Truth, Computing and Fail

I had my computer programming in C++ lab test this saturday (i.e. 24th) and there is no doubt about the fact that this test forced me to look at programming in a more serious way than I am used to. But then again, it was a great learning experience. So much so that the night before the test, I spent hours reading up on the Fibonacci numbers. Not that I needed to read that much to generate the sequence, but I found it interesting as I started digging deeper into it.

The Fibonacci sequence as some of us might be knowing consists of the numbers
1,1,2,3,5,8,13,21… and so on

The nth term of the sequence is of the form:

t_n=t_{n-1}+t_{n-2}

If I recall correctly, this sequence came to enter the layman’s lexicon with the wildly popular novel by Dan Brown: Da Vinci Code.

Without trying to pretend that I know quite a lot, I would advise you to rather head to Mathworld’s entry on this topic. These things are better left to specialists!

The sequence of Fibonacci numbers is present all throughout the nature and the Universe. This only adds to its mysterious nature.

Now coming back to Da Vinci Code, if you may remember Robert Langdon mentioning something about the ‘Golden Ratio’, also denoted as

\phi

(Phi). This golden ratio is also ubiquitous in nature occuring at the strangest of places like in the pyramids of Giza in Egypt, the Parthenon at Athens and even in the human anatomy. Again head to its Mathworld entry if you want to know more.

This Golden ratio is also linked to Fibonacci numbers, both present in abundance in nature and universe’s creations.

It is related by an infinite series involving the Fibonacci numbers:

\phi=1+\sum_{n=1}^\infty\frac{(-1)^{n+1}}{F_n F_{n+1}}