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Sacred Geometry:
The cumulative effect of sacred
geometry is the connection between the microcosm and the macrocosm.
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What Exactly 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:
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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 this fact is important in
the understanding of the significance of this geometry, and part of the
reason why it eventually became 'secret' or 'sacred'...
The modern expression 'sacred geometry' can be
easily 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.
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
even the builders of the megaliths who all 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 be aware of it.
One of
the most common shapes in nature is the circle, it is
therefore significant that all other geometric shapes can be determined from a
circle...with the use of only a compass (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 etc
etc..
A continuation of this procedure 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 natural formations, or whether it came as a result
of intellectual development, but it is clear that these natural mathematical
building blocks began to be used in the design of many important man-made
structures.
The exterior angle of the 'Great pyramid of Ghiza' 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.
Ghiza and the Sacred-mean:
The 5:8 ratio can be seen
in the layout of the three Ghiza pyramids, incidentally resulting in the
significant 30°
angle.
(Click here for more about the
geometry of the Great pyramid)
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Sacred Geometry and Music:
'If one draws at
the bow of a violin over a tuned metal plate sprinkled with light
powder (lycopodium powder is best), the grains line up in complex
patterns... It shows the direct relevance of certain geometrical
patterns'. (2)
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The Sacred mean - (5:8 or 1:1.618 or
Φ)
(The Golden Section, Golden ratio)
One of the Key-stones of sacred geometry is the 'sacred mean' or
'golden section'.
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 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).
The Golden section is a ratio which has been used in sophisticated
artwork and in sacred architecture from the period of ancient Egypt
(1).
One of the raw
mathematical products of the sacred mean is the spiral, as shown
above.
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'The golden section exists between two measurable quantities of any
kind when the ratio between the smaller and the larger one is equal to the
ratio between the sum of the two and the larger one'
(1).
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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...
Mathematically, the same proportion is generated with the following
formula:
√5+1 / 2
The ratio may also be generated from 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
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 centre of each circle is on the circumference of six
surrounding circles of the same diameter.
The Osireion,
Abydoss:
There are 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 metres in height. This suggests
the Osireion was half filled with sand prior to the circles being
drawn and therefore likely to have been well after the end of the
Ptolemaic dynasty.
(More
about Abydoss 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 mathematical harmony of
the universe is visible in the proportions of the planets of our own solar
system as the
following examples illustrate:
Sacred Venus :
The ratio of the 'Sacred mean' can also be seen in the
rotations of Venus and the Earth around the sun.
(For each five years that Earth rotates around the Sun,
Venus manages to rotate it eight times)
(584 X 5 = 2920 days)
and
(365.25 X 8 = 2920 days)
The result of this motion is that Venus
'draws' a pentagon around the
sun every eight years.
(with Venus passing between the Earth and Sun each 584
days).
Bode’s law:
Shows the simple mathematical relationship for the distances of the planets from the
our sun.
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Planet
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Formula
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Distance from Sun
(Millions of Km’s) |
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Bodes prediction |
Actual |
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Mercury
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0 + 4 / 10 = 0.4
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60
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58
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Venus
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3 + 4 / 10 = 0.7
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105
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108
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Earth
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6 + 4 / 10 = Au
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150
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150
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Mars
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12 + 4 /
10 = 1.6
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240
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228
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(Asteroid belt)
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24 + 4 /
10 = 2.8
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420
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550 wide
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Jupiter
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48 + 4 /
10 = 5.2
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780
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779
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Saturn
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96 + 4 /
10 = 10
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1500
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1427
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Uranus
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192 + 4 / 10 =
19.6
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2940
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2869
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Neptune
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384 + 4 / 10 =
38.8
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4470
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4496
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Pluto
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768 + 4 / 10 =
77.2
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11580
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5899
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In addition to
which...
Keplers 3rd Harmonic law
– Shows that the period of a planet or comets orbit is relate to its
distance from the sun in the following equally simple equation:.
(p² = a³)
( Where p
= period of revolution and a
= the distance from sun in astronomical units ‘Au’).
The diameter of the sun (864,000 miles) is the same as the perimeter of the
square of the moon (4).
(Archaeoastronomy)
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Sacred Geometry and the Megaliths: |
Following
his renowned survey of over 600 English stone circles, Prof. Alexander
Thom concluded that geometry had been used in their design.
Thom
also realised that common mathematical units of measurement (the
megalithic yard), had been used in order to achieve these geometric
results. Surprising 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 such as the sacred mean 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 type I and II circles
show the application of the Vesica-Pisces and 3:4:5 triangles)
The Application of Sacred Geometry
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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)..
What happens when a
building is constructed with sacred geometry in its proportions?
infinite numbers produce an infinite space...
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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).
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