Good morning! I hope you all enjoyed your Thanksgiving Holidays. Both boys came home for the weekend, which was a treat. =)

On Wednesday I got a text wishing me a Happy Fibonacci Day. I had to think a minute: Nov 23, so 1123, from the sequence 1, 1, 2, 3, 5, 8, 13,…. And this inspired this week’s post about Fibonacci.

Leonardo Pisano was born around 1170 in Italy, probably Pisa — hence the “Pisano” part of his name. He was born to the Bonacci family — hence the “filuis Bonacci” (abbreviated to “Fibonacci”) part of his name. His father was a diplomat, and as a result of his father’s post Leonardo was educated in North Africa and traveled widely, which meant he was exposed to different number systems, including the base ten number system that we use today. Indeed, it is likely that Leonardo himself is the reason we use it: he found it to be much better for calculation than the Roman number system (which would have used XXIII for a number like 23). He returned to Pisa around 1200 and wrote several books that illustrated this system, the most famous of which is *Liber Abaci* (*Book of Calculation* – abaci is related to abacus). Here’s a statue, by Giovanni Paganucci, of Fibonacci holding a book (CC license).

Although Fibonacci’s most significant mathematical contributions are related to his books sharing the decimal number system and methods of calculation with western Europe, he has become most famous because of a single problem that was in the 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?

This problem leads to the number system 1, 1, 2, 3, 5, 8, …, where each number is the sum of the previous two, which now bears the name the Fibonacci sequence in his honor. Although maybe it shouldn’t – the sequence was known in India well before Fibonacci. By whom, you might wonder? I started to write a brief summary, but realized I didn’t know enough about the history myself to do it justice so that will have to wait for next week…

Sources:

- http://www-groups.dcs.st-and.ac.uk/history/Biographies/Fibonacci.html
- “The so-called fibonacci numbers in ancient and medieval India” by ParmanandSingh,
*Historia Mathematica*, Vol. 12, Issue 3, August 1985, pp. 229-244 https://www.sciencedirect.com/science/article/pii/0315086085900217?via%3Dihub

November 28, 2022 at 1:31 pm |

Incidentally, it was Édouard Lucas in the 19th century who gave the Fibonacci sequence that name: around that time, it was rarely known and when used was called by many names including “the sequence of Lamé” (as Gabriel Lamé had used the sequence for analysis of the Euclidean algorithm). It was Lucas who noticed that one of the many problems in Fibonacci’s book involved that sequence, and started calling it the Fibonacci sequence. He was the one who discovered many properties and thereby made the sequence a worthy object of study (and “Lucas sequence” is now used as a general term that includes the Fibonacci sequence but also many others).

For the history of this sequence in India (specifically, how they arose in the study of Sanskrit/Prakrit prosody), I had posted some pictures online a few years ago, from the respective pages of the original sources, e.g. here https://twitter.com/svat/status/868964211644284928 you can see red circles around the Sanskrit words for “1”, “2”, “3”, “5”, “8”, “13”, “21”.

December 5, 2022 at 7:04 am |

[…] a French mathematician for whom a similar sequence: 1, 3, 4, 7, 11, … is named. Blog commenter S shared that leading up to that time “it was rarely known and when used was called by many […]