On Fri, 7 Jul 2006, padawan12 wrote:
Mathieu Bouchard wrote:
This is because if a is the golden section and b=-1/a, then: Fib(n) = (a^n - b^n)/(a-b) so: Fib(n+1)/Fib(n) = (a^(n+1) - b^(n+1))/(a^n - b^n)
I found a closed ofrm of fib which goes fib(n) = (phi^n - (1-phi)^n)/sqrt(5)
That's the same, cause a=phi, b=-1/a=1-a, a-b=sqrt(5)
It seems to be with the second numerator term, the Pd [pow] doesn't like non integer negatives.
It's not well-defined to compute a negative number to a non-integer power. "Not well-defined" means that there are several possible answers, or no answer, or even both (depending on the way of looking at it).
(1-phi)^n for even n is a positive value.
(1-phi)^n for odd n is a negative value.
(1-phi)^n for noninteger n would be a value for which the sign is unknown, but for which you know the absolute value. In another way, it can be argued that it should be a complex number, and in yet another way it can be argued that it can be a set of complex numbers.
If any other object actually gives an answer for that, I can't guarantee that your results will make sense.
_ _ __ ___ _____ ________ _____________ _____________________ ... | Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju | Freelance Digital Arts Engineer, Montréal QC Canada