Fibonacci Sequence Essay

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Fibonacci Sequence The Fibonacci sequence was named after Leonardo of Pisa, “son of Bonaccio", who was known as Fibonacci. Fibonacci introduced a simple series of numbers in his book Liber abaci in 1202. In his book Fibonacci examined a problem whose solution was the Fibonacci sequence as we know it today. The original problem was about how fast rabbits could breed in ideal circumstances. He proposed this puzzle: Beginning with a single pair of rabbits, if every month each productive pairs bears a new pair, which becomes productive when they are 1 month old, how many rabbits will there be after n months? At the end of the first month, they mate, but there is still only 1 pair. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits. At the end of the third month, the original female produces a second pair, making 3 pairs in all. At the end of the fourth month, the original female has produced another new pair, and the female born two months ago produces her first pair also, making 5 pairs. From this puzzle he proposed that at the end of the nth month, the number of pairs of rabbits is equal to the number of new pairs (which is the number of pairs in month n − 2) plus the number of pairs alive last month (n − 1). This is the nth Fibonacci number. Each term in the Fibonacci sequence is called a Fibonacci number. Each Fibonacci number is obtained by adding the two previous Fibonacci numbers together. The first two numbers in the series are one and one. To obtain each number of the series you add the two numbers that came before it. In other words, each number of the series is the sum of the two numbers preceding it. Historically some mathematicians have considered zero to be a Fibonacci number placing it before the first 1 in the series. It is known as the zeroth Fibonacci number and has no real practical merit. In

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