# Kili's Reviews > The Man of Numbers: Fibonacci's Arithmetic Revolution

The Man of Numbers: Fibonacci's Arithmetic Revolution

by Keith J. Devlin

by Keith J. Devlin

All computer science students know Fibonacci numbers: F(1) = F(2) = 1, n > 2: F(n) = F(n-1) + F(n-2). Remembering Fibonacci for this series is much like people in 2816 calling the hypertext abstraction Job text. That's not exactly right - the people in 2816 would also have to think that Steve Job's name was Appledad.

Fibonacci was named Leonardo, and came from Pisa, hence his name in his time would have been "Leonardo Pisano" (Leonard from Pisa). The name "Fibonacci" comes from "Filius Bonaccio" - eg, the Bonaccio Family - which is perhaps the name of his Grandfather.

I especially enjoyed the view this book gave into the state of European mathematics at the beginning of the 1200's. Roman numerals aren't that hard for addition or subtraction (I didn't know that) - it's multiplication and division that is difficult with them. There were elaborate methods of computation that used fingers, and the Europeans of his era had their own kind of abacus (different from the Chinese one). Leonardo introduced to a broad public not only "Arabic" numerals, but also the algorithms we use to multiply and divide with them - as well as methods for computing square roots, cubic roots, and approaches for many kinds of practical problems. His book Liber Abbaci was scholarly, but it caught on and revolutionized the way merchants computed. His role was not unlike Steve Jobs or Bill Gates - taking known technology and making it available for the people who could take practical advantage of it. The book that did this was titled Liber Abbaci.

Leonardo wrote many books in his time, and was hugely influential in many kinds of mathematics. He was widely recognized for his role, but when books started to be printed, his own books (hand copied and thus relatively rare rare) became less important.

Then again, does the common person remember Brahmagupta as the first person to give the rules for the mathematical properties of 0? He is the person who first wrote rules like 0*x = 0, and 0 - x has the opposite sign of x. He did say that 0/0 = 0, but Newton and his science of infitesimals was a thousand years in the future. This was a revolutionary discovery of the 600s - a fact I also learned from this book.

Fibonacci numbers are an example that Lorenzo included in Liber Abbaci. From that book:

HOW MANY PAIRS OF RABBITS ARE CREATED BY ONE PAIR IN A YEAR

A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature of them in a single month to bear another pair, and in the second month those born to bear another.

---

At first, this sounded like an exponential series to me, but the key is that it takes a month for rabbits to become fertile. So, if the number of pairs of rabbits at month n is the number of pairs of rabbits at month n-1 (none died) plus the number of pairs rabbits at month n-2 (these are all now fertile).

I wish the book had been longer - some of the text is too terse to fully appreciate. For example, Devlin describes the occurrence of Fibonacci numbers in nature (eg, the number of petals on a flower is almost always a Fibonacci number). I learned why this is the case in another book (that I'm reading now).

Fibonacci was named Leonardo, and came from Pisa, hence his name in his time would have been "Leonardo Pisano" (Leonard from Pisa). The name "Fibonacci" comes from "Filius Bonaccio" - eg, the Bonaccio Family - which is perhaps the name of his Grandfather.

I especially enjoyed the view this book gave into the state of European mathematics at the beginning of the 1200's. Roman numerals aren't that hard for addition or subtraction (I didn't know that) - it's multiplication and division that is difficult with them. There were elaborate methods of computation that used fingers, and the Europeans of his era had their own kind of abacus (different from the Chinese one). Leonardo introduced to a broad public not only "Arabic" numerals, but also the algorithms we use to multiply and divide with them - as well as methods for computing square roots, cubic roots, and approaches for many kinds of practical problems. His book Liber Abbaci was scholarly, but it caught on and revolutionized the way merchants computed. His role was not unlike Steve Jobs or Bill Gates - taking known technology and making it available for the people who could take practical advantage of it. The book that did this was titled Liber Abbaci.

Leonardo wrote many books in his time, and was hugely influential in many kinds of mathematics. He was widely recognized for his role, but when books started to be printed, his own books (hand copied and thus relatively rare rare) became less important.

Then again, does the common person remember Brahmagupta as the first person to give the rules for the mathematical properties of 0? He is the person who first wrote rules like 0*x = 0, and 0 - x has the opposite sign of x. He did say that 0/0 = 0, but Newton and his science of infitesimals was a thousand years in the future. This was a revolutionary discovery of the 600s - a fact I also learned from this book.

Fibonacci numbers are an example that Lorenzo included in Liber Abbaci. From that book:

HOW MANY PAIRS OF RABBITS ARE CREATED BY ONE PAIR IN A YEAR

A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature of them in a single month to bear another pair, and in the second month those born to bear another.

---

At first, this sounded like an exponential series to me, but the key is that it takes a month for rabbits to become fertile. So, if the number of pairs of rabbits at month n is the number of pairs of rabbits at month n-1 (none died) plus the number of pairs rabbits at month n-2 (these are all now fertile).

I wish the book had been longer - some of the text is too terse to fully appreciate. For example, Devlin describes the occurrence of Fibonacci numbers in nature (eg, the number of petals on a flower is almost always a Fibonacci number). I learned why this is the case in another book (that I'm reading now).

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*The Man of Numbers*.