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 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.

As far back as Greek Mystery schools 2500 years ago, we as a species were taught that there are five perfect 3-dimensional forms -The tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. Collectively these are known as The Platonic Solids -- and are the foundation of everything in the physical world. Modern scholars ridiculed this idea until the 1980's, when Professor Robert Moon at the University of Chicago demonstrated that the entire Periodic Table of Elements -- literally everything in the physical world -- is based on these same five forms! In fact, throughout modern Physics, Chemistry, and Biology, the sacred geometric patterns of creation are being rediscovered, but often without the greater context of spiritual understanding which protects against their misuse. One of our intentions with lightSource, is to provide a bridge to an intuitive spiritual understanding that is in alignment with the appropriate use of this knowledge.

Sacred Geometry
Geometric shapes actually represent the manifest stages of 'becoming'. To see and work with unity and wholeness in geometry can help abolish our false notion of separateness from nature and from each other. Through Sacred Geometry we can discover the inherent proportion, balance and harmony that exists in any situation, all manifest reality and even the circumstances of our day-to-day life.

It was Marcel Proust who said, " The real voyage of discovery consists not in seeking new lands but seeing with new eyes."
The Energy in Action
Leonardo Fibonacci was an Italian mathematician who introduced to Europe and popularized the Hindu-Arabic number system (also called the decimal system). He contributed greatly to number theory, and during his life published many important texts. He is also known for the Fibonacci Series, a numerical series found frequently in the natural world.
The Fibonacci sequence is generated by adding the previous two numbers in the list together to form the next and so on and so on.(1, 1, 2, 3, 5, 8, 13, 21, 34, 55...). Divide any number in the Fibonacci sequence by the one before it, for example 55/34, or 21/13, and the answer is always close to 1.61803. This is known as the Golden Ratio.

One of the most profound and significant activities encompassed within sacred geometry is the 'Golden Mean Spiral', derived by using the 'Golden Ratio'.
The Golden Mean was used in the design of sacred buildings in ancient architecture to produce spiritual energy that facilitated connectivity with spiritual realms through prayer. Our reality is very structured, and indeed Life is even more structured. This is reflected though Nature in the form of geometry. Geometry is the very basis of our reality, and hence we live in a coherent world governed by unseen laws. These are always manifested in our world. The Golden Mean governs the proportion of our world and it can be found even in the most seemingly proportion-less (active) living forms. Clear examples of Sacred Geometry (and Golden Mean geometry) in Nature and matter: All types of crystals, natural and cultured. The hexagonal geometry of snowflakes. Creatures exhibiting logarithmic spiral patterns: e.g. snails and various shell fish. Birds and flying insects, exhibiting clear Golden Mean proportions in bodies & wings. The way in which lightning forms branches. The way in which rivers branch. The geometric molecular and atomic patterns that all solid metals exhibit. The way in which a tree spans out so that all its branches receive sunlight Another, perhaps less obvious but most significant example of this special ratio can be found in Deoxyribonucleic Acid (DNA) - the foundation and guiding mechanism of all living organisms. Click this picture of the Sri Yantra to see how it is it created :) The understanding of geometry as an underlying part of our existence is nothing new, and in fact the Golden Mean and other forms of geometry can be seen imbedded in many of the ancient monuments that still exist today. The Great Pyramid (the oldest of these structures) at Giza is a good example of this. The height of this pyramid is in Phi ratio (e.g. the Golden Mean Ratio) to its base. In fact, the geometry in this particular structure is far more accurate than that found in any of today's modern buildings.

This explains why popular among spiritually significant shapes are pyramids and hemispheres (e.g. the domes, that are the basis of religious buildings, be it a mosque, a church or a synagogue). These particular shapes are energy emitters; they are shapes that produce a type of penetrating carrier wave which Chaumery and De Belizal named negative green (which acts as carrier-like radio waves that carry sound information). The vibrational quality of the Golden Mean gives it very strong communication properties, which facilitate resonance with higher realms in prayer.

We live in the 3rd dimension, or the 'Plane of Manifestation'. The Golden Mean is an intra-dimensional doorway though which matter emerges into manifest 3-D reality. For example, when a star is born it follows specific number sequences or universal rules, the same rules of life in the expansion process. Then we see the light!

Thus the Golden Mean is the "fingerprint" of creation. When we re-create this moving and always expanding sequence, we have in effect - 'the exact movement of creation in the expansion process'.

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.

The Sphere
(charcoal sketch of a sphere by Nancy Bolton-Rawles) 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.

The Circle
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.

The Point
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.

The Square Root of Two
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!

The Golden Ratio


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.

width=200 height=200 style="margin: 10px; float:left "alt="Omega432™ The Flower of Life" title="The Flower of Life" border="0"/> The outline of the Parthenon at the Acropolis near Athens, Greece is enclosed by a Golden Rectangle by design.
The Square Root of 3 and the Vesica Piscis
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.

Spirals
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.

Toroids
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.

Dimensionality
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?

Fractals and Recursive Geometries
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.

Perfect Right Triangles
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 Platonic Solids
Here are LOTS of math details and images of the Platonic Solids and Archimedean Solids.
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.

Here are some animations of counter-rotating polyhedra and images of the Platonic solids showing their relationships as duals.
Here are fold-up patterns for the Platonic Solids.

The Archimedean Solids
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.


Stellations of The Platonic Solids and The Archimedean Solids


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.

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