The Leaning Tower of Pisa


Fibonacci aka Leonardo of Pisa

Known by several other names, Leonardo of Pisa ( aka Fibonacci) has been hailed as one of the premiere mathematicians of the middle ages.

Despite his numerous aliases, his national notoriety for his work in mathematics was immense. He is most famous for the Fibonacci Sequence that many people have incorrectly given him credit for discovering.



In fact, Leonardo Pisano Fibonacci's main achievements were:

Fibonacci aka Leonardo of Pisa
  • Helping promote the use of the Hindu/Arabic numeral system in Europe - His 13th century book, Liber Adaci , is the main text credited for this.
  • Pioneered the continued use of Egyptian fractions - Though not the inventor of fractions, Leonardo Fibonacci used them quite often in his calculations and documented seven different conversion methods.
  • Of course, the Fibonacci Numbers - Though not necessarily the person who discovered the sequence, he did make use of them in Liber Abaci .

The history of Fibonacci is not a hard one to find- Fibonacci was born in Pisa around 1170. He gained his nickname "Fibonacci" due to his father's nickname (Bonaccio - "good natured"). Fibonacci is derived from filius Bonacci , which literally means "son of Bonaccio"). His mother, Alessandra, died when he was 9 years old.


The Liber Abaci

Fibonicci Statue

Fibonacci statue at the Camposanto in Pisa

Leonardo Fibonacci was one of the first mathematicians of the time that recognized that performing calculations with Hindu/Arabic numerals was much easier than using Roman numerals, and during a period of time where he went traveling throughout the Mediterranean he learned the various ways that the characters could be used, at the age of 32 he published the Liber Abaci . This one document was the defining piece of text that effectively introduced Europe to the character set. This document was published in 1202.

The Livery Abaci promoted the adaptation of a new form of numeration system. Whereas Roman numerals had a specific symbol for each number, the system that Fibonacci was endorsing gave each number (0-9) a place value. By using 10 different digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) you are able to express any quantity possible so long as it remains a whole quotient. The addition of a decimal allows for the expression of any mathematical figure.

The book was enthusiastically received throughout educated Europe , though it would be nearly three centuries before decimals were widely used (thanks to the introduction of the printing press). Though the number system was known to Indian mathematicians in the early 6 th century, it was Leonardo Fibonacci and his infamous book that introduced it to the western world.

For many people, the resounding question is "what is the Fibonacci Sequence?" Unfortunately, the Liber Abaci doesn't quite answer that question, thought it does use the Fibonacci Sequence (or Fibonacci's Numbers as they're often referred to as) in a few examples within the book.


The Fibonacci Sequence

Fibonacci is the most famous for the Fibonacci Sequence.

The Fibonacci numbers go like this:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...

How is the Fibonacci Sequence formed? It's quiet easy:

  • The first two numbers are 0 and 1
  • Each following number is the sum of the previous two.

Leonardo of Pisa didn't invent the Fibonacci numbers though, they were long known in India before they came to Europe.

Here's the Fibonacci sequence formula:

Fibonacci sequence formula


And what is a Fibonacci Spiral? The Fibonacci spiral is a special kind of golden spiral whose ratio increases by the factor 1.618 (the golden ratio). Have a look at the following illustration and you'll recognize how the Fibonacci numbers relate to the spiral:

Fibonacci spiral

The Fibonacci spiral illustrates the connection between the Fibonacci numbers and nature. The Fibonacci series can be found in for example the head of a sunflower (florets in spirals), artichokes, the ancestry of bees, ...

In 1240 the Republic of Pisa honored Leonardo Fibonacci, referring to him as Leonardo Bigollo and granting him a salary. He was around 80 years old when he died around the year 1250.