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Fibonacci Sequence


The Fibonacci sequence was invented by the Italian Leonardo Pisano Bigollo (1180-1250), who is known in mathematical history by several names: Leonardo of Pisa (Pisano means "from Pisa") and Fibonacci (which means "son of Bonacci").

Fibonacci, the son of an Italian businessman from the city of Pisa, grew up in a trading colony in North Africa during the Middle Ages. Italians were some of the western world's most proficient traders and merchants during the Middle Ages, and they needed arithmetic to keep track of their commercial transactions. Mathematical calculations were made using the Roman numeral system (I, II, III, IV, V, VI, etc.), but that system made it hard to do the addition, subtraction, multiplication, and division that merchants needed to keep track of their transactions.

While growing up in North Africa, Fibonacci learned the more efficient Hindu-Arabic system of arithmetical

  Newborns (can't reproduce)   One-month-olds (can't reproduce)   Mature Pairs (can reproduce)   Total Pairs
Each number in the tablerepresents a pair of rabbits. Each pair of rabbits can only give birth after its first month of life. Beginning in the third month, the number in the "Mature pairs" column represents the number of pairs that can bear rabbits. The numbers in the "Total Pairs" column represent the Fibonacci sequence.
Month 1 1 + 0 + 0 = 1
Month 2 0 + 1 + 0 = 1
Month 3 1 + 0 + 1 = 2
Month 4 1 + 1 + 1 = 3
Month 5 2 + 1 + 2 = 5
Month 6 3 + 2 + 3 = 8
Month 7 5 + 3 + 5 = 13
Month 8 8 + 5 + 8 = 21
Month 9 13 + 8 + 13 = 34
Month 10 21 + 13 + 21 = 55

notation (1, 2, 3, 4...) from an Arab teacher. In 1202, he published his knowledge in a famous book called the Liber Abaci (which means the "book of the abacus," even though it had nothing to do with the abacus). The Liber Abaci showed how superior the Hindu-Arabic arithmetic system was to the Roman numeral system, and it showed how the Hindu-Arabic system of arithmetic could be applied to benefit Italian merchants.

The Fibonacci sequence was the outcome of a mathematical problem about rabbit breeding that was posed in the Liber Abaci. The problem was this: Beginning with a single pair of rabbits (one male and one female), how many pairs of rabbits will be born in a year, assuming that every month each male and female rabbit gives birth to a new pair of rabbits, and the new pair of rabbits itself starts giving birth to additional pairs of rabbits after the first month of their birth?

Table 1 illustrates one way of looking at Fibonacci's solution to this problem.

Additional topics

Science EncyclopediaScience & Philosophy: Ferroelectric materials to Form and matterFibonacci Sequence - History, Other Fibonacci Sequences, The Fibonacci Sequence In Nature