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Sacred Geometry Sacred Geometry: The cumulative effect of sacred geometry is the connection between the microcosm and the macrocosm. What is 'Sacred' Geometry' : The synchronicity of the universe is determined by certain mathematical constants which express themselves in the form of 'patterns' and 'cycles' in nature. The outcome of this process can be seen throughout the natural world as the following examples demonstrate: The Passion-flower Spiral galaxy M74 Giant's causeway, Ireland. Spiral snail shells. These displays of mathematical and geometric constants are confirmation that certain proportions are woven into the very fabric of nature. Recognising the significance of this simple fact offers us the means to understand how and why such matters were considered sacred. They and everything around us, are the product of the delicate balance between chaos and order. The word 'geometry' can be traced through its component parts: The word 'Geo-metry' comes from the Greek words Geos meaning 'Earth' and Metron meaning 'To measure', which together literally translate as the 'Measuring of the earth' or 'Earthly measurements', an art which was traditionally restricted to the priest-hood. Sacred geometry has existed in many forms across the ages It is often mistakenly said that geometry began with the Greeks, but before them were the Minoans, the Egyptians, Sumerians, Indus valley, Chinese, Phoenicians and of course, the builders of the western European megaliths all of whom left clear geometric fingerprints in their greatest constructions. The Greeks may well have been the first to have offered geometry to the public at large, but they were by no means the first to realise it. Sacred-Geometry: The First Step. One of the most common shapes in nature is the circle, it is therefore extremely significant to understand that all other geometric shapes can be determined from a circle...with the use of only a compass (or string) and a ruler (straight edge) as the following procedure illustrates... Starting with the Vesica-pisces...from which one is able to produce... An Equilateral triangle, Hexagon, Pentagon, Square and so on and so on.. The Vesica Pisces is one of the key starting blocks from which sacred geometry was applied to life. A continuation of the geometric Vesica Pisces results in the geometric matrix named Ad- triangulum...as used for the design of many of Europe's greatest Cathedrals... Featured Articles: The Harmony of the Spheres. The first confirmed record of a knowledge of the relationship between astronomy, music and geometry comes (almost predictably) from the Greeks: in particular, Pythagoras who wrote of the 'Harmony of the Spheres', and of whom it was said: '...of all men, he alone [Pythagoras] could hear the music of the spheres...' Labyrinths: The symbol for the Labyrinth has been found associated with 'sacred' places for thousands of years from all around the ancient world. More recently, more especially from the middle ages onward, it has been used as a tool for pilgrimage - representing our metaphorical path through life. The Flower of Life: The flower of life symbol has found its way into the human consciousness, it is no more than an elaborate extension of the Vesica pisces, but one within people have found themselves lost in a state of perpetual imaginative bloom. It is said to contain values that depict the fundamental geometry of time and space. Spirals: Form and Function. Spirals are one of the most a common forms of natural geometry, being a product of the sacred mean. They are associated with omphalos and earth-navels and are regularly found engraved on megaliths. Their original meaning is lost today but spiral designs at such noticeable sites as Newgrange and Chaco Canyon, has led many to believe they were primarily astronomical. Geodesy and the World Grid: This section examines the theory that geometry was applied in the placement of certain prominent (sacred) prehistoric sites, based on an understanding of longitude and latitude. The 'linear-mentality' of our ancestors seems to have had no frontiers, but what if any, was the origin and purpose of networking sacred sites, and how Petrospheres and the Platonic Solids. Of the hundreds of small carved stone balls fond in Scotland, over 75% have been found to conform to the five Platonic solids. This remarkable discovery suggests an association as yet undetermined. Although it is generally believed that the Greeks discovered this mathematical principle, these come from over a thousand years earlier. The Myth of Precession. It has been proposed that the understanding of sacred geometry extended into time and space, as realised through the 'Platonic Year'. Santillana (6) and others have shown that certain precessionary numbers were encoded into ancient