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In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers , commonly denoted F n .
In reading Liber Abaci, it is helpful to understand Fibonacci's notation for rational numbers, a notation that is intermediate in form between the Egyptian fractions commonly used until that time and the vulgar fractions still in use today. [13] Fibonacci's notation differs from modern fraction notation in three key ways:
In the Fibonacci sequence, each number is the sum of the previous two numbers. Fibonacci omitted the "0" and first "1" included today and began the sequence with 1, 2, 3, ... . He carried the calculation up to the thirteenth place, the value 233, though another manuscript carries it to the next place, the value 377.
For any integer n, the sequence of Fibonacci numbers F i taken modulo n is periodic. The Pisano period, denoted π ( n ), is the length of the period of this sequence. For example, the sequence of Fibonacci numbers modulo 3 begins:
In 1202, Leonardo Fibonacci introduced the Fibonacci sequence to the western world with his book Liber Abaci. [5] Fibonacci presented a thought experiment on the growth of an idealized rabbit population. [6] Johannes Kepler (1571–1630) pointed out the presence of the Fibonacci sequence in nature, using