Ø - Phi — 1.618:1 — the Phi Rectangle
The Golden Section, phi, 1.618:
In the Beginning was the One. In order to observe itself, it cut part of itself away to make 'Other'. This Golden Section is in beautiful proportion.
As the subdividing continued away from the One, they continued in this phi ratio. This can be used to go back to the One as well. It is in this sense that three is farther away from the One than two is.
Have you ever noticed that it is easier mathematically to go away from One than to go towards it? In other words, it is easier to add and multiply than it is to subtract and divide.
3:5 : : 5:8. This ratio indicates that it is part of this series: 1 • 2 • 3 • 5 • 8 • 13 • 21 • 34 • 55 • 89, and so on. This is called the Fibonacci Series. Start anywhere in the series, add the number below, and you get the next number (for example, 21 + 13 = 34).
As one ascends up the series, any number in the series, when divided into the next one up, gets closer and closer to (but never hits exactly) 1.618, phi, the Golden Section.
|On a line create square (ABCD) where AB = 1.|
|Divide lines (AD) and (BC) in half at (F) and (E). (BC) = 1, (EC) = .5.
Double square (ECDF) is thus created with a diagonal of (ED).
Using (ED) as a radius swing arc from (D) downwards to intersect the initial base line at (G).
Extend line (AFD), and create a perpendicular to line (BECG) at (G) so that it intersects line (AFD) at (H), thus creating phi rectangle (ABGH).
The formula that shows this is:
(BE) = 1/2. (ED) = 5/2 .5 + 1.118 = 1.618
Phi and the Square Root of Five:
|Extend arc (DG) through (A) to (I). Note the clear relationship between phi and the square root of five.|
Solomon's Temple also contains phi. The Vestibule (DCBA) measures twelve cubits by twenty cubits. 12 to 20 can be reduced to 6 to 10 and further to 3 to 5. Three and five are two numbers in the fibonacci series. 3/5 = 1.6, a close approximation to 1.618, or phi (Ø).
There is also a solid astronomical alignment to the Equinox Sunrise for this chamber as well.
Designed by Phidias, the Parthenon is the Queen of Greek Temples, and personifies their interest in Sacred Geometry. If the height of the Parthenon is 1, its width is phi (Ø) 1.618, and its length is 2.236 (√5). You can see this relationship more clearly at the bottom of the preceding page.
1.618 (phi or ø) + .618 = 2.236 (√5). So there is a clear relationship between phi (ø), and the square root of five (5).
These are the 5 sacred geometrical ratios - pi (π), (√2),(√3),(√5) and phi (ø). They are found in sacred spaces all over the world.
Remember, sacred geometry is basically simple, AND you must do it with your hands, if you want to really gnow sacred geometry. (Western Man's left brain got the best of him, and so, unfortunately, the closer we get to the present, the more complicated it gets - but it should be basically simple!)