10.)
Explain the concepts of Fibonacci in nature using three items as examples.

Fibonacci
used his pattern (0, 1, 1, 2, 3, 5, 8, 13, 21...keep adding the previous
two digits) to describe and count a honeybee's ancestors. There is one
queen, many worker bees, and some drone bees. The females are produced
when the queen mates with a male; therefore, they have two parents.
Male bees, however, only have one parent, a female. Male drone bees
have 1 parent, 2 grandparents, 3 great-grandparents, 5 great-great grandparents,
and so on. Female bees have 2 parents, 3 grandparents, 5 great-grandparents,
8 great-great grandparents, and so on, continuing with the Fibonacci
numbers.

Fibonacci
also used his spiral pattern to describe the distribution of segments
of the pinecones. One pattern is shown above in the yellow, the other
in the green. There are 8 or 13 whirls on a pinecone, depending on which
direction you follow. Each level, when viewed from the side, has a certain
number of scales that matches a Fibonacci number.

You
can also explain how plant leaves go up in spirals, so that, when viewed
from the top, we can see that each leaf gets as much sunlight as possible.
These spirals are in increments and proportions according to Fibonacci
numbers.

**Fibonacci
picture found at http://www.math.gatech.edu/~morley/images/Fibonacci.jpeg**

**Information
on honeybees found at http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html**

**Information
and pictures of pinecones and plants found at http://www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/fibonacci2.html**