Fibonacci Numbers

The phrase Fibonacci numbers refers to a sequence of numbers studied by a man named Leonardo of Pisa, who was nicknamed "Fibonacci". He was the first Italian person to study the sequence of Fibonacci numbers and he was also the one who spread the sequence's system through Europe in the early 13th century. Fibonacci also published the book Liber Abaci that made the sequence well-known. Today, he is known as one of the greatest - if not the greatest - mathematician of the Middle Ages.

Fibonacci was born in 1170. His father was named Guglielmo and nicknamed Bonaccio (meaning good natured) and his mother, who died when he was only nine, was named Alessandra. Fibonacci was not given his famous nickname until years after his death. "Fibonacci" comes from filius Bonacci which means son of Bonaccio.

Fibonacci often traveled with his father, who owned a trading post in a port called Bugia in North Africa. It was there that Fibonacci learned the Hindu-Arabic system of numerals. The Hindu-Arabic system is naturally more efficient than Roman numerals and Fibonacci was inspired to travel the Mediterranean, studying under countless brilliant Arab mathematicians. By 1200, he had completed his extensive travels, and in 1202, when he was only 32, he published everything he had learned in Liber Abaci.

The book's title translated to Book of Calculation or Book of Abacus and it was the first time anyone outside the Arab world had been introduced to the Hindu-Arab system of numerals. Fibonacci himself earned a lot of respect after the book was published and he even became friends with Emperor Fredrick II. The Emperor himself enjoyed both science and mathematics. In fact, Fibonacci was so respected that in 1240, he was honored with a special salary by the Republic of Pisa. Fibonacci died in Pisa sometime after the year 1240 and that year seems to be the last time he has appeared in historical records.

While Fibonacci himself did not discover Fibonacci numbers (they were named after him), he did use them in Liber Abaci. The numbers originate back to ancient India,and was used quite frequently in metrical sciences. Fibonacci introduced these numbers to Europe in his book, thus changing the way mathematics was seen.

The Fibonacci sequence itself can be explained like this: each number in the sequence is the sum of the two previous numbers in the sequence. Therefore, the sequence begins with 0, and then continues on like this: 1, 1, 2, 3, 5, 8, etc. The higher up the chain you go, the consecutive numbers would also then be divisible by each other to obtain what's called the "golden ratio" that became a staple in Renaissance painting proportions. The ratio works out to be 1:1.618 which painters used to proportion their work because they believed it to be much more aesthetically pleasing. This same ratio is found time and again in nature as well, making it fascinating for scientists to study the sequence organically.

These are some comprehensive websites to learn about Fibonacci numbers:

Although he is often overlooked by modern-day historians, Fibonacci's decision to introduce the Fibonacci number sequence to the western world greatly impacted the study of both mathematics and nature afterwards. The sequence can be found in both manmade items like paintings, barcode labels, and nature as well.