Fibonacci

Nature contains many patterns. Fibonacci numbers are a fascinating sequence. This sequence models and predicts financial markets and natural phenomena.

Computational methods

We can compute Fibonacci numbers in C# code with recursion. This approach can be slow. It is also possible to use iteration.

Input and output

To begin, we should review the sequence of numbers itself. When we design our program, we can test against these values.

Numbers:
0, 1, 1, 2, 3, 5, 8, 13...

An example

This is an iterative method. Conceptually, an iterative Fibonacci method stores the result of the previous Fibonacci number before computing the next one.

Note To compute a Fibonacci number at a certain position N, we have to loop through all previous numbers starting at position 0.

Tip If you just want to list Fibonacci numbers, you could change Fibonacci() to simply use Console.WriteLine.

And This would make the method print out each number as it is computed, which would reduce the total amount of computation required.

using System;

class Program
{
    public static int Fibonacci(int n)
    {
        int a = 0;
        int b = 1;
        // In N steps, compute Fibonacci sequence iteratively.
        for (int i = 0; i < n; i++)
        {
            int temp = a;
            a = b;
            b = temp + b;
        }
        return a;
    }

    static void Main()
    {
        for (int i = 0; i < 15; i++)
        {
            Console.WriteLine(Fibonacci(i));
        }
    }
}0
1
1
2
3
5
8
13
21
34
55
89
144
233
377

Problem, overflow

One problem with this implementation is that the int types will overflow past the 47th Fibonacci number. It cannot be used on large numbers.

Tip To solve this problem, you can change Fibonacci() to return double. Also change a, b, and temp to be of type double.

Discussion

The Fibonacci sequence begins with zero. Fibonacci himself, in 1202, began it with 1, but modern scientists just use his name, not his version of the sequence.

Tip I tested the output of the program and it is correct. I usually try to post correct code.

A summary

Fibonacci numbers are a useful pattern. But they also teach us about programming. By storing the previous value in a local variable, we avoid computational work.