1 Jul
2006
1 Jul
'06
2:40 a.m.
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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