Fibonacci - His Career

Fibonacci solved the Arithmetic Series before Gauss!
There is a famous story about the German mathematician Carl Friedrich Gauss. As told by Brian Hayes in The American Scientist,

In the 1780s a provincial German schoolmaster gave his class the tedious assignment of summing the first 100 integers. The teacher's aim was to keep the kids quiet for half an hour, but one young pupil almost immediately produced an answer: 1 + 2 + 3 + ... + 98 + 99 + 100 = 5,050. The smart aleck was Carl Friedrich Gauss, who would go on to join the short list of candidates for greatest mathematician ever. Gauss was not a calculating prodigy who added up all those numbers in his head. He had a deeper insight: If you "fold" the series of numbers in the middle and add them in pairs—1 + 100, 2 + 99, 3 + 98, and so on—all the pairs sum to 101. There are 50 such pairs, and so the grand total is simply 50×101. The more general formula, for a list of consecutive numbers from 1 through n, is n(n + 1)/2.

The first method presented in Chapter 12 of Liber Abaci is how to calculate an arithmetic series. He gives the same solution as Gauss. I do not claim that Gauss learned it by reading Fibonacci's book. I expect he re-discovered it himself, much to his credit. It is worth knowing, however, that the formula was known perhaps 1,000 years before Gauss presented it to his teacher.

Liber Abaci

Fibonacci wrote his first book in 1202 (2nd edition 1228). It was written in Latin and entitled Liber Abaci, which is best translated as The Book of Calculation. This book transformed Europe as businessmen replaced the cumbersome Roman Numeral system in favor of the numbers 1 to 9 (as well as 0) which came to the Muslim world from the Hindus. A modern comparison to this, although on a much smaller scale, is the adoption of the Metric System (meters for distance, kilograms for weight) for scientific work, rather than the use of the ancient Imperial System of measures (inches, feet and miles for distance, ounces and pounds for weight).

Practica Geometriae

His second book, Practica Geometriae (1220), was a collection of problems in geometry and trigonometry, again with practical applications.

Flos

Fibonacci had been introduced to the Holy Roman Emperor of the time, Frederick II, a patron of science and learning and a religious skeptic. Fibonacci was often challenged to answer mathematical problems for the emperor. In

Flos ("The Flower"), written in 1225, he presented solutions to these problems.

Liber quadratorum

Liber quadratorum, ("The Book of Squares"), also published in 1225, was on Diophantine equations. It was dedicated to Holy Roman Emperor, Frederick II.

Two other publications by Fibonacci have been lost:

* Di minor guisa (on commercial arithmetic)

* Commentary on Book X of Euclid's Elements