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THE
GOLDEN MEAN SPIRAL: |
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This crop
circle shape known as the "Hackpen Hill
Formation" appeared in an English wheat
fielding 1999. It's structure represents
two well known sacred geometry shapes: the
golden mean (phi) spiral and fibonacci
spiral. Both of these two spirals
represent the Christ nsciousness grid of
the human race that had been destroyed
some 13000 years ago; this event caused
future generations to perceive reality
through low consciousness levels thus
creating fear and chaos. |
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On the third
dimension the grid looks like two spirals
(if all the major ancient monuments upon
this planet were to be connected we would
discover the beginning of the spirals in
Egypt). On the fourth dimension the grid
resembles a combination of two Platonic
Solids-the dodecahedron and the
icosahedrons. the golden mean spiral can
be found in another constant
proportion incorporated into the Pyramid
of giza which is that of phi, the golden
mean. Phi is a constant value which is
even more mysterious and profound in its
implications than pi. Like pi, phi is a
number with no arithmetical solution. The
decimals just keep on going into infinity
without ever repeating themselves. The
unique thing about this number is that it
can be found incorporated in all known
organic structures. From the bone
structure of human beings to the seed
pattern of a sunflower to the spiral of a
sea shell, the phi proportion is there,
underlying all biological structure,
seeming to be a geometrical blueprint for
life itself. Plato went so far as to call
the phi ratio the "key to the physics of
the cosmos."
Phi is calculated at 1.6180339+..., and
while it cannot be worked out
arithmetically, it can be easily obtained
with a compass and straightedge. Two
simple ways of finding the Golden Section
geometrically are as follows: If you take
two equal squares, side by side, (a 1x2
rectangle,) divide one of the squares in
half, and with a compass, swing the
diagonal down to the base of the other
square, the point where the diagonal
touches the base will be phi, or
1.6180339+, in relation to the side of the
square, which is 1. ( This formula also
describes exactly the rectangular floor of
the King's Chamber.) The other simple
method of determining the Golden Section
is by dividing a line segment , AB, at a
point, C, in such a way that the whole
line is longer than the first part in the
same proportion as the first part is
longer than the remainder. AB/AC = AC/CB =
1.6180339. ( Notice the fractal and
holographic nature of this ratio...) The
phi ratio is found in the architecture of
the Great Pyramid in the triangle formed
by the height, half-base, and the apothem,
or diagonal. In other words, the basic
cross-section of the structure
demonstrates the Golden Section. If the
half-base is given a value of 1,this gives
the value of phi for the apothem, and the
square root of phi for the height. The
Golden Section shows up again and again in
Giza, and in much more baffling and
terious ways. (Entire volumes have been
written on the geometries involved in the
pyramids' construction, we're just
covering a few of the basics here.) There
is a number sequence, known as the
Fibonacci Sequence, which bears a special
relationship to phi, and to the pyramids
at Giza. First postulated by the medieval
mathematician Leonardo Fibonacci, this
sequence was used to describe the growth
patterns of plants. It goes:
1,1,2,3,5,8,13,21,34,55,89,144,233, etc.
It is made by adding the last two numbers
of the sequence to get the next one, like
so: 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13,
etc. This sequence's relationship to phi
is that if you divide one term of the
sequence into the next one, he result
begins to quickly approach the
transcendental number 1.6180339+... (I
won't make you do the math. Just watch...)
1/1=1 2\1=2 3\2=1.5 5\3=1.66 13/8=1.625
21/13=1.615 34\21=1.619 55\34=1.617
89\55=1.6181
The further you go down the sequence, the
closer you get to phi. Of course, you can
never actually get to it exactly, since it
has no mathematical solution, it just
keeps getting closer and closer, ad
infinitum. Anyway, the sequence can be
graphed out in the form of a spiral,
called the Fibonacci Spiral. This spiral
is almost identical to the graph of the
logarithmic spiral of the phi ratio, known
as the Golden Mean Spiral. (The difference
is that the Fibonacci spiral is a
whole-number interpretation of the
arithmetically impossible Golden Mean
spiral, which has no beginning or end. The
Fibonacci spiral has a definite
beginning.) click on image for better
view.
Aerial photographs show that the pyramids
at Giza are positioned in such a way that
they fall on a line which accurately
defines a Fibonacci spiral. The spiral
passes exactly through the centers of each
pyramid.
Source: Golden Spiral
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