# Leonardo Fibonacci and Fibonacci Numbers

## The history of Leonardo Fibonacci and Fibonacci numbers

Many people who have done some units in mathematics have come across the name Fibonacci. Fibonacci is one of the middle age scholars that have contributed highly to mathematic but most especially to the knowledge of numbers. Fibonacci was born Leonardo Pisano in Italy. He was however known by the nick-name Fibonacci and also used the name Bigollo. Fibonacci was born in Pisa, today in Italy, in 1170. His father was Guililmo. Fibonacci got his education in North Africa where he had accompanied his father. It was in North Africa that Fibonacci was introduced to mathematics and knowledge of numbers. Fibonacci was taught ancient mathematic skills at a place known as Bugia, North Africa (Posamentier & Lehmann 23). Apart from learning mathematics, Fibonacci also traveled a lot as he accompanied his father in his duties as a diplomat. During his travels, Fibonacci observed and was moved by various applications of mathematics systems in various countries. This early experience and foundation in ancient mathematical concepts motivated him to make very important contribution to mathematics.

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Fibonacci returned to Pisa after his experience in North Africa and made very important contributions to mathematics. At Pisa, Fibonacci wrote various texts on mathematics. These text remains to be very important to study ancient mathematics skills. Although some of his works were lost, his remaining text offers great information on mathematical concepts. Unlike other mathematicians in his time, Fibonacci was greatly interested in practical application of mathematics rather than only addressing abstract concepts. It would have been expected that Fibonacci work would have attracted attention but his approach to mathematical concepts to Fibonacci was acclaimed. Among Fibonacci texts include Liber abaci, Flos, Liber quadratorum and Practica geometriae. In these texts, Fibonacci solves interesting mathematical problems and develop new concept in mathematics (Posamentier & Lehmann 78). Fibonacci approach to mathematics was unique. He tried to use mathematical concepts to solve day-to-day problems or unravel mathematical puzzles.

Fibonacci has a lot of contributions to mathematics. Fibonacci was the first scholar to introduce decimal number system in Europe. By his travels, Fibonacci came across the Hindu-Arab system of numbering. When he returned to Europe, Fibonacci introduced the concept. This concept constitutes the basic ways of manipulating numbers such as addition, subtraction and multiplication. Unlike the earlier Roman numerals, decimal number system is easier to use.

Among Fibonacci contributions, it is the concept of Fibonacci numbers that is highly featured and associated with him. Fibonacci number is found in one of his books: Laber Abacci. The title of this book means ‘a book of calculation ‘. The Fibonacci numbers developed from a challenge given to Fibonacci. Fibonacci was asked to calculate the number of pairs of rabbits that would be there if a person put a pair of rabbits for one year, given that each pair begot a pair every month and the new pair became productive after one month. As a solution to this problem, Fibonacci developed the Fibonacci sequence, 1, 1, 2, 3, 5…., as a solution (Dunlap 59). This series consisted of numbers whose each number is a sum of two subsequent numbers. However, the series does not have a zero.

A concept that developed from the rabbit problem, Fibonacci numbers have developed to be an important concept in mathematic. Fibonacci did not carry any analysis of the number he had developed other than show that each number was a sum of subsequent numbers. However, Fibonacci numbers and series have become a subject of analysis to many scholars from time to time. The main reason for Fibonacci numbers to be of great interest to scholars is the fact that it was found to be applicable in many life situations (Obara par 7). Although Fibonacci numbers and series are associated with Fibonacci, it is possible that he did not develop the numbers. In Liber Abaci, Fibonacci claimed that he had recorded the concepts to demonstrate how Indian figures were used in arithmetic. Thus, the numbers may have been used by Indian scholars before him. Despite this claim, it is appreciated he helped pass on the concept in modern society. Fibonacci Numbers are applied in many areas. Among the areas where Fibonacci numbers are used include music, poetry, art and architecture.

## Fibonacci numbers in music and poetry

Fibonacci numbers have been applied in various areas. In music and poetry, Fibonacci numbers were used to develop rhyme and rhythm. There is a lot of early music and poems that were structured in the Fibonacci series. The structure of music uses Fibonacci in various ways Music instruments, frequency and other aspects of early music show evidence of Fibonacci numbers. Observing a keyboard shows clear evidence of the use of Fibonacci numbers. For example, a keyboard has thirteen notes between two notes through the octave (Posamentier & Lehmann 78). The scale used in music consists of 8 notes, where eight is a Fibonacci number. Observing the scale it is observed that the fifth and third notes form the foundation of all chords in music. In addition, it is observed that the scale is based on whole notes that are two steps from the first note. Music frequencies also show relationship with Fibonacci numbers. For example, natural harmonic in music follows ratios of frequency (Obara par 4). These frequency ratios relate closely with the first seven numbers of Fibonacci numbers. In poems, Fibonacci numbers are observed in the structure of the poems. Structure-based on Fibonacci numbers is used to bring out rhythms, alternation and emotional saturation. Most poems have been observed to be structured on Fibonacci numbers. For, example Pushkin’s poems were observed to have the size of 5,8,13, which are Fibonacci numbers.

## Fibonacci numbers in art and architecture

Fibonacci numbers and golden ratio is highly applied in art and architecture. Famous ancient works of art and architectural works have a close relation to Fibonacci numbers and Fibonacci ratio. Many artists and architects in the past proportioned to the golden ratio. Golden ratio is used in various ancient architectural works. For example, the Great Pyramid of Giza shows clear indication of golden ratio. In this famous pyramid, the base is 766 feet while the height is 481 feet. The ratio of base to height is thus 1.5717 which is a golden ratio. Great artists such as Leonardo Da Vinci structured their artworks to fit in the Fibonacci ratio. His drawing of the head of an old man is good evidence of Fibonacci ratio. The drawing can be subdivided into squares and rectangles that are close to golden rectangles (Dunlap 67-71).

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Leonardo Fibonacci is perpetuated by his discoveries. Fibonacci numbers have close correlation to nature, art, music and other aspects. The significance of the Fibonacci number in modern days shows that Fibonacci was a great man.

## Works Cited

Dunlap, Ronald. The golden ratio and Fibonacci number. London, World Scientific, 1997. Print.

Obara, Samuel. Golden Ratio in Art and Architecture. 2008. Web.

Posamentier, Alfred. & Lehmann, Ingmar. The fabulous Fibonacci numbers. New York: Prometheus Books, 2007.

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