Hi Jim & all

Jim said (refering to the ratio of worker's and drone's parents)

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

Providentially my February copy of AN BEACHAIRE (the Irish Beekeeper) popped
through my letterbox.

Pages 38 and 39 have a dissertation on the subject...

Titled
   BEES AND MATHEMATICS
DENIS J MORGAN C.F.L. NAT CERT SC. (APIC)
           CO DUBLIN B.K.A,

Fibonacci has given his name to the sequence of
numbers 1, 1, 2, 3, 5, 8, 13, 21, 34... 144, 233...

He invented the sequence when investigating a problem about the
growth of a population of rabbits.

each number is the sum of the two previous numbers. It is a
recursive sequence where the first two values are 1 and each successive
term is obtained by adding together the two previous terms. Thus, the
sequence begins 1, 1, 2, 3, 5, 8, .. that is 1+1=2, then 1+2-3,
then 2+3=5 etc.

Number of                            Drones       Workers
Parents                                       1                 2
Grandparents                              2                 3
Great grandparents                      3                 5
Great-great grandparents             5                 8
Great-great-great grandparents    8                13

(Appologies if the tabs do not line up well)

The above fragments are from the text and I will be seeking permission to
turn the whole article into a web page.

AN BEACHAIRE (pronounced ann backerie)
subscription details are on...

http://website.lineone.net/~dave.cushman/magazine.html


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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