| 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 2-square and
the 3-square (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:
Artists throughout history have followed the Greek interest in
the connections between numbers and nature:
|