Translation and analysis of words by ChatGPT artificial intelligence
On this page you can get a detailed analysis of a word or phrase, produced by the best artificial intelligence technology to date:
- how the word is used
- frequency of use
- it is used more often in oral or written speech
- word translation options
- usage examples (several phrases with translation)
- etymology
Fibonacci numbers - 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]].")
![[[Priest]], [[Levite]], and furnishings of the [[Tabernacle]]](https://commons.wikimedia.org/wiki/Special:FilePath/Figures.jpg?width=200 "[[Priest]], [[Levite]], and furnishings of the [[Tabernacle]]")
![[[Balaam]] and the Angel (illustration from the 1493 ''[[Nuremberg Chronicle]]'')](https://commons.wikimedia.org/wiki/Special:FilePath/Nuremberg chronicles f 30r 2.png?width=200 "[[Balaam]] and the Angel (illustration from the 1493 ''[[Nuremberg Chronicle]]'')")
Definition
Wikipedia
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the first few values in the sequence are:
- 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, also known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book Liber Abaci.
Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the Fibonacci Quarterly. Applications of Fibonacci numbers include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern, and the arrangement of a pine cone's bracts.
Fibonacci numbers are also strongly related to the golden ratio: Binet's formula expresses the nth Fibonacci number in terms of n and the golden ratio, and implies that the ratio of two consecutive Fibonacci numbers tends to the golden ratio as n increases. Fibonacci numbers are also closely related to Lucas numbers, which obey the same recurrence relation and with the Fibonacci numbers form a complementary pair of Lucas sequences.
