Fibonacci-Zahle ... | nemačko - engleski prevod



Nach dem italien. Mathematiker L. Fibonacci (um 1170, +nach 1240) benannte rekursive Zahlenfolge 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144., in der jedes Glied die Summe der beiden vorangehenden Glieder ist. Im 19. Jh. entdeckte man, daß die F. auch in der Natur vorkommen, z.B. in der anordnung der Knospen an einem Stengel, bei der Vermehrung von Tieren, in den Spiralen von Sonnenblumen.

1. Fibonacci numbers


In mathematics, an infinite series in which each successive integer is the sum of the two integers that precede it—for example, 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . . Fibonacci numbers are named for the thirteenth-century mathematician Leonardo Fibonacci of Pisa. In computing, Fibonacci numbers are used to speed binary searches by repeatedly dividing a set of data into groups in accordance with successively smaller pairs of numbers in the Fibonacci sequence. For example, a data set of 34 items would be divided into one group of 21 and another of 13. If the item being sought is in the group of 13, the group of 21 is discarded, and the group of 13 is divided into groups of 5 and 8; the search would continue until the item was located. The ratio of two successive terms in the Fibonacci sequence converges on the Golden Ratio, a “magic number” that seems to represent the proportions of an ideal rectangle. The number describes many things, from the curve of a nautilus shell to the proportions of playing cards or, intentionally, the Parthenon, in Athens, Greece. See also binary search.

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