Visual Basic.NET How to Program (PDF)

Chapter 6 Procedures 221
40
41 End Function ' Factorial
42
43 End Class ' FrmFactorial
Fig. Fig. 6.19 6.19 Recursive factorial program (part 2 of 2).
Common Programming Error 6.8
Forgetting to return a value from a recursive procedure can result in logic errors. 6.8
Common Programming Error 6.9
Omitting the base case or writing the recursive step so that it does not converge on the base
case will cause infinite recursion, eventually exhausting memory. This is analogous to the
problem of an infinite loop in an iterative (nonrecursive) solution. 6.9
6.15 Example Using Recursion: Fibonacci Series
The Fibonacci series
0, 1, 1, 2, 3, 5, 8, 13, 21, …
begins with 0 and 1 and defines each subsequent Fibonacci number as 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 near 1.618. This number
occurs repeatedly 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 so that their ratios of length to width are equal to the golden
mean. Similarly, postcards often are designed with a golden-mean width-to-height ratio.