sacred buildings, texts and mythologies. these same numbers appear to be reflected in the natural geometry of the universe. Other Articles: Sacred Geometry and the Great Pyramid of Giza: The exterior angle of the 'Great pyramid of Giza' can be reproduced with the Vesica- pisces. It has been long suspected that the Great pyramid was a subsidiary of geometric knowledge. There are several other indications that sacred geometry was an important factor in the design of the pyramid. The Sacred mean (Phi), was also recorded into the dimensions of the pyramid itself. Pi and the Pyramid. Egyptian mathematicians arrived at a figure of 3.16 (as shown on the Rhind Papyrus), written 600 to 800 years later and far cruder than the precise ratio the great Pyramid seems to express. The figure of Pi is recorded into the dimensions of the Great Pyramid several times; As well as the Height/Perimeter ratio of the pyramid itself (2∏x H = Perimeter) The perimeter of its main compartment, the so called “King’s Chamber,” is also exactly 3.14 times its length, and the large granite coffer or sarcophagus in this room shows the same proportion. In the earlier, rhomboidal or “Bent Pyramid” at Dashur, a few miles to the south, the sides begin to ascend at the same 2-Pi angle as the Great Pyramid, then change half way up to 3-Pi (43 ½º ) ratio. Pyramid Geometry and Latitude. The exterior angle of the Great pyramid is the exact same latitude that Silbury Hill was built, and at the same time. It is perhaps no coincidence to find that exterior angle of the Silbury monument has an exterior angle of 30°, the same as the latitude of Giza. This exact angle is also found at nearby Stonehenge in the orientation of The Avenue, which points towards the sunrise on the summer solstice. Stonehenge sits exactly 1/4 of a degree of longitude south of Avebury. This fact is just one of many in the increasingly convincing argument in favour of the existence of applied sacred geometry in prehistory. The Sacred Mean: 'Phi'. The Sacred mean - (5:8 or 1:1.618 or Φ) (The Divine Proportion, Golden Section, Golden ratio, Phi, ) One of the Key-stones of sacred geometry is the 'sacred mean' or 'golden section'. The Mathematics of the Golden Ratio (Phi). The golden section exists between measurable quantities of any kind where the ratio between the smallest and the next size up is equal to the ratio of the sum of the first two to the third. Mathematically, the same proportion is generated with the following formula: √5+1 / 2 In numerical terms, the 'Golden ratio' was first popularised by Leonardo Bigollo Fibonacci, the founder of the 'Fibonacci sequence', a numerical series which simply follows the rule that the next number is the sum of the previous two numbers.. as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 etc... Vitruvian Man: Leonardo Da Vinci. One of the fundamental products of this underlying mathematical structure is the 'sacred mean', a mathematical constant which is visible across the spectrum of the natural world. The sacred mean is one of the defining geometric qualities of life itself, as it plays an integral part of the complex process of division and variation. Leonardo da Vinci illustrated both the mathematical proportions of the human body, (which are based on ratios of 1.618), and the concept of 'squaring the circle' with his famous drawing (right). Da Vinci was engrossed by Vitruvius, who had written that human proportions should have a relationship in architecture. Vitruvius believed that if human proportions could be incorporated into buildings they would become perfect in their geometry. One of Da Vinci's greatest discoveries was the division of the body into proportions of whole numbers which he called 'cubits'. For example, while the body is 4 cubits high, it can be seen on the same body that 1 cubit is both the length from shoulder to shoulder and from elbow to fingertips. According to Vitruvius, the distance from fingertip to fingertip should be the same as that from head to toe. The sacred mean can be seen in the ratios of body parts. In the arm of the Vitruvian man for example, we can see that the ratio of A is to B is the same as that of B to C. The same rules apply throughout the human body. One of the mathematical products of the sacred mean is the spiral, commonly found in nature. The sacred mean is also found in the geometry of the pentagram and its associated pentagon, where the ratio between the sides of the pentagon and its extension into the pentagram also demonstrate a ratio of 1:1.618. In the above diagram, Phi is found in the ratios of a:b, b:c, c:d, d:e and e:f. The Flower of Life: The Flower of Life symbol is considered to be sacred among many cultures around the world, it is considered by some to be an 'Akashic Record'.
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