Fibonacci Sequence

The Golden Ratio and the Fibonacci Sequence

Fibonacci Sequence: F(1)=1, F(2)=1, F(n)=F(n-1)+F(n-2)
The Golden Ratio is a number which is equal to its own reciprical plus one.
The square of the Golden Ratio is equal to itself plus one.
Golden Ratio = 1.618033989...
Ratio of Fibonacci Sequence Numbers F(n)/F(n-1) underneath:
1 1 2 3 5 8 13 21 34 55
\/ \/ \/ \/ \/ \/ \/ \/ \/
1 2 1.5 1.66 1.6 1.625 1.61538 1.619047 1.617647
As shown right above, the ratio of the Fibonacci numbers approaches that of the golden ratio as the Fibonacci Sequence continues.

Java applet only works with Internet Explorer or Netscape 6 and newer.
Fibonacci.java