Bronze Age oracles. Such figures, referred to as "king-priests", were held to have supernatural powers because of their ability to predict accurately the correct time for sowing, planting and harvesting crops.

  "They would have been regarded as Lords of Time who had access to a divine knowledge that enabled them to look into the future," said Wilfried Menghin, the director of the Berlin Museum which has been carrying out detailed research on a 3,000-year-old 30 inch high Bronze Age cone of beaten gold that was discovered in Switzerland in 1995 and purchased by the museum the following year.

  Mr Menghin and his researchers discovered that the 1,739 sun and half-moon symbols decorating the Berlin cone's surface make up a scientific code which corresponds almost exactly to the "Metonic cycle" discovered by the Greek astronomer Meton in 432 BC - about 500 years after the cone was made - which explains the relationship between moon and sun years. "The symbols on the hat are a logarithmic table which enables the movements of the sun and the moon to be calculated in advance," Mr Menghin said. "They suggest that Bronze Age man would have been able to make long-term, empirical astrological observations," he added.

  The findings radically alter the standard image of the European Bronze Age as an era in which a society of primitive farmers lived in smoke-filled wooden huts eking out an existence from the land with the most basic of tools.

  Another cone, found near the German town of Schifferstadt in 1835, had a chin strap attached to it. The cone, which is also studded with sun and moon symbols, is the earliest example found and dates back to 1,300bc.

  Other German archaeologists have suggested that the gold-hatted king-priests were to be found across much of prehistoric Europe. Prof Sabine Gerloff, a German archaeologist from Erlangen University, has found evidence that five similar golden cones were exhumed by peat diggers in Ireland during the 17th and 18th centuries.

  These objects, described at the time as "vases", have disappeared. Prof Gerloff says, however, that her research suggests almost conclusively that they were hats worn by Bronze Age king-priests. She is also convinced that a Bronze Age cape of beaten gold - the "Gold Cape of Mold" discovered in Wales in 1831 - was part of a king-priest's ceremonial dress. Prof Gerloff has used computers to create an impression of a Bronze Age oracle wearing a golden hat and with an elaborately decorated golden cape wrapped tightly around the shoulders.

A conical hat is a hat shaped like a cone. Conical hats and caps can generally be subdivided into two types by the angle through their cross-section.

• acute angle: pointy hat
• obtuse angle: conical straw hat

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Wow girlfriend. Only read about a quarter of what is written here - my brain can't handle any more tonight - and found it to be totally awesome. Might take me a while to finish it and not sure I could even add anything. You have a lot of information here. It's great. Thank you so much for pointing this out.

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Hi Jilly, thank, Urock2! This subject is endless and this thread could go on for eternity. I was just admiring a flower of life poster in my office and then saw your post on this thread. I was just thinking how it is the ONE thing I feel that I understand about the universe on some level. If you think of the masculine energy being he generator behind it and what we see is maya (feminine) illusion. You will begin to see these patterns emerge from pretty much everything if you study the sacred geometry enough. It also works to stimulate and open dormant brain power so even if you just sit and stare at the image you are consciously evolving by doing so...

Blessings!

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http://www.youtube.com/watch?v=cAYO7ENPMk0

The second video from thetemplateorg.com. The Template is a holonomic model of transcendence; a journey of remembrance, forgiveness, resurrection and ultimately transcendence of the dualistic mortal paradigm.

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http://www.youtube.com/watch?v=CKdCfi5KNko

Are we listening to hyms of offering?
Have we eyes to see that love is gathering?


http://www.youtube.com/watch?v=WEIZ3WASl3I

Oh let the sun beat down upon my face, stars to fill my dream
I am a traveler of both time and space, to be where I have been
To sit with elders of the gentle race, this world has seldom seen
They talk of days for which they sit and wait and all will be revealed...

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How to Draw the Face of the Goddess Sekhmet using the Geometry of the Square Root of Five and Phi

© 1998 DARLENE aka Lady Sekhmet

Creating Sekhmet’s likeness using Sacred Geometry by DARLENE

The above pdf contains the sacred geometry of drawing the Face of the Goddess Sekhmet and is the same as given below:

Let’s first understand some basic concepts. To divide any line at its golden mean, construct a double square upon it. Draw a line from the lower left corner of the first square to the upper right corner of the right square, making a triangle.

Then place the compass as shown below and open it to the apex of the right angle at the bottom. Swing the compass until it passes the diagonal.

Open the compass to the point just made. Swing the compass downward to see it cross the original line at its golden mean balance.

The Square Root of five derives from the vesica pisces, a symbol of the fusion of opposites. It is defined by the interlap of two circles at the center.

Starting with the double cube, the upper circle will be Sekhmet’s Celestial orb and the lower will comprise Her face.

The Golden Section represents the most reduced relationship through which unity may be expressed in proportional form.

When the phi relationship within each square has been determined, draw circles in relationship to the phi divisions.

Working on the lower circle, Sekhmet’s head, divide the upper circle into quarters, the lower circle in half. Then mark off each half of the upper horizontal line into thirds. Extend the two lines closest to the center a little above the horizontal line.

Extend the lines mentioned above to the boundary of the upper circle. Then make an X by extending each to the other side, ending at the horizontal line which divides the lower circle in half.

Base the size of the ears on the double square. At this point, you are free to begin diverging from the compass to be more loose when sketching in the features—the eyes, nose and muzzle.

When working on the proportions of the cobra, divide the phi circle in half and fit two circles vertically within. Divide the uypper smaller circle horizontally and repeat the process. The head of the cobra is created by the upper boundary of the smaller circles.

Add the details. Sketch in the mane behind the ears and each side.
TIPS: Draw eyelids coming off of original horizontal line. Let them curve in and connect with the nose. When drawing the eyes, make a circle, then cut off its top with the brow line and corner lines.

http://allthingssekhmet.com/?page_id=163

Have FUN. Many differing lion faces can be drawn
using this basic template.

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http://www.youtube.com/watch?v=4eRlfyaLwss

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