locrian at gmail.com
Fri Mar 12 16:25:21 EST 2010
i was just talking about "fibonacci day" with a friend a couple days ago, but phi day makes more sense.
> 0.6180340 is an *inverse* ratio and not the actual ratio of phi which is 1.61803399
> and hence is NOT the number the fibonacci series converges to
sorry to make my first post on the list a correction, but i just wanted to clarify that a fibonacci sequence (0, 1, 1, 2, 3, 5 ... and also any sequence: m, n, m+n, m+2n ... ) does not converge. convergence of a sequence mean that the limit as n approaches infinity of x(n) = some finite value.
the sequence of numbers that are the ratio between a number in the fibonacci sequence and the previous number converges to phi (1.618..). of course, this means that the sequence of numbers that are the ratio between a number in the fibonacci sequence and the *next* number (the inverse ratio) converges to the reciprocal of phi or 1/phi (0.618).
. . . hopefully i'm getting all the terms correct, although i'm not sure. anyway, i think this is clearer.
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