Symbol of Harmony and Beauty

Golden spiral - Gold |
Golden spiral - Silver |

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.

Method one

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).

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...).

Whoever cultivates the golden
mean,

avoids both the poverty of a hovel and the envy of a palace.

(Ancient Roman poet)

avoids both the poverty of a hovel and the envy of a palace.

(Ancient Roman poet)

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, as in: 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, the 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, to infinity.

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).

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