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Two significant sacred geometry designs, the Fibonacci spiral and the golden mean (phi) spiral are combined to create the Golden Spiral pattern.
PHI – The Geometric Blueprint for Life
Because the digits utterly go on forever without reoccurring, there is no mathematical solution to Phi. The unique thing about this number is that it can be found incorporated in all known organic structures. The universal design of the golden mean seems to be a geometrical blueprint for life itself. Phi can be seen in all biological configurations such as the seed pattern of a sunflower, the spiral pattern of a sea shell, the proportions of human and animal skeletons, and in the patterns of certain types of cactus plants. This value was known by Plato as being “the key to the physics of the cosmos.” Phi is approximately 1.6180339+…, yet it’s entire sequence cannot be worked out arithmetically, Phi can be easily obtained with a compass and straightedge.
How to Determine the Golden Mean
The Golden Section can be found in two fairly straightforward ways:
Method one: If you take two equal squares, side by side, (a 1×2 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).
Method two: The other 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 being longer than the remainder. AB/AC = AC/CB = 1.6180339 (notice the fractal and holographic nature of this ratio…).
The Golden Mean in Art and Architecture
The Golden Mean number can often be found in many forms of art, in symbols of religion, and in architecture. The golden mean is usually seen in the paintings of Da Vinci and Kandinsky. Frank Lloyd Wright designed the Guggenheim Museum like a shell. Whatever exhibits the golden mean measurements, whether it be a face, a work of art or a building, people will tend to find it quite elegant. “Whoever cultivates the golden mean, avoids both the poverty of a hovel and the envy of a palace.” –Ancient Roman poet
The Phi ratio can be recognized in the composition of the Great Pyramid in the triangle created by the height, half-base, and the apothem, or diagonal. The Golden Section can be found in the main cross-section of the structure. 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 can be found to show up repeatedly in Giza and in much more mysterious and exhausting ways. There are many publications (entire volumes of diagrams and written material) available regarding the geometries involved in the pyramid’s construction. In addition to the above proportional relationships, photographs from the air reveal that each of the center points of the pyramids at Giza precisely line up in a way that defines a Fibonacci spiral.
How the Fibonacci Sequence Relates to Phi, the Proportion of the Golden Spiral
The Fibonacci sequence is a progression of numbers that have a highly relevant correlation with Phi. Leonardo Fibonacci (1170-1250), an Italian mathematician from the Middle Ages, first discovered this progression while trying to understand the growth patterns of plants. This progression is: 1,1,2,3,5,8,13,21,34,55,89,144,233, etc., which is created by combining the previous two figures of the progression to get the succeeding number, for example: 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, etc.
How does this progression of numbers relate to Phi? By dividing the next number with the previous number, and the further down along the succession one gets, one arrives closer and closer to the hypothetical number of Phi which is best described as: “1.6180339+…” For example: 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 … Phi, or “1.6180339+…” can never be arrived at exactly, because it cannot be solved mathematically, instead it only approaches closer and closer to an infinite sequence of numbers looking more and more like this: “1.6180339887498948482045868343656381177203091798057+…” Go here to see what Phi looks like at 2000 decimal places and here for 10,000 decimal places at the Golden Section ratio: Phi website.
The Fibonacci Spiral is a graph of the Fibonacci procession of numbers in the shape of a spiral. This spiral is nearly the same as the diagram of the logarithmic spiral of the Phi ratio, or the Golden Mean Spiral. The Fibonacci spiral is based on a whole number equivalent of the arithmetically impossible Golden Mean spiral, which has no start or finish, while the the Fibonacci spiral has an obvious beginning.
Sacred geometry illustrates the unity of life in our world like no other field of study can. The sacred geometry symbol, Flower of Life, for instance, adorned churches, cathedrals, temples and pyramids for centuries with its amazing beauty, while bridging all manner of religions, cultures and times. There seems to be something deeply natural, spiritual and aesthetically pleasing about the Flower of Life, for example. From both a mystical and analytical direction of approach, the concepts of sacred geometry have always been quite fascinating. This subject is ancient, vast and versatile. Nearly all classic artwork and architecture is based on it. Sacred geometry can be either taught for scientific reasons or enjoyed for its mystical and spiritual enrichment.
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