## Monday, November 3, 2014

### Preparation for Fibonacci Day - Fibonacci Bees

Male bees come from unfertilized eggs, so they have mothers but no fathers. Females come from fertilized eggs, so they have parents of both sexes. This produces an interesting pattern: The number of males in a given generation equals the number of females in the succeeding generation. And the number of females in a given generation equals the number of females in the succeeding two generations:
 Genealogy of a male bee, beginning with his "mom" at the bottom level of the chart above (which is the second generation going backwards).
One male be has 1 parent , 2 grand-parents, 3 great grand-parents, 5 great great grand-parents, 8 great great great grand-parents, 13 great great great great grand-parents, ...
So the total number of bees, male and female, (but not counting siblings) in generation n is the Fibonacci number F(n).

W. Hope-Jones discovered the relationship in 1921; this example is from Thomas Koshy’s “Fibonacci and Lucas Numbers With Applications”, 2001.

Reference:

David