Fibonacci (Leonardo of Pisa)
Summary
- 1170-1240
- Italian mathematician who introduced indo-arabic numbers to the west and also discovered the Fibonacci sequence
Details
- In 1202 he wrote a book on maths called 'Liber Abaci' that introduced Indo-arabic numbers to the West, which were way better than the commonly used Roman numerals
- He described the 'Fibonacci sequence' of numbers ( 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...) that occur when the 2 preceding numbers are added together. This series appears often in nature, and is also the basis for the 'golden mean'
References
Quotes
The man who reintroduced zero to the West was Leonardo of Pisa. The son of an Italian trader, he traveled to northern Africa. There the young man—better known as Fibonacci—learned mathematics from the Muslims and soon became a good mathematician in his own right.
Fibonacci is best remembered for a silly little problem he posed in his book, Liber Abaci, which was published in 1202. Imagine that a farmer has a pair of baby rabbits. Babies take two months to reach maturity, and from then on they produce another pair of rabbits at the beginning of every month. As these rabbits mature and reproduce, and those rabbits mature and reproduce, and so on, how many pairs of rabbits do you have during any given month?
Well, during the first month, you have one pair of rabbits, and since they haven’t matured, they can’t reproduce. During the second month you still have only one pair.
But at the beginning of the third month, the first pair reproduces: you’ve got two pairs. At the beginning of the fourth month, the first pair reproduces again, but the second pair is not mature enough: three pairs. The next month the first pair reproduces, the second pair reproduces, since it has reached maturity, but the third pair is too young. That is two additional pairs of rabbits: five in all.
The number of rabbits goes as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,…; the number of rabbits you have in any given month is the sum of the rabbits that you had in each of the two previous months. Mathematicians instantly realized the importance of this series. Take any term and divide it by its previous term. For instance, 8/5 = 1.6; 13/8 = 1.625; 21/13 =1.61538…. These ratios approach a particularly interesting number: the golden ratio, which is 1.61803….
Pythagoras had noticed that nature seemed to be governed by the golden ratio. Fibonacci discovered the sequence that is responsible. The size of the chambers of the nautilus and the number of clockwise grooves to counterclockwise grooves in the pineapple are governed by this sequence. This is why their ratios approach the golden ratio.
Though this sequence is the source of Fibonacci’s fame, Fibonacci’s Liber Abaci had a much more important purpose than animal husbandry. Fibonacci had learned his mathematics from the Muslims, so he knew about Arabic numerals, including zero. He included the new system in Liber Abaci, finally introducing Europe to zero. The book showed how useful Arabic numerals were for doing complex calculations, and the Italian merchants and bankers quickly seized upon the new system, zero included.