[PD] converting decimal to binary

Mathieu Bouchard matju at artengine.ca
Sat Jul 1 02:40:56 CEST 2006


On Thu, 29 Jun 2006, Federico wrote:

> and also: if you divide any fib number by its preceeding number, you get
> the "magic" number (the one of Pitagora's sectio aurea)
> (this works better with numbers > 100)

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)

and because |b|<1, b^n converges towards zero, so:

   lim n->infinity Fib(n+1)/Fib(n)
      = lim n->infinity a^(n+1)/a^n
      = a

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| Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
| Freelance Digital Arts Engineer, Montréal QC Canada


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