At 01:56 PM 6/6/2005, you wrote:
>I received a question from someone who read The Da Vinci Code.  I am one of
>the few who have not yet read it.  My reading friend says the book contends
>that the golden ratio - 1.618 - is, among other naturally occuring things,
>the ration between male and female bees in the hive.


The book is incorrect.  The ratio of male and female bees is hardly
constant,  and the only colonies I've seen with that high a drone count
either have a drone laying queen or laying worker.  In either case the hive
is pretty much doomed if left alone and a 1.6 ratio is far from healthy.

However the number of ancestors a given generation of male and female bees
has forms a fibonacci sequence.  The ratio of two successive numbers in a
fibonacci sequence approaches the golden number.  See
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#bees

-Tim


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