Hi Jim & all

> And how does even this calculation leave one with Phi?
> x / y ~ 1.618...?

The way I understand it...

The golden mean 'tends to' 1.6180

1/1 = 1
2/1 = 2
3/2 = 1.5
5/3 = 1.6666...
8/5 = 1.6
13/8 = 1.625
21/13 = 1.61538...
34/21 = 1.61904...
and so on, with each addition coming ever closer to multiplying by some
as-yet-undetermined number.


The number that this ratio is oscillating around is phi
(1.6180339887499...).

In the case of large numbers of generations having already passed then the
number of parents in the family tree of drones and the number of parents in
the family tree of the workers in that colony is Phi because drones are one
step back in the sequence due to not having a father.


Best Regards & 73s, Dave Cushman... G8MZY
Beekeeping & Bee Breeding Website
Email: [log in to unmask] or  [log in to unmask]
http://website.lineone.net/~dave.cushman & http://www.dave-cushman.net

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