T  H  E    G  O  L  D  E  N    R  A  T  I  O

and the Fibonacci series of numbers


The Fibonacci series of numbers is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...

Each number after the first two is the sum of the previous two.



Sets of adjacent numbers in the Fibonacci series can be applied to the sides of rectangles
to compare their proportions.

1/1=1
2/1=2
3/2=1.5
5/3=1.66666666666...
8/5=1.6
13/8=1.625
21/13=1.61538446154...
34/21=1.619047619...
55/34=1.6176470588...
89/55=1.6181818182...
144/89=1.6179775281...
233/144=1.6180555556...
377/233=1.6180555556...
610/377=1.6180371353...
987/610=1.6180327869...
1597/987=1.6180344478...


As the numbers get larger, the ratio between adjacent numbers approaches the value called phi (
f) which is equal to 1.618033989...
This is also referred to as the Golden Ratio.



x
And this is a golden rectangle.   x / y = 1.618033989...
And, coincidentally, y / x = 0.618033989...
It's easy to construct from a square.
 
y