# Fibonacci

> Italian mathematician (c.1170–c.1240/50)

**Wikidata**: [Q8763](https://www.wikidata.org/wiki/Q8763)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Fibonacci)  
**Source**: https://4ort.xyz/entity/fibonacci

## Summary
Fibonacci was an Italian mathematician from the Republic of Pisa, best known for introducing the Hindu-Arabic numeral system to Europe and for the Fibonacci sequence, a series of numbers where each number is the sum of the two preceding ones. His work, particularly *Liber Abaci*, revolutionized European mathematics and commerce.

## Biography
- **Born**: c. 1170–1175, Republic of Pisa (modern-day Italy)
- **Nationality**: Italian
- **Known for**: Introducing the Hindu-Arabic numeral system to Europe, the Fibonacci sequence, and contributions to number theory
- **Field(s)**: Mathematics, number theory

## Contributions
Fibonacci's most significant work is *Liber Abaci* (1202), which introduced the Hindu-Arabic numeral system to Europe, replacing Roman numerals and simplifying arithmetic. He also authored *The Book of Squares*, a treatise on algebra and number theory. The Fibonacci sequence, described in *Liber Abaci*, became foundational in mathematics, appearing in various natural phenomena and mathematical models. His work on the Brahmagupta–Fibonacci identity expanded the understanding of sums of squares.

## FAQs
### What is the Fibonacci sequence?
The Fibonacci sequence is an infinite series of integers where each number is the sum of the two preceding ones, starting from 0 and 1 (0, 1, 1, 2, 3, 5, 8, 13, ...). It appears in nature, art, and computer science.

### What is *Liber Abaci*?
*Liber Abaci* is a seminal book by Fibonacci, published in 1202, that introduced the Hindu-Arabic numeral system to Europe. It also included practical applications for merchants and the Fibonacci sequence.

### Where was Fibonacci from?
Fibonacci was from the Republic of Pisa, a de facto independent state in modern-day Italy, active from the 10th to 15th centuries.

### What other works did Fibonacci write?
Besides *Liber Abaci*, Fibonacci wrote *The Book of Squares*, which explored algebraic equations and number theory, and contributed to the Brahmagupta–Fibonacci identity.

## Why They Matter
Fibonacci's introduction of the Hindu-Arabic numeral system transformed European mathematics, commerce, and science by making calculations more efficient. The Fibonacci sequence became a cornerstone of number theory and appears in diverse fields like biology, finance, and computer algorithms. His work laid the groundwork for modern arithmetic and influenced later mathematicians in Europe and beyond.

## Notable For
- Introducing the Hindu-Arabic numeral system to Europe via *Liber Abaci*
- Discovering the Fibonacci sequence, a fundamental concept in mathematics
- Authoring *The Book of Squares*, a key text in algebra and number theory
- Contributing to the Brahmagupta–Fibonacci identity
- Influencing the development of European mathematics during the Middle Ages

## Body
### Early Life and Background
Fibonacci was born around 1170–1175 in the Republic of Pisa, a prominent maritime city-state in medieval Italy. His father, Guglielmo Bonacci, was a merchant, which likely exposed Fibonacci to the practical applications of mathematics in trade.

### *Liber Abaci* and the Hindu-Arabic Numeral System
In 1202, Fibonacci published *Liber Abaci*, a groundbreaking work that introduced the Hindu-Arabic numeral system (0–9) to Europe. This system simplified arithmetic compared to Roman numerals, facilitating commerce and scientific calculations. The book also included the Fibonacci sequence, which he used to model rabbit population growth.

### The Fibonacci Sequence
The Fibonacci sequence is defined as a series where each number is the sum of the two preceding ones (e.g., 0, 1, 1, 2, 3, 5, 8, ...). It appears in natural patterns, such as the arrangement of leaves and petals, and is widely used in mathematics, computer science, and finance.

### *The Book of Squares*
Fibonacci's *The Book of Squares* (1225) focused on algebraic equations and number theory, including the Brahmagupta–Fibonacci identity, which expresses the product of sums of squares as a sum of squares.

### Influence and Legacy
Fibonacci's work bridged Eastern and Western mathematics, revolutionizing European arithmetic and commerce. His ideas influenced later mathematicians, including those in the Renaissance, and his sequence remains a fundamental concept in modern mathematics. The Republic of Pisa, his birthplace, was a hub of medieval trade and learning, further amplifying his impact.

### Related Concepts
- **Fibonacci number**: Any integer in the Fibonacci sequence.
- **Fibonacci prime**: A prime number within the Fibonacci sequence.
- **Pisano period**: The period of the Fibonacci sequence modulo an integer.
- **Fibonacci polynomials**: A generalization of Fibonacci numbers in polynomial form.

### Connections to Other Mathematicians
Fibonacci was influenced by earlier mathematicians, such as the Islamic scholar Abū Kāmil Shujāʿ ibn Aslam, and his work laid the foundation for later European advancements in algebra and number theory.

## References

1. Dizionario Biografico degli Italiani. 1997
2. BnF authorities
3. Dictionary of African Biography
4. Genealogics
5. Czech National Authority Database
6. Find a Grave
7. Virtual International Authority File
8. CiNii Research
9. Integrated Authority File
10. [MacTutor History of Mathematics archive](http://www-history.mcs.st-andrews.ac.uk/Biographies/Fibonacci.html)
11. [University of Surrey](http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibBio.html)
12. Enciclopedia Federiciana
13. [Source](https://r-knott.surrey.ac.uk/Fibonacci/fibBio.html)
14. Freebase Data Dumps. 2013
15. [Source](https://mathshistory.st-andrews.ac.uk/Biographies/Abu_Kamil/)
16. MacTutor History of Mathematics archive
17. [Source](http://digitale.beic.it/primo_library/libweb/action/search.do?fn=search&vid=BEIC&vl%283134987UI0%29=creator&vl%28freeText0%29=Fibonacci%20Leonardo)
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