Leonardo Bonacci (around 1170 to around 1240–50), often called Fibonacci, was an Italian mathematician from the Republic of Pisa. He is regarded as "the most talented Western mathematician of the Middle Ages."

The name "Fibonacci" first appears in a modern source in a 1838 text by the Franco-Italian mathematician Guglielmo Libri. It is short for "filius Bonacci," meaning "son of Bonacci." However, as early as 1506, Perizolo, a notary of the Holy Roman Empire, referred to him as "Lionardo Fibonacci."

Fibonacci helped spread the Indo–Arabic numeral system in the Western world, mainly through his book Liber Abaci (Book of Calculation), written in 1202. He also introduced Europe to the Fibonacci numbers, which he used as an example in Liber Abaci.

Biography

Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official who managed a trading post in Bugia, which is now known as Béjaïa, Algeria. Fibonacci traveled with him as a young boy. He was educated in Bugia, where he learned about the Hindu–Arabic numeral system.

Fibonacci traveled around the Mediterranean coast, meeting many merchants and learning about their methods of performing arithmetic. He quickly realized the advantages of the Hindu–Arabic system, which, unlike the Roman numerals used at the time, made calculations easier through a place-value system. In 1202, he completed the Liber Abaci (Book of Abacus or The Book of Calculation), which helped spread the use of Hindu–Arabic numerals in Europe.

Fibonacci was a guest of Emperor Frederick II, who was interested in mathematics and science. John of Palermo, a member of Frederick II’s court, asked Fibonacci to solve several problems based on Arab mathematical works. In 1240, the Republic of Pisa honored Fibonacci (known as Leonardo Bigollo) by giving him a salary in a decree that recognized his contributions to the city as an advisor on accounting and as a teacher to citizens.

Fibonacci is believed to have died between 1240 and 1250 in Pisa.

Liber Abaci

In the book Liber Abaci (1202), Fibonacci introduced the modus Indorum (method of the Indians), now called the Hindu–Arabic numeral system. This system uses ten digits, including zero, and a method where the position of a digit determines its value. The book demonstrated how these numerals could be used in practical ways, such as keeping business records, converting measurements, calculating interest, and exchanging money. The book was widely accepted in educated Europe and greatly influenced European thinking. It replaced older methods like Roman numerals, ancient Egyptian multiplication, and the abacus, making business calculations faster and easier. This advancement helped banking and accounting grow in Europe.

The original 1202 manuscript is not known to survive. A 1228 copy of the manuscript includes a section that explains the Hindu–Arabic numeral system and compares it to other systems, such as Roman numerals, and describes how to convert numbers into this system. Another section shows how the numerals were used in business, such as converting currencies and calculating profit and interest, which were important for banking. The book also discusses topics like irrational numbers and prime numbers.

Fibonacci sequence

Liber Abaci presented and solved a problem about how a rabbit population grows under simple assumptions. The solution, step by step, created a sequence of numbers later called Fibonacci numbers. Although Liber Abaci contains the earliest known description of this sequence outside of India, Indian mathematicians had described the sequence as early as the sixth century.

In the Fibonacci sequence, each number is the total of the two numbers before it. Fibonacci did not include the "0" and the first "1" that are used today, starting instead with 1, 2, 3, and so on. He calculated up to the thirteenth number, which was 233, though another version of the text shows the calculation continuing to the next number, 377. Fibonacci did not mention the golden ratio as the limit of the ratio between numbers in this sequence.

Legacy

In the 19th century, a statue of Fibonacci was placed in Pisa. Today, it is located in the western gallery of the Camposanto, a historical cemetery on Piazza dei Miracoli.

Many mathematical ideas are named after Fibonacci because of their connection to the Fibonacci numbers. Examples include the Brahmagupta–Fibonacci identity, the Fibonacci search technique, and the Pisano period. Other namesakes of Fibonacci include the asteroid 6765 Fibonacci and the art rock band The Fibonaccis.

Works

• Liber Abaci (1202), a book about calculations (English translation by Laurence Sigler, 2002).
• Practica Geometriae (1220), a collection of methods for surveying, measuring and dividing areas and volumes, and other practical geometry topics (English translation by Barnabas Hughes, Springer, 2008).
• Flos (1225), solutions to problems presented by Johannes of Palermo.
• Liber quadratorum ("The Book of Squares"), a work about Diophantine equations, written for Emperor Frederick II. This text includes information about the congruum and the Brahmagupta–Fibonacci identity.
• Di minor guisa (a book on commercial arithmetic; no copies remain).
• Commentary on Book X of Euclid's Elements (no copies remain).