Fibonacci (pronounced fib-on-arch-ee) was an Italian mathematician who lived from 1175 to 1250. He was instrumental in bringing the Arabic numbering system to Europe. Up until his time Europe still used the Roman numeral system. There are many websites dedicated to Fibonacci if you would like to find out more about him.
The Fibonacci Series is a string of numbers with a particular relationship. The best way to describe the relationship is with an example.
1. 17
2. 84
3. 101
4. 185
5. 286
6. 471
7. 757 * 11 = 8327
8. 1228
9. 1985
10. 3213
_____
Total 8327
Add the first two numbers together to get the third number. Add the 2nd number to the 3rd to get the 4th, add the 3rd to the 4th to get the 5th. Continue in this way until you have ten numbers and then sum them to arrive at a total.
What makes this interesting is the fact that when the number in position 7 is multiplied by 11 it always equals the sum of all ten numbers. We can use this to build a software installation key.
This is also an excellent introduction to recursion. The formula is simple enough to follow but very powerful thanks to recursion.
Fibonacci (seed1;seed2;iterations)
// This function dramatically demonstrates the power of recursion. The function itself is very simple but it can produce spectacular results.
If ( iterations > 0 ;
seed1 + seed2 & "¶" & Fibonacci ( seed2; seed1 + seed2; iterations - 1);
""
)