The Golden Ratio

References:

• Golden Ratio at the WikiPedia.

Two quantities are in their golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities:

(a + b)   a    (1 + sqrt(5))
------- = - =  -------------
   a      b         2

The Golden Ratio a.k.a. Phi is about 1.618. Phi is derived from the Fibonacci sequence:

1, 1, 2, 3, 5, 8, 13, 21, 34 ...

Each number in it is the sum of the preceding two numbers:

1+1=2, 2+1=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21, 13+21=34 ...

The quotients of successive adjacent terms:

2  3  5  8      34
-, -, -, -, ... --
1  2  3  5      21

converge on Phi as you get further out.