Fibonacci numbers

Fibonacci numbers

In mathematics, a sequence of numbers with surprisingly useful applications in botany and other natural sciences. Beginning with two 1's, each new term is generated as the sum of the previous two: 1, 1, 2, 3, 5, 8, 13, . . . . The 13th-century mathematician Leonardo of Pisa (c. 1170–after 1240), also known as Fibonacci, discovered the sequence but did not explore its uses, which have turned out to be wide and various. For example, the number of petals in most types of flowers and numbers involved in branching and seed-formation patterns come from the Fibonacci sequence. The ratio of any two successive terms approaches the value of the golden ratio as the terms become large.

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A series of whole numbers in which each number is the sum of the two preceding ones: 1, 1, 2, 3, 5, 8, 13, etc. It is used to speed up binary searches by dividing the search into the two lower numbers; for example, 13 items would be divided into 5 and 8 items; 8 items would be divided into 5 and 3.