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Part II: Fibonacci's applications

Wed, Jun 14 2006, 12:24 GMT
by Facundo Molina

MolFX - Management

The verification of the Fibonacci Sequence in many real phenomenon’s, makes lots of people decide to study the relationship between these mathematics of nature and the behavior of the financial markets.

May be this is the most curious and captivating, so it has be proved that the Fibonacci Sequence appears in nature, forming physical structures and defining the process of chance of this dynamics structures. Many authors have mentioned this concept in theirs books.

At the end of XIX Century, a botanist calls A. H. Church, had discovered, studying the sunflower the presence of Fibonacci. His seeds are arranged around the middle in 89 curves, turning 55 of these in one direction and the others 34 to the opposite direction.

From here, the botanists have found Fibonacci numbers in different pieces of Nature. For example, the margarita forms spiral model similar of the sunflower in the middle of his flower. There are also many varieties of flowers where the numbers of petals are Fibo numbers.

A mathematician from Arizona University, Alan Newell, and his pupil Patrick Shipman have been studying recently the cactus to determinate the reason why this numeric pattern is universal. These researchers analyzed the form of this plant, his skin size, and another biomechanics that surge in his growth. When their introduced all of the data in the computer, found by surprise, that the more stable configuration followed the forms based of the Fibonacci Sequence.

We can find other applications, for example the spiral that many trees developed in their branches; the number of little branches in a big one, and the follow of the same vertical is a Fibonacci number, if we use to calculated one of the to branches.

The Fibonacci numbers appear also, in the human body. The men have five appendixes (two arms, two legs, and a head); each arm and each leg are divide in three parts, ending each of them in five appendixes (five fingers), divide each of them in three little phalanx, except two of them which have just two. In the same way, the head has three outstanding characteristics (two ears and a nose), and three inlaid characteristics (two eyes and a mouth). In the end, the human body has five physical senses: sight, ear, sense of smell, taste, and touch.

”The human body presents the golden number or phi”. Leonardo Da Vinci, in his famous picture, the Vitrubio man, illustrated the Luca Pacioli book “Divine Proportion” edited in 1509. This book, describes witch must be the proportion of artistic creations. He proposes that a human figure where each part of the body must respect a specific proportion to be harmonic. This perfect man, for Pacioli, is based on the following mathematical calculation: the high of the men, (side of the square) divided the distance between the navel and the extreme of the extended hand (circle radio), represents the divine number.



Also, many animals body have a trunk and five appendixes, (head and four legs); birds have 5 projections too: a head two legs, two wings.

Fibonacci is also present in music: see for example the piano. The division of the keyboard in scales of eight white keys and five black ones; the black keys are distributed all along the keyboard in groups of three and two. A complete keyboard has eleven scales, and could have one more key, meaning 89.
The chords that allow us to identify any tone are formed by the first, third, fifth and eight note of the scale.

Since professors Church and Hambridge, the interest on Fibonacci numbers by many researchers end in the creation in 1963 of the Fibonacci Society in California, formed by mathematics, witch main objective is exchange ideas and stimulate research on Fibonacci’s relationship with nature.

It has been proved that the Fibonacci sequence is highly connected with the progressive development of dynamical structures, an as society is a dynamical system, human history could be running according to this Nature Law, based on the proportion 3-5 or 0,618; if we add to this concept, the idea that financial markets are the reflect of mass behavior, we can conclude that Fibonacci sequence could be applicable to those markets.

In the next session based on these concepts, we will develop a model to prove the proposed objective on this work.

Published on  Tue, Aug 15 2006, 07:36 GMT