| The fibonacci
sequence is my favorite number sequence. It starts with 0 and 1, and the
next Fibonacci number is made by adding the two previous numbers together,
etc. Here are the first few fibonacci numbers: 0, 1, 1, 2, 3, 5,
8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597 ... |
| The golden
ratio, Phi, is the ratio of two adjecant Fibonacci numbers. It is an
irrational number, approximately 1.618, that possesses many interesting
properties. Since the early Greeks, a ratio of length to width of approximately
1.618, has been considered the most visually appealing. This ratio, called
the golden ratio, not only appears in art and architecture, but also in
natural structures (like the natalis shell). |
| Fibonacci numbers also appear when we examine the number of petals of
certain common flowers: Iris 3 petals , Primrose 5 petals, Ragwort 13 petals,
and Daisies have 34, 55, and 89 petals. This poppy seed head has 13 ridges
on top. Some common trees with their Fibonacci leaf arrangement numbers
are: 1/2 elm, linden, lime, grasses ... 1/3 beech, hazel, grasses, blackberry
... 2/5 oak, cherry, apple, holly, plum, common groundsel ... 3/8 poplar,
rose, pear, willow ... 5/13 pussy willow, almond
What about a banana? Count how many "flat" surfaces it is
made from - is it 3 or perhaps 5? When you've peeled it, cut it in half
(as if breaking it in half, not lengthwise) and look again. Surprise!
There's a Fibonacci number. What about an apple? Instead of cutting it
from the stalk to the opposite end (where the flower was), ie from "North
pole" to "South pole", try cutting it along the "Equator".
Surprise! there's your Fibonacci number!
Look at your own hand ... you have ... 2 hands each of which has ...
5 fingers, each of which has ... 3 parts separated by ... 2 knuckles.
However, if you measure the lengths of the bones in your finger (best
seen by slightly bending the finger) does it look as if the ratio of the
longest bone in a finger to the middle bone is Phi? What about the ratio
of the middle bone to the shortest bone (at the end of the finger) - Phi
again?
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