About Fibinacci Numbers

Discovered a few new facts about Fibonacci numbers. All I knew about Fibonacci numbers what that it is the sequence 1,1,2,3,5,8,13,21.... , where the nth number was the sum of the (n-1)th and (n-2)the Fibonacci number. Well, I have always wondered what makes these numbers special. Turns out the nth Fibonacci number can be defined as the number of ways n can be represented as a sum of 1's and 2's. That gives a combinatorial interpretation to the Fibonacci numbers, and raises them from being outcomes of a mere uninteresting addition process. I got to know about this fact during a fascinating talk at IIT, Bombay by Prof. Manjul Bhargava from Princeton. (More about that talk later).

And that's not all about the Fibonacci numbers. It turns out that any number can be represented as the sum of Fibonacci numbers. That means Fibonacci numbers can serve as a base system. However, there could be more than one way of representing the same number as a sum pf Fibonacci number. Check this to know more.

To finish this post, Fibonacci numbers were first described by the Indian linguist Hemachandra about a 100 years before Fibonacci described them and probably by Pingala in 200 B.C. too.