The Fibonacci sequence is one of the most famous formulas in mathematics. Each number in the sequence is the sum of the two numbers that precede it. So, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. The mathematical equation describing it is Xn+2= Xn+1 + Xn.
The Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of the preceding two numbers. If the Fibonacci sequence is denoted F (n), where n is the first term in the sequence, the following equation obtains for n = 0, where the first two terms are defined as 0 and 1 by convention:
F (0) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ...
In some texts, it is customary to use n = 1. In that case, the first two terms are defined as 1 and 1 by default, and therefore:
F (1) = 1, 1, 2, 3, 5, 8, 13, 21, 34 ...
The Fibonacci sequence is named for Leonardo Pisano (also known as Leonardo Pisano or Fibonacci), an Italian mathematician who lived from 1170 - 1250. Fibonacci used the arithmetic series to illustrate a problem based on a pair of breeding rabbits:
"How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?" The result can be expressed numerically as: 1, 1, 2, 3, 5, 8, 13, 21, 34 ...
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