fibonacci everywhere ?

Well, I have come across this sequence before in csc148 where I wrote a program to calculate Fib(n). As to its applications, I would really be interested to know more about that. I mean sooner or later theory must show where it is applied. This sequence and its sum F(n+2) - 1 is more interesting to work with as it is less linear and thereby more challenging.

It was valuable to see the re-arrangement of the function in the definition of the function without changing the overall result. Makes me look at things with a different perspective in mind when trying to tackle a proof. Though not evident at first because of the procedural thinking that we are taught by, it soon becomes another method of approach.

Maybe we should think differently and instead of coming up with solutions in a procedural form try using some simple algorithm whose logic derives the very essence of what we are trying to prove. Perhaps then we would not need to make bulky and highly inefficient applications. There is a limit as to how much you can optimize a procedure. Although some people look at algorithms as procedures in mathematical terms and therefor see no difference.