Leonardo Fibonacci (1175 AD), a great mathematician of the Middle Ages discovered the Fibonacci sequence by studying nature. He studied the growth of rabbit populations and the growth of leaves and petals and discovered a well-defined mathematical sequence in all of this.
This is the Fibonacci sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 …………etc.
number in the sequence is the sum of the two preceding numbers starting
with the root number 1.
1+2=3, 2+3=5, 3+5=8, 5+8=13, ……...
Fibonacci sequence progresses towards the Golden Mean if we
divide two successive numbers in the sequence.
The Fibonacci sequence propagates towards Phi (Ø) but never reaches it since it is an irrational or transcendent number.
Fibonacci spirals and Golden Mean ratios appear everywhere in the universe. The spiral is the natural flow form of water when it is going down the drain. It is also the natural flow form of air in tornados and hurricanes. Here’s another beautiful example of a Fibonacci spiral in nature, it’s the Nautilus shell and every book about sacred geometry contains one:
The Golden Mean ratio is all over the human body, in the ratios between the bones, the length of your arms and legs. The Golden Mean is also the ratio in the distance from the navel to your toe and the distance from your navel to the top of your head. Michelangelo has beautifully hidden these Golden Mean ratios in his fresco on the ceiling of the Sistine Chapel in Rome:
and the Phi ratios in the human hand
Now here’s an interesting drawing from Leonardo Da Vinci. What he is showing in this sketch is that the human body ‘squares the circle’. When man stretches his arms and holds them horizontally, man’s body will perfectly fit into the square. On the other hand, when he spreads his legs and raises his arms as in the sketch, man’s body can be perfectly circumscribed by a circle. The circumference of the square ‘equals’ that of the circle.
A lot has been written about this sketch alone, it contains a whole lot of hidden sacred geometry. We will not go into all the details here, but I want to show you some very amazing things. Ancient wisdom, the Hermetic tradition tells us that the human body can be regarded as a blueprint for the universe by means of all the ratios that are found within the body. This may indeed be true. Let’s have a look at the following picture:
This is the same picture as above, in the picture there are now two red circles added. The biggest red circle fits perfectly and is inscribed by the square. The smaller red circle’s is centered between the outer circle and the inner red circle and tangentially touches both.
our surprise, the upper red circle represents the moon and the lower red
circle represents the Earth! In mathematical terms: The ratio of the
diameter of the smaller red circle to the bigger red circle r / R equals
the ratio of the diameter of the moon to the diameter of the Earth! Now let’s prove it:
of the moon : r
Now ‘squaring the circle’ makes the perimeter of the square equal to the circle:
8 R = 2 p ( r + R )
8 R - 2 p R = 2 p r
R (8 – 2 p) = 2 p r
r / R = (8 – 2 p) / 2 p = (4 – p) / p
radius = 6,370,973 m
Quod Erat Demonstrandum!
There is another mysterious relation to be discovered in the sketch of the Vitruvian man by Leonardo Da Vinci. The Great Pyramid at the Giza plateau in Egypt called after the pharaoh that is supposedly buried there named Khufu (Cheops in Greek), holds a perfect geometrical relation to the squaring of the circle and the Vitruvian man as depicted by Leonardo Da Vinci!
Look at the picture below:
Great Piramid at Giza in relation to Vitruvius man
triangle in the picture is the exact geometrical proportion of the Great
Pyramid at the Giza Plateau near Cairo, Egypt. The angles between the base
and the apex (top) of the pyramid are exactly 51 degrees and 51 seconds.
The point I want to make here is that the Egyptians were aware of the art of sacred geometry and how it relates to the universe, as the Giza plateau and in particular the Great Pyramid proves.
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Monday, November 02, 2009