Topics and Glossary
The cube also contains the symbolism of the number six, since it has six sides. It also represents the "four corners" of the world, or the World Age as defined by the two equinoxes and two solstices and the attendant constellations rising helically thereon.
The Fibonacci Sequence is Mother Nature's way of interpreting the Golden Mean relationship. When a little bush sprouts, it first grows one leaf. In a little while it grows one more leaf and then two more. And then three, five, eight, thirteen, twenty one, thirty four, and on and on. Numerous flowers use one of these Fibonacci numbers for the number of its pedals, 3, 5, 8, 13, 21, etc.
The Fibonacci Sequence also manifests in beautiful natural spirals of all types, like the pine cone, the nautilus shell, and the face of a sun flower. 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. The mathematical relationship between sequential numbers of the Fibonacci Sequence very quickly comes extremely close to the Golden Mean Phi Ratio (1.6180339)and the larger the numbers, the closer they get.
The role of geometry in the process of creation is covered well by Robert Lawlor, in his fascinating book Sacred Geometry:Philosophy and Practice (Thames and Hudson, London, 1982). In it he says the following:
"The perspective of volume offers yet another metaphor for the original and ever-continuing creative act of the materialization of Spirit and the creation of form. The very ancient creation myth coming from Heliopolis in Egypt gives an example of this mode of envisioning. Nun, the Cosmic Ocean, represents pure, undifferentiated spirit-space, without limit or form. It is prior to any extensive, any specificity, any god. It is pure potentiality. By the seed or will of the Creator, who is implicit within this Nun, the undifferentiated space is impelled to contract or coagulate itself into volume. Thus Atum, the creator, first creates himself or distinguishes himself from the undefinable Nun by volumizing, in order that creation might begin. "
The hexagram is the shape created naturally by bees in the hive. The symbolism of bees thus becomes linked to that of the hexagram, and by extension, the number six and the Seal of Solomon (or Star of David). The hexagram - and resultant star - is the one of the most powerful mystic symbols. It represents the Sixth Principle: That of a consciousness united fully with the Manas or Universe. It is two triangles overlapping - the balance of Man and Universe, each with its own triangle of balance. Most often the figure is drawn with one triangle white and the other black, to represent a perfect union of the Spiritual and Material, or the Macrocosm and Microcosm. This is the loss of the Individual within the Universal -- the ultimate goal of all Magi often thought of as "Oneness" with the universe.
Pi is the ratio of the circumference of the circle to its diameter: Pi is a transcendental or so called irrational number having a value(to eight places) of 3.14159265. For practical purposes, the value of Pi is 3.1416.
This principle of IMPLODING waves causes them to stabilize and store charge, making a container that is harmonically inclusive, where no detrimental energy can exist and everything is sorted and self-aware.
By creating our buildings using the principles of sacred geometry, which reflect the patterns underlying all of life, we create spaces that resonate with the Order of Things (fractal) and which corral energy in a balanced and restorative way.
"The bee hive and the pine cone are excellent examples of sacred architecture because as biological capacitors they implode charge, making life and bliss possible and sustainable. They are made of biologic di-electric (self-similar at atomic and molecular symmetry levels), what Reich used to call orgone material, really names for fractal capacitive di-electric. The reason a beehive or a celtic straw hut in sea spray makes things live so long, is because they are good capacitors. Ancient dolmen sites, fresh eggs and even cathedrals hold life in bliss in the spell of their charge, because they are 'in charge' - that is - FULL OF CHARGE. Life occurs when biological structures learn to gather charge in enough different wavelengths to cause them to compress or 'implode'. When enough different waves gather in one place in the Golden Mean ratio they begin to suck in an infinite number of other waves - but always in Golden Mean ratio. This is the only way the universe has of arranging an infinite (in-PHI-knit) number of waves to gather at ONE point without hurting each other."
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. Mother nature uses geometry everywhere you look, from the spirals of the nautilus shell, sunflower centre and spiral galaxies to the hexagon symmetry of snowflakes, flower petals and honeycomb.
Sacred Geometry is also the modern bridge between Science, Physics and Spirituality. Sacred Geometry is currently rediscovered as a knowledge KEY for shifting to a new paradigm of universal wholeness and the loving inter-connectedness of the Web of Life. Traditional wisdom holds the universe to exist because of a profound harmonic order. From quantum foam to atoms to DNA to galaxies, certain precisely reoccuring ratios and geometric symmetries are the foundation of the whole cosmos.
We live in a mathematically ordered world. All actions on the physical plane obey distinct mathematical laws. All existence exteriorizes itself through harmonic economy. From the dance of atoms to spiraling galaxies, every type of growth and motion is governed by the same set of laws. Sacred geometry describes these laws through a language of number, angle, shape, form and ratio (relationship). It is a universal language of pure mathematical truths based upon the inner workings of nature and the inherent qualities of the circle and sphere.
Sacred geometry shows how primordial forces are transformed to cosmological order. It measures the harmonic vibrations that sustain life on all levels. Sacred geometry shows the quality of relatedness between unique and individual differences, and demonstrates how diverse elements can be organized into a whole, while still preserving their individuality.
Sacred geometry integrates the physical, tangible aspects of creation with the spiritual essence behind them. It is an interface between the seen and the unseen, the manifest and the un-manifest, the finite and the infinite, the mundane and the profound. Sacred geometry has played an integral role in the art,architecture and philosophy of numerous cultures for thousands of years. In the Pythagorean system, as well as other systems, geometric symbolism was held to account for all known states of being.
The ancient Greeks had a geometric/harmonic view of universal order. They saw the world as a vast array of diverse elements, unified and blended into a cosmos through the essence of harmony. Sacred geometry was used as a valuable tool of self discovery in the ancient mystery schools. The goal of many of the arcane schools was to help lead the mind back towards a sense of Oneness.
