The Fibonacci sequence
0 1 1 2 3 5 8 13 21 34 55 89 144 233
This is an exemple of a recusive sequence,obeying the simple rule that to calculate the next term one simply sums the proceeding two:
0+1=1+1=2+1=3+2=5+3=8+5=13+8=21+13=34........
This sequence is found everywhere:



Many plants produce new petals in quantities that are based on the Fibonacci numbers.

In music:
13 notes make the octave of 8 notes in a scale,of which the 1st,3rd,and 5th notes create the basic foundation of all chords,and the whole tone is 2 steps from the root note
But it gets better:
Lets look at the ratios when you take a Fibonacci number and divide it by the prvious number:
1/1=1; 2/1=2; 3/2=1,5; 5/3=1.66; 8/5=1.625; 13/8=1,615384614; 21/13=1.1619047619; 34/21=1,617647059
You will see that te ratios converge towards 1,6180339887 otherwise known as Phi or
The golden ratio

Not only is the golden ratio everywherre it is also associated with how we perceive beauty:
The features of Jessica's simpson face are proportionatly placed according to the golden ratio.
This mask of the human face is based on the Golden Ratio. The proportions of the length of the nose, the position of the eyes and the length of the chin, all conform to some aspect of the golden ratio

When placed over the photo of Jessica Simpson, we see there is a good fit (that is, the proportions of her face fit the geometrically "nice" proportions of the mask, based on the Golden Ratio).

In the solar system
The average of the mean orbital distance of each succesive planet expressed in relation to the one before it is approximates phi

In music and acoustics

Fibonacci and phi are used in the design of violins and even in the design of high quality speaker wire
It is believed the Greeks used Golden Section to achieve the wonderful sound and "ideal acoustics" that Golden Proportion rooms have. Many cathedrals also use the Golden Section, in part, for the same reason. The Golden Section not only minimizes acoustic resonance, it also imparts a very musical quality to the remaining sound.
Phi and Fibonacci numbers are used in technical analysis of stock charts,but I'll spare you that one.