One of Europe's greatest mathematicians of the middle ages was Leonardo of Pisa, born in 1175. He was called "Fibonacci", which is short for the son of Bonacci and was one of the first mathematicians to introduce the Hindu-Arabic number system to Europe.
The Hindu-Arabic system is essentially our present decimal number system. It supplanted Roman numerals and other methods of counting making life and arithmetic very much easier. I mean, have you ever tried to add in Roman numerals? If Fibonacci had done nothing else, this should have been sufficient to guarantee his fame!
However, he made many other contributions to modern mathematics. In particular, in 1202, he became interested in rabbits or, more accurately, in how fast rabbits could or would breed under ideal conditions. Is there a mathematical law or relationship that explains the breeding of rabbits?
Suppose that rabbits are sexually mature and active after one month and that they have a one month gestation period. Fibonacci used these suppositions along with two premises - that rabbits live a long time and that the offspring would consist of a breeding male/female pair - to try and model the growth in rabbit population that would occur over, for example, a year.
Starting with a single pair, what he found was that after one month, there would be one pair of rabbits, after two months, two pairs, followed by three pairs after three months but after four there would be five pairs and after five months, eight pairs. Halfway through the year, after six months, thirteen pairs, and the number would increase rapidly leading to an inundation of rabbits.
From this sequence, he generated a number series which bears his name and goes:
1 1 2 3 5 8 13 21 34 etc.
and, like one of those questions that appear on IQ tests - the ones that ask you for the next number in the sequence - there is a simple mathematical rule for generating the next term. You simple add the previous two terms together. That is, 3 + 5 make 8, 5 + 8 make 13, 13 + 21 make 34, 21 and 34 make 55 and so on.
Unfortunately, as models go, this is not a particularly good one for actual rabbit breeding. It ignores "inbreeding" and the fact that rabbits rarely have a single pair of male and female offspring. If this had only been an intellectual exercise to explain rabbit populations and that was all the Fibonacci series did, then it would have been an interesting tidbit in the history of mathematics but nothing else.
However, the Fibonacci series has been found to permeate biology, accounting for such diverse things as the shape of the shells of snails, the distribution of leaves on branches, and the structure of seed pods and petals for flowers. For example, looking down the stem of some plants or the petals of some flowers, the successive rows form a Fibonacci sequence.
It is also found in physics and chemistry. The successive reactions of particles or the structure of organic molecules often follows a pattern that can be modelled with the Fibonacci sequence. Indeed, even the reaction of chemical compounds can be found to follow a Fibonacci sequence.
The sequential relationship even finds its way into both art and architecture. The ratio between successive terms in the sequence settles down to an approximation of the Golden Numbers, which are 0.61803... and 1.61803... etcetera. Sometimes these numbers are referred to as the Golden Mean.
Both of these numbers are "irrational", meaning that they just keep going without repeating and they have the unusual property of being each other's inverse. They also have the property that 1 divided by 0.61803... is the same as 1 plus 0.61803... or 1.61803... so as numbers go, they carry a certain intrigue similar to pi.
These numbers form the Golden Ratio which is a particularly pleasing proportionality used in paintings, such as the Mona Lisa, and architectural design, such as the Parthenon in Athens. The Golden Ratio can even be found in the construction of the buildings at UNBC, such as the floor tiles in the Winter Garden.
The Golden Ratio is either of these two numbers in ratio to 1 - it makes no difference since the proportions are always the same and provide the most aesthetically pleasing view. Fibonacci numbers are a simple series originally intended to model rabbit breading but they actually have profound and far reaching applications that permeate many different disciplines.
This is why basic science is so important. You never know where one idea might lead.