It is through the experience of the Oneness of all things that Individual Consciousness can harmonize with Universal Consciousness. Before birth, we resided on the spiritual plane of existence. During the transition to the material plane we assumed a physical form. We cannot return to the spiritual plane as long as we have a body, because the resistance of matter prevents it. However, through the spiritualization of matter we can reach an awakened state of spiritual awareness.
The spiritualization of matter occurs when we experience the divine presence in every aspect of creation, but most particularly within ourselves. To achieve this, look within. We are an embodiment of sacred geometry. We unite within ourselves the diversities of heaven and earth. We are spirit and matter combined. We are spiritual beings having a human experience.
We are a microcosmic reflection of the macrocosm. The structure of the human body is based upon the same set of principles that are found functioning on all levels of creation. Our body contains within it holographically all the information of the universe.
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.
Are our buildings shaped by sacred numbers and hidden codes? Architecture begins with geometry. Since earliest times, architects have relied on mathematical principles. The ancient Roman architect Marcus Vitruvius believed that builders should always use precise ratios when constructing temples. "For without symmetry and proportion no temple can have a regular plan," Vitruvius wrote in his famous treatise De Architectura.
The proportion Vitruvius recommended was modeled after the human body. He observed that all human beings are shaped according to a ratio that is astonishingly precise and uniform. For example, Vitruvius found that the human face equals one tenth of the total body height. The foot equals one sixth of the total body height. And so on.
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Scientists and philosophers later discovered that the same ratio Vitruvius saw in the human body - 1 to PHI (1.618) - exists in every part of nature, from swimming fish to swirling planets.
Sacred geometry, or spiritual geometry, is the belief that numbers and patterns such as the divine ratio have sacred significance. Many mystical and spiritual practices, including astrology, numerology, tarot, and feng shui, begin with a fundamental belief in sacred geometry. Architects and designers may draw upon concepts of sacred geometry when they choose particular geometric forms to create pleasing, soul-satisfying spaces.
The vibrations we call sound follow sacred, archetypal patterns. For this reason, you may find that certain sound sequences can stimulate the intellect, inspire creativity, and evoke a deep sense of joy.
Nature's archetypes are reflected in the crystalline forms of gems and stones. Amazingly, the patterns found in your diamond engagement ring may resemble the formation of snowflakes and the shape of your own cells.
Nature's patterns are echoed in the movement of planets and stars and the cycles of the moon. Perhaps this is why astrology lies at the heart of so many spiritual beliefs.
Similar shapes and numbers are found beneath the sea, from the swirl of a nautilus shell to the movement of the tides.
When studied under the microscope, living cells reveal a highly ordered system of shapes and patterns. From the shape of your DNA to the cornea of your eye, every part of your body follows the same predictable patterns.
Most significant example of this special ratio can be found in Deoxyribonucleic Acid (DNA) - the foundation and guiding mechanism of all living organisms.
Dan Winter has used the theory of the Golden Mean in his teaching of the FRACTAL UNIVERSE and his IMPLOSION theories.
The Greek letter phi (Ø) signifies the golden section, also known as the divine proportion of 1.618 to one. The mathematical formula for f is the square root of five plus one, divided by two.If a line is divided with the ratio of f between the longer segment and the shorter segment, the ratio between the whole line and the longer segment is also f. Given a length of one for the shorter segment, the length of the longer segment is Ø and the length of the entire segment is Ø plus one. Ø plus one is also equal to Ø
The jigsaw puzzle of life is made up of recurring shapes and numbers; leaves, flowers, seeds, and other living things share the same patterns of spirals and other shapes. Honeybees and many insects live highly structured lives that mimic these patterns on another level. When we create a floral arrangement or walk through a labyrinth, we celebrate nature's innate forms. Take a look around and you will see for yourself the garden is a place replete with sacred geometry.
Stonehenge, metalithic tombs, and other ancient sites stretch across the globe along underground electromagnetic tracks, or ley lines. The energy grid formed by these lines suggest sacred shapes and ratios.
The Golden Ratio, or Divine Proportion, is the key proportion behind these processes that beget life. This is a universal principle that can be found on all levels of existence. The golden ratio describes the special relationship found in nature between two parts of a whole. It can be described in terms of number, length, area, volume and, to a certain degree, beauty and consciousness.
The golden ratio is the mathematical proportion 1:1.618034...ad infinitum. Often called by its Greek name phi, it is also known as the Divine Proportion, the Golden Ratio, the Golden Section and the Golden Mean. It is indelibly inscribed in the heart of nature and man. Trace the thread of this "golden mean" from daisy to pyramid, from pine cone to Parthenon. Or from seashell to spiral nebulae as described above. The cosmos weaves its garments with perfect integrity, laced by the golden ratio. It is so omnipresent that many philosophers, artists, mathematicians, and scientists have considered it an essential component of beauty, perhaps integral to life itself. Plato considered it the key to the physics of cosmos. The Egyptians thought it more than a number and believed it symbolized the creative process and the fire of life.
The numerical value of the golden ratio is unending, and usually rounded off to three decimal places at 1.618. This value is applied to related objects of different sizes. The simplest example is two straight lines of different lengths. If the length of the shorter line is given the value of 1 unit of measurement, the other line is then 1.618 times longer than that.
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.
Two overlapping circles with a common radius, create the second enclosed form of Sacred Geometry. The ancients called this archetype the Vesica Piscis. ALL FORM, literally ALL the dimensional forms of this cosmos evolve from this football like shape. The Vesica Piscis is literally the womb of the universe . . . the ever unfolding Mother of Sacred Geometry.