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Fibonacci$500692$ - translation to English
![[[Yellow chamomile]] head showing the arrangement in 21 (blue) and 13 (cyan) spirals. Such arrangements involving consecutive Fibonacci numbers appear in a wide variety of plants.](https://commons.wikimedia.org/wiki/Special:FilePath/FibonacciChamomile.PNG?width=200 "[[Yellow chamomile]] head showing the arrangement in 21 (blue) and 13 (cyan) spirals. Such arrangements involving consecutive Fibonacci numbers appear in a wide variety of plants.")
![The Fibonacci spiral: an approximation of the [[golden spiral]] created by drawing [[circular arc]]s connecting the opposite corners of squares in the Fibonacci tiling; (see preceding image)](https://commons.wikimedia.org/wiki/Special:FilePath/Fibonacci Spiral.svg?width=200 "The Fibonacci spiral: an approximation of the [[golden spiral]] created by drawing [[circular arc]]s connecting the opposite corners of squares in the Fibonacci tiling; (see preceding image)")
![Balance factor]]s green; heights red.<br />The keys in the left spine are Fibonacci numbers.](https://commons.wikimedia.org/wiki/Special:FilePath/Fibonacci Tree 6.svg?width=200 "Balance factor]]s green; heights red.<br />The keys in the left spine are Fibonacci numbers.")
![Biblioteca Nazionale di Firenze]] showing (in box on right) 13 entries of the Fibonacci sequence:<br /> the indices from present to XII (months) as Latin ordinals and Roman numerals and the numbers (of rabbit pairs) as Hindu-Arabic numerals starting with 1, 2, 3, 5 and ending with 377.](https://commons.wikimedia.org/wiki/Special:FilePath/Liber abbaci magliab f124r.jpg?width=200 "Biblioteca Nazionale di Firenze]] showing (in box on right) 13 entries of the Fibonacci sequence:<br /> the indices from present to XII (months) as Latin ordinals and Roman numerals and the numbers (of rabbit pairs) as Hindu-Arabic numerals starting with 1, 2, 3, 5 and ending with 377.")
![The Fibonacci numbers are the sums of the "shallow" diagonals (shown in red) of [[Pascal's triangle]].](https://commons.wikimedia.org/wiki/Special:FilePath/PascalTriangleFibanacci.svg?width=200 "The Fibonacci numbers are the sums of the \"shallow\" diagonals (shown in red) of [[Pascal's triangle]].")
Definition
Wikipedia
In mathematics and computing, Fibonacci coding is a universal code which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers. Each code word ends with "11" and contains no other instances of "11" before the end.
The Fibonacci code is closely related to the Zeckendorf representation, a positional numeral system that uses Zeckendorf's theorem and has the property that no number has a representation with consecutive 1s. The Fibonacci code word for a particular integer is exactly the integer's Zeckendorf representation with the order of its digits reversed and an additional "1" appended to the end.
