18.5 Example Using Recursion: Fibonacci Series
The Fibonacci series,
0, 1, 1, 2, 3, 5, 8, 13, 21, ...
begins with 0 and 1 and has the property that each subsequent Fibonacci number is the sum of the previous two. This series occurs in nature and describes a form of spiral. The ratio of successive Fibonacci numbers converges on a constant value of 1.618..., a number that has been called the golden ratio or the golden mean. Humans tend to find the golden mean aesthetically pleasing. Architects often design windows, rooms and buildings whose length and width are in the ratio of the golden mean. Postcards are often designed with a golden-mean length-to-width ratio.
The Fibonacci series may be defined recursively as follows:
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