golden rectangle

[fathomthepower]

actually, the golden rectangle is constructed as follows:

draw a square of any dimension. from any corner of the square, draw an arc starting from the opposite corner from the center of the arc. where this arc intersects with the line paralell to the original point of the arc, this is the longer side of the rectangle.

it turns out, when this is rectange is constructed, there exists an interesting ratio between the length and width of the rectangle. this ratio is called the PHI ratio. there are many instances of this ratio found in nature, particularly related to growth of organisms from the microscopic level to animals such as ourselves to giant redwoods--some of the largest living organisms in the planet.

the PHI ratio, as it turns out, sets up a system of proportions that governs the size of cells and their interations with other cells. these proportions are also the same proportions that govern the ratios found in: you guessed it--the SPIRAL

if this in incomprehensible, it could be because i'm a little buzzed right now, but i just wanted to throw in my two cents.

...keep going...

[Roona-Spism]

Cool, I love hearing about PHI its so interesting, to square it you can just add 1! WEIRD!!! PHI^2 = PHI + 1. The first I heard of this ratio was on a show hosted by John Cleese and Liz Hurley. It was on the human face. On the show a plastic sugeron used this ratio to construct "The Perfect Face" for which he modeled all his surgery on. I wonder if there is a guitar chord which is based around this ratio?

[jpmanson]

all we need now is someone to mention the fibonacci sequence..

[Roona-Spism]

What has the fibonacci sequence got to do with it? PHI is (1 + 5^1/2) / 2. Where as fibonacci is just the last number plus the next number. I don't understand?

[jpmanson]

if the fibanacci sequence were a function, say f(x) then

f(x) = 1/5^(1/2) * ((phi)^x - (1-phi)^x)

[eek]

What has the fibonacci sequence got to do with it? PHI is (1 + 5^1/2) / 2. Where as fibonacci is just the last number plus the next number. I don't understand?

It works like this:
The relation of the numbers of the Fibonacci sequence is the same as the ratio of the sides of the golden section rectangle to each other. The subtraction of the square (or if you like to do it the other way - the foundation of the square) yeilds ever more golden sections.

Still don't get it? It's beautifully illustrated here:
http://textism.com/bucket/fib.html

Drawing a golden rectangle (as mentioned above) illustrated:
http://textism.com/bucket/fibsquare.html