Just a slight correction........
The RATIO is 1:1.618. It is NOT the NUMBER 1.618.
The RATIO is often called the Golden Mean and it is found both Geometrically (The diagonal of 1/2 a square added to the square), and mathematically as Zargon has demonstrated. This mathematical progression is called the Fibonacci Series after the Latin mathematician who discovered it. It works by adding the 2 preceeding numbers to obtain the next in the series and if you move far enough into the series (55/89) you get 1:1.618.
The RATIO is 1:1.618. It is NOT the NUMBER 1.618.
The RATIO is often called the Golden Mean and it is found both Geometrically (The diagonal of 1/2 a square added to the square), and mathematically as Zargon has demonstrated. This mathematical progression is called the Fibonacci Series after the Latin mathematician who discovered it. It works by adding the 2 preceeding numbers to obtain the next in the series and if you move far enough into the series (55/89) you get 1:1.618.