6.20. 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 Fibonacci numbers.
The series occurs in nature and, in particular, describes a form of spiral. The ratio of successive Fibonacci numbers converges on a constant value of 1.618.... This number frequently occurs in nature and 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/width ratio.