Sacred Geometry


Many times we see some geometry common in all religious places like we see a star-like geometry in all Jew’s synagogues, so what does this geometry mean? Is it just a drawing or it carries some special meaning in it? All ancient structures like pyramids built in a particular geometry must have some significance in it. Actually the truth is that they are built following a geometry called sacred geometry.





Introduction:


Let me first describe the word geometry, the word geometry is made up of two Greek words geo and metric. The word 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.

Now let me tell you something about sacred geometry.


According to Wikipedia:

Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. It is associated with the belief that a god is the geometer of the world. The geometry used in the design and construction of religious structures such as churches, temples, mosques, religious monuments, altars, and tabernacles has sometimes been considered sacred. The concept applies also to sacred spaces such as temenoi, sacred groves, village greens, and holy wells, and the creation of religious art.”


Sacred geometry has existed in many forms across the ages

It is often mistakenly said that geometry began with the Greeks, but before they 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 realize it.

It encompasses the religious, philosophical, and spiritual beliefs that have sprung up around geometry in all the major cultures during the course of human history. The geometrical laws from the flower of life produce the blueprint of the one consciousness that created life and existence.

Primeval Culture, including Hindus, Egyptians, Greeks, Christians, believes that certain geometric patterns or shapes are recurring in nature.


For example; a snail’s shell is a spiral, the cells of a honeycomb are hexagons, and the passionflower grows in a logarithmic spiral.

These standard forms are the sacred geometry symbols. These shapes were broken down by the ancients into numerous mathematical formulas; various numbers and specific symbols that were the foundation for everything in the Universe.

While it may be esoteric, a fundamental knowledge of these patterns and shapes in nature can help us see our world in a new light. It is an essential factor when constructing sacred structures such as mosques, temples, megaliths, and monuments. Besides, tabernacles and altars, as well as meeting places such as village greens, holy groves, and sacred wells which are sacred all have a kind of geometric symbols in their structures.

The creation of religious art, using divine proportions and iconography are all connected to this school of thought. Also, arts-based on this type of geometry may be ephemeral such as medicine wheels, sand painting, and visualization.


It’s significance in different fields:


Art


There are many locations in the world where these geometric figures are in art. Some of them are in temples, synagogues, and churches in the following countries: China, Israel, Turkey, India, Spain, and Italy.


Science


The theory is also in modern science. The little patterns that form the basis of life are indeed the same patterns acknowledged by ancient cultures. Science believed the knowledge of the mathematical formulas and sacred symbols were instrumental to most of the construction in early civilizations such as the Greek Parthenon, the great pyramids of Egypt, and the intricate temples discovered all over Central and South America.


Religion


Sacred geometry patterns consider particular geometric shapes and some geometric proportions as holy or sacred. It attributes figurative meanings to these shapes and forms, and it is connected with the belief that God is the geometer of the world.

Forms and shapes that have been traditionally in architecture, arts, and meditation since the ancient period are sacred geometry symbols. Similar forms and shapes are also in natural organisms.

It is also a worldview of pattern recognition, an intricate system of religious characters and configuration which includes time, space, and form. There are designs, patterns, and structures from the tiniest element, to the manifestation of life visible to the human eyes, to the unseen. The essential models of life are sacred.

According to this principle, the basic patterns of existence are regarded as sacred. By connecting with these, a believer reflects on the Great Design and the Great mysteries. Moreover, by studying these relationships, forms, and their connections, one will gain insight into the secrets of the Universe, as well as its laws and lore.


Geometric Patterns


We find patterns, designs, and structures in nature. These forms, without doubt, are of geometrical representation, which makes known to us the quality of each kind and its vibrancy. These patterns are also a symbol and mean that the part cannot be separated from the whole.

This underlying metaphysical principle of oneness is infused into the design of all forms in its infinite diversity. This belief in inseparability, interconnectivity, and harmony is a constant reminder of our link to the whole. We are not just an individual; we are part of a higher concept in the scheme of things.

Hence, it is like an outline for the mind to the holy foundation of all things.

Universal patterns found in the design of everything in our reality have their origin in these sacred patterns. It is in sacred art and architecture. There is a fundamental conviction that geometry and mathematical ratios, proportions, and harmonics are present in light, music, and cosmology. This value system is perceived as prevalent since the beginning of time, the social connectivity of everything in the universe.



Some examples of sacred geometry:

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 Kingïs 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 halfway up to 3-Pi (43 �� ) ratio. (More on the Geometry of the Great pyramid) 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 the 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 favor of the existence of applied sacred geometry in prehistory. (British Geodesy) (Egyptian Geodesy) (Geodesy Homepage)

The sacred mean "phi":

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 that is visible across the spectrum of the natural world. The sacred meaning is one of the defining geometric qualities of life itself, as it plays an integral part in 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 means is the spiral, commonly found in nature.

(Spirals Homepage)



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:

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'.


The Flower of Life is the modern name given to a geometrical figure composed of multiple evenly-spaced, overlapping circles. They are arranged to form a flower-like pattern with a six-fold symmetry, similar to a hexagon. The center of each circle is on the circumference of six surrounding circles of the same diameter.


The earliest confirmed example of the pattern can be seen in the Assyrian rooms of the Louvre museum in Paris. The design forms part of a gypsum or alabaster threshold step measuring 2.07 x 1.26 meters (6.8 x 4.1 feet) that originally existed in one of the palaces of King Ashurbanipal, and has been dated to c. 645 BC. (7)

The Osireion, Abydos:


There is five possible 'Flower of Life' patterns on one of the granite columns and a further five on a column opposite of the Osireion. Some are very faint and hard to distinguish. They have not been carved into the granite but been drawn in red ochre with careful precision.

Recent research suggests that these symbols can be no earlier than 535 B.C., and most probably date to the 2nd and 4th century AD, based on photographic evidence of Greek text, still to be fully deciphered, seen alongside the Flower of Life circles and the position of the circles close to the top of columns, which are over 4 meters in height. This suggests the Osireion was half-filled with sand prior to the circles being drawn which were therefore likely to have been well after the end of the Ptolemaic dynasty.

(More about Abydos and the Osireion)

The Hebrew 'Tree of Life'.


The Tree of Life is most widely recognized as a concept within the Kabbalah, which is used to understand the nature of God and the manner in which he created the world. The Kabbalists developed this concept into a full model of reality, using the tree to depict a "map" of creation. The tree of life has been called the "cosmology" of the Kabbalah.





The Flower of life and the Platonic Solids.



The 'Platonic Solids' are the names given to the five �perfect shapes� formed when dividing a sphere into three-dimensional forms, with each division having the exact same shape and angle.


The Greeks taught that these five solids were the core patterns of physical creation. Four of the solids were seen as the archetypal patterns behind the four elements (earth, air, fire, and water), while the fifth was held to be the pattern behind the life force itself, the Greeks' ether. These shapes predominated in the hundreds of carved prehistoric petrospheres found in Scotland with over 75% representing one of the Platonic Solids. They came from a time over a thousand years earlier than the Greeks. These same shapes are now realized to be intimately related to the arrangements of protons and neutrons in the elements of the periodic table.



(More About the Scottish Petrospheres)

Stonehenge and The Flower of Life.



The geometry of the 'Flower of Life' was recognized in the dimensions of Stonehenge.

Image Credits: Andrew Monkman. (The World Grid: The invisible Made Visible)

(The Geometry of Stonehenge)

Celestial Geometry :



The mathematical harmony of the universe is visible in the proportions of the planets of our own solar system as the following examples illustrate:

The diameter of the sun (864,000 miles) is the same as the perimeter of the square of the moon (4).

Sacred Venus : 'The Synodic Cycle'

The ratio of the 'Sacred mean' can also be seen in the rotations of Venus and the Earth around the sun so that for each five years that Earth rotates around the Sun, Venus manages to rotate it eight times).

Venus orbits the Sun in 224.701 Earth days ( ~.615 Earth years ), moving slightly faster than Earth. Because of the two different orbital rates of Venus and Earth, Venus must orbit the sun 2.6 times while Earth orbits 1.6 times before the two planets align. This period (583.92 Earth days) is called the Earth-Venus synodic cycle (synod means "place of meeting"). (3)



The result of this motion is that Venus 'draws' a pentagon around the sun every eight years.

Bode's law: Shows the simple mathematical relationship for the distances of the planets from our sun.

Planet Formula Distance from Sun (Millions of km) Bode's prediction Actual

Mercury 0 + 4 / 10 = 0.4 60 58

Venus 3 + 4 / 10 = 0.7 105 108

Earth 6 + 4 / 10 = Au 150 150

Mars 12 + 4 / 10 = 1.6 240 228

(Asteroid belt) 24 + 4 / 10 = 2.8 420 550(wide)

Jupiter 48 + 4 / 10 = 5.2 780 779

Saturn 96 + 4 / 10 = 10 1500 1427

Uranus 192 + 4 / 10 = 19.6 2940 2869

Neptune 384 + 4 / 10 = 38.8 5820 4496

Pluto 768 + 4 / 10 = 77.2 11580 5899

In addition to which...

