Notes
from http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#spiral
1. The Fibonacci Sequence
What
is the relationship between the following numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,
377, 610, 987...

2. The Golden Ratio
Take
the ratio of two successive numbers in Fibonacci's series and divide
each by the number before it. What number is being approached in this
series?
This number is called Phi.

3. The Golden Rectangle/ The Fibonacci Spiral
Take
a piece of paper and draw two small squares of size 1 next to each
other. On top of both of these draw a square of size 2 (=1+1).
Draw a new square  touching both a unit square
and the latest square of side 2  so having sides 3 units long; and
then another touching both the 2square and the 3square (which has
sides of 5 units).
Repeat.
You should end up with a drawing that looks like
this:
If you draw a half circle through each of the squares, you wind up with
a spiral that looks like this:

4. The Fibonacci Spiral in Nature
Once
the Greeks had discovered this intriguing number, they began to notice
that it showed up in various forms in nature:
Many seed heads on plants have patterns which
appear to be the Fibonacci Spiral:
Look at this pinecone:
The leaf arrangements of common plants follow the
spiral as well:
You even see it in cauliflower:
Here you can see the same spiral in the shape of a
snail:
When the Greeks noticed the connection between the
Fibonacci sequence and many organic (living) forms, they believed that
they had discovered a divine number.
What would Plato have argued in a discussion of
the Fibonacci Sequence?

5. The Golden Rectangle in Architecture:
The Greeks celebrated the Fibonacci sequence in their
art and architecture:
Check out the Parthenon. See the Fibonacci Spiral?
Look again: (animation)
Artists
throughout history have followed the Greek interest in the
connections between numbers and nature:
