The Fibonacci Sequence and the Mathematics of Nature
The Fibonacci sequence, named after its discoverer, Leonard of Pisa (also called Fibonacci), is a sequence derived by summing the previous sum with the second factor of the previous addition product. Thus, the sequence is derived by:
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
| 8 + 13 = 21
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Fibonnaci proposed the sequence in 1202 as a solution to the
reproduction of rabbits. Yet, the sequence has far ranging implications for many aspects of nature.
Flowering plants will very likely have a number of petals equal to a Fibonnaci number.
For example, lilies have three petals, while buttercups have five petals.
Daises will have 34, 55 or even 89 petals. Fibonnaci sequences also occur in the seed arrangements of
sunflowers and the arrangement of pinecones. The probable reason for the Fibonnaci arrangement of these
items is to maximally pack the objects with constant density.
A derivation of the Fibonacci sequence is the so-called “golden ratio.” The golden ratio is equal to
(1 + sqrt(5))/2, and is formed by the ratio of the sides of a rectangle formed from “Fibonacci squares.”
(Figure 1)
Figure 1: Rectangles formed from Fibonacci-Lengthed Squares
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| As more and more Fibonacci-lengthed squares are added,
the ratio of the sides approaches the “golden ratio.” The shells of many animals, such as nautiluses,
have a Fibonacci type curve, as shown overlaid on the larger Fibonacci rectangles. (figure 2)
Objects containing the golden ratio are considered aesthetically pleasing to the human mind,
as shown in an issue of Discover Magazine. For example, the most aesthetically pleasing faces
had the distance between eyes and the distance from the nose to the point between the eyes in
proportion to the golden ratio.
Figure 2: Fibonacci "Curve," as seen in Nautilus shells
| Further Reading and Bibliography
 Fibonacci Numbers and Nature
| | Math and Music
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Mathematics
