Saturday, 28 February 2009

The Curious Sequence

A few days ago during my mathematical investigations, I discovered something of an anomaly. 

A normal Arithmetic or Geometric progression can be accurately represented by a formula which can be used to find the (n)th term of that progression. In this particular situation, I was working on the Fibonacci Sequence in which each term is the  sum of the previous two numbers.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 .......................................

Now I thought it was a normal geometric progression and applied the formula to find out the (n)th term. First I divided successive terms to find a definite ratio between the numbers. To my surprise, there was none. I then tried to find the formula  thinking that it was an arithmetic progression. I tried to find the difference between the terms, and to my utter surprise found that each time I tried to find the constant difference between, a new Fibonacci Sequence is formed. Amazing, isn't it? 


rgdinmalaysia said...

You should tell someone abpout this....Seriously, you may have discovered something important.

They can call it the NARAYAN ANAMOLY.

Discoveries of import don't just come from labs and PHD's.

Ashwin said...

No mr. Raj, I did a bit of research on it in the internet. Tis anomaly has been discovered before by many mathematicians. They've even developed a formula to get the (n)th term of the Fibonacci sequance using the ratio Phi(1.618....) and the surds. It is just that I discovered the anomaly Independently not knowing that it has already been discovered.