Leonardo Pisano Fibonacci (1170–1240 or 1250) was an Italian number theorist. He introduced the world to such wide-ranging mathematical concepts as what is now known as the Arabic numbering system, the concept of square roots, number sequencing, and even math word problems.

### Fast Facts: Leonardo Pisano Fibonacci

**Known For:**Noted Italian mathematician and number theorist; developed Fibonacci Numbers and the Fibonacci Sequence**Also Known As:**Leonard of Pisa**Born:**1170 in Pisa, Italy**Father:**Guglielmo**Died:**Between 1240 and 1250, most likely Pisa**Education:**Educated in North Africa; studied mathematics in Bugia, Algeria**Published Works: "**Liber Abaci (The Book of Calculation)," 1202 and 1228; "Practica Geometriae (The Practice of Geometry)," 1220; "Liber Quadratorum (The Book of Square Numbers)," 1225**Awards and Honors:**The Republic of Pisa honored Fibonacci in 1240 for advising the city and its citizens on accounting issues.**Notable Quote:**“If by chance I have omitted anything more or less proper or necessary, I beg forgiveness, since there is no one who is without fault and circumspect in all matters.”

### Early Years and Education

Fibonacci was born in Italy but obtained his education in North Africa. Very little is known about him or his family and there are no photographs or drawings of him. Much of the information about Fibonacci has been gathered by his autobiographical notes, which he included in his books.

### Mathematical Contributions

Fibonacci is considered to be one of the most talented mathematicians of the Middle Ages. Few people realize that it was Fibonacci that gave the world the decimal number system (Hindu-Arabic numbering system), which replaced the Roman numeral system. When he was studying mathematics, he used the Hindu-Arabic (0-9) symbols instead of Roman symbols, which didn't have zeros and lacked place value.

In fact, when using the Roman numeral system, an abacus was usually required. There is no doubt that Fibonacci saw the superiority of using Hindu-Arabic system over the Roman Numerals.

### Liber Abaci

Fibonacci showed the world how to use what is now our current numbering system in his book "Liber Abaci," which he published in 1202. The title translates as "The Book of Calculation." The following problem was written in his book:

"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?"

It was this problem that led Fibonacci to the introduction of the Fibonacci Numbers and the Fibonacci Sequence, which is what he remains famous for to this day.

The sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55... This sequence shows that each number is the sum of the two preceding numbers. It is a sequence that is seen and used in many different areas of mathematics and science today. The sequence is an example of a recursive sequence.

The Fibonacci Sequence defines the curvature of naturally occurring spirals, such as snail shells and even the pattern of seeds in flowering plants. The Fibonacci Sequence was actually given the name by a French mathematician Edouard Lucas in the 1870s.

### Death and Legacy

In addition to "Liber Abaci," Fibonacci authored several other books on mathematical topics ranging from geometry to squaring numbers (multiplying numbers by themselves). The city of Pisa (technically a republic at that time) honored Fibonacci and granted him a salary in 1240 for his help in advising Pisa and its citizens on accounting issues. Fibonacci died between 1240 and 1250 in Pisa.

Fibonacci is famous for his contributions to number theory.

- In his book, "Liber Abaci," he introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe.
- He introduced the bar that is used for fractions today; previous to this, the numerator had quotations around it.
- The square root notation is also a Fibonacci method.

It has been said that the Fibonacci Numbers are nature's numbering system and that they apply to the growth of living things, including cells, petals on a flower, wheat, honeycomb, pine cones, and much more.

### Sources

- “Leonardo Pisano Fibonacci.”
*Fibonacci (1170-1250)*, www-history.mcs.st-andrews.ac.uk. *Leonardo Pisano (Fibonacci).*www2.stetson.edu.- Knott, R. “Who was Fibonacci?”