Fibonacci





Fibonacci has been called the greatest mathematician of the middle ages, even though while he was living, he was mostly ignored. Even now, people do not know about most of his accomplishments, only the Fibonacci sequence (rabbit problem) and his spreading of the Hindu-Arabic numerals. Many of Fibonacci's other achievments have gone un-noticed.

Leonardo de Pisa was born in Pisa, Italy around the year 1175. His father was named Guilielmo, but went by the nickname Bonacci, which means "the good natured one". Leonardo de Pisa is known by many names, but the most famous of these names is Fibonacci, from filus bonacci, meaning son of the good natured one. Guilielmo wanted Fibonacci to become a merchant, and had intended to bring him up as one, but when they lived in Algeria, he was introduced to numbers instead.

Guilielmo was a Customs officer for the city of Bugia, and a secretary for the republic of Pisa, which meant Fibonacci was educated in Algeria. Here he learned the Hindu-Arabic number system, and realized how much easier it was to use than the Roman numerals currently being used in Europe.

When Fibonacci finished his travels around 1200, he returned to Pisa and started to write. His most famous text was //Liber Abaci//, meaning book of the abacus, which he wrote in 1202. //Liber Abaci// was devoted to arithmetic and linear equations, but it was also used to introduce the Hindu-Arabic number system to Europe. It included a table of prime numbers from one to onne-hundred, and discussed perfect numbers and the Chinese remainder theorem. ([]) In //Liber Abaci,// Fibonacci posed his famous rabbit problem;

//A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive? // //~Liber Abaci //

The answer to this problem gives you the famous Fibonacci sequence;

//1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… //  The definition of the Fibonacci sequence is; // F(n+1) = F(n-1) + F(n), if n>1 and F(0) = 0, F(1) = 1 //

Each number is the sum of the two previous terms. These numbers come up many times in nature, but in the form of a spiral or a curve. When you chart these numbers on a graph, you get the Fibonacci spiral. The swirl of seashells, ridges of pinecones, curve of animals’ nails, centers of sunflowers, even human teeth curve in the Fibonacci spiral.

The Fibonacci sequence was not named this way until the 1800’s by Edouard Lucas, a French mathematician. ([])  The second text written by Fibonacci was //Practica geometriae,// meaning  practical geometry, in 1220. This book was all about geometric problems, but also talked about how to measure tall objects using triangles of similar shape, and included many every-day, helpful information for surveyors. ([])

Also written was //Liber quadratorum // in 1225. Some say this was Fibonacci's most impressive accomplishment, even though it is not what he is famous for. //Liber quadratorum,// the book of squares, is a number theory book, which talks about Pythagorean triples and defines the concept of a congruum. ([]) In it, Fibonacci proves many number theories like;

//"there is no x, y such that x²+y² and x²-y² are both squares, and x-y cannot be a square." // //~Liber quadratorum //  In 1225, Emperor Fredrick II stopped in Pisa to test Fibonacci. He had heard about him, and so he had John of Palermo create test questions. In //Flos//, written in 1225, Fibonacci gave his answer. He calculated 10x+2x²+3³=20 in sexagesimal notation, and got it correct to nine decimal places, which was an amazing achievement. None of the other competitors reached a correct answer.

In 1228, Fibonacci produced a second edition of //Liber abaci//, with a preface. Because all books had to be hand written, there were not many made, although Fibonacci wrote other manuscripts, they are lost. Among the books that were lost was the original version of //Liber abaci,// only the preface version has been found.

Much about Fibonacci’s life is unknown. There is no records about his family, whether he had any siblings, or whether he had a family of his own. His birthday is approximate and so is his death. He died in Pisa around 1250, of unknown causes. Today, there is a statue is Fibonacci in the Giardino Scotto in Pisa, Italy to commemorate all Fibonacci has accomplished.



<span style="font-family: 'Arial','sans-serif'; font-size: 12pt; line-height: 115%;">I think the most interesting thing about Fibonacci was the fact that his name changed so much. He was born Leonardo de Pisa, but most people know him today as Fibonacci. In his written work he referred to himself as Leonardo Bigollo, or just Bigollo, which means “traveler”. It was almost confusing because at first I wasn’t sure if I still had the right person.

I also think that the Fibonacci sequence is a very interesting concept. It comes up in many times in nature, exactly the same numbers, in places around the world. None of these seashells and sunflowers interacted, and yet they both came up with the same spiral, and the same numbers. It is something that we think we understand, but we probably haven’t even scratched the surface of the things it explains and the things it can do.