Fibonacci Sequence
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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
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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.