Keplers 3rd Harmonic law


Kepler initially used the geometry of the Platonic solids to calculate the distances of the planets from the sun. In doing so, he attempted to revive the ancient tradition of Sacred Geometry with astronomy. Although this met with reasonable success, proving the ancient systems to be accurate, he eventually determined that the period of a planet or comets orbit is related to its distance from the sun in the following simple mathematical equation:


(p = a)


( Where p = period of revolution and a = the distance from the sun in astronomical units Au).


Kepler furthered the research of Aristotle who first realized the concept of the Harmony of the Spheres in which the planets positions and 'noise' were predicted according to musical harmonic ratios.

(Archaeoastronomy)

Sacred Geometry and the Harmony of the Spheres.



The theory of the 'Harmony of the Spheres' was originally proposed by Plato, in which he envisioned the five 'perfect' solids to be enclosed within imaginary spheres, each placed within the other. He proposed that the distances of the planets from the sun showed similar ratios from each other as the spheres surrounding each solid did. Modern science has indeed shown that planets have unique 'vibrations', or 'sounds' supporting Plato's conjecture.

(More about the Harmony of the Spheres)

Sacred Geometry in Architecture:


What Happens when geometric constants are placed into the dimensions of buildings.?

Some of the best examples of the application of sacred geometry can be seen in constructions from the ancient world. It has been shown (1), that ancient sacred and ceremonial sites were invariably built with dimensions that incorporate mathematical figures such as infinite numbers, astronomical or mathematical constants (such as Pi or the 'sacred' mean), and the use of geometry (3:4:5 Pythagorean triangle, etc). The application of 'sacred' geometry in our most important buildings is a reflection of the importance attached to it, but exactly how early was such information realized?


Following his renowned survey of over 600 English stone circles, Prof. Alexander Thom concluded that geometry had been used in their design.

Thom also proposed that common mathematical units of measurement (the megalithic yard), had been used in order to achieve these geometric results. Surprisingly as this might sound, one finds that as well as working with common units of measurement, the Neolithic people were also apparently aware of geometric constants as the following examples demonstrate.



The geometric design above was discovered by Prof A. Thom to have been used as a ground-plan for many European 'Type I' and 'Type II' flattened stone circles (Such as at Avebury, England).

(Note: Both types I and II circles show the application of the Vesica-Pisces and 3:4:5 triangles)

Sacred geometry, involving both astronomy and geometry appears to have been applied to prehistoric quadrangles. It has been shown by Thom etc, that the Quadrangles at both Stonehenge and Carnac have incorporated into them geometric constants that relate to the latitude upon which they were built.

(More about Quadrangles)

The Golden section is a ratio that has been used in sophisticated artwork and in sacred architecture from the period of ancient Egypt (1).

Freemasonry and Sacred Geometry.


Following the collapse of the Roman empire, architects versed in geometry grouped together into 'guild's', thus forming the roots of 'Freemasonry'. The tradition of building sacred/holy structures with applied sacred (euclidian), geometry was continued into the middle ages by the 'Templars', who envisioned their (mostly round) churches as 'microcosms of the world' (1). This idea was soon adopted by the Christian church, who began to employ 'sacred' dimensions into their religious buildings. These traditions were carried in the form of 'freemasonry' until, as Pennick aptly quotes - 'The lodges of freemasons closed down one by one. The last to go was the premiere lodge of Europe - Strasbourg, which shut shop in 1777. From then on, the arts and mysteries of freemasonry were carried on exclusively by 'Speculative masons' (1).

(Chartres Cathedral and Harmonic Ratios)

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...



We may never know for sure whether such geometry was identified first from the observation of natural formations, or whether it came as a result of an intellectual quest, but whichever, it is clear that these natural mathematical building blocks began to be used in the design of many important man-made structures

Conclusion:


These geometries had been a part of our rich history and monuments. I am not telling that they really are sacred but they are part of our history and should be given importance.


Sources:

  1. http://www.ancient-wisdom.com/sacredgeometry.htm

  2. https://en.wikipedia.org/wiki/Sacred_geometry

  3. https://www.themystica.com/sacred-geometry/





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