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Sacred geometry:
(geometry
- earthly measurements)
The
cumulative effect of sacred geometry is the connection
between the microcosm and the macrocosm.
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(Scroll down for more)
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What is 'Sacred
Geometry'...?
The synchronicity of the universe is greatly 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 geometry was an important factor in the design of
the pyramid.
(Click here for more about the
geometry of the Great pyramid)
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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
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).
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.
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Celestial
geometry - The 'Harmony of the Spheres'..
The mathematical harmony of
the universe is visible in the proportions of the planets of our own solar
system as the
following examples illustrate:
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).
(Ancient astronomers)
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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.
He even found evidence that
certain
spirals had been drawn with a constant measurement which he termed
the 'megalithic inch'.
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
.
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 triangle)..
What happens when a
building is constructed with sacred geometry in its proportions?
infinite numbers produce an infinite space...
endows the structure with universal proportions...more at
ease with the surroundings...
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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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