Problem of the Week: Fibonacci Numbers

Leonardo Fibonacci

Leonardo Fibonacci was born in Italy way back in 1170. When Fibonacci began using numbers he used numbers just like everyone else in Italy at the time: III + IV = ???. Infact he was one of the first people in Europe to say, "hey there must be an easier way!"

As a young man he helped his father, a merchant, with the family business. As a merchant, Fibonacci travelled to Africa where he learned 3+4=7. It was the first time he encountered Arabic numbers. He loved them so much that he wrote a book to tell all of the Italy about the new numerical system.

Here's one of the first patterns he came up with:

0,1,1,2,3,5,8,13,21,34

Continue the pattern. What do you notice? How does it increase? Does it relate to Pascal's Triangle? Does it have a real world application?