### Topic Page: Fibonacci numbers

**Fibonacci sequence**

*The Penguin Dictionary of Mathematics*

The sequence 1, 1, 2, 3, 5, 8, 13, 21, … where each term, after the first two, is the sum of the preceding pair of terms. Sometimes the sequence is begun 0, 1, 1, …. These Fibonacci numbers originally arose from a problem about the breeding of rabbits posed by Fibonacci in his Liber abaci. But they also occur elsewhere in the natural world, for example as the numbers of ancestors of a male honeybee in different generations. The sequence also has several interesting mathematical properties: for example, every two adjacent terms are relatively prime; any natural number is a sum of distinct Fibonacci numbers; and the ratios of successive terms, 1/1, 2/1, 3/2, 5/3, … get closer and closer to the golden ratio (see golden section).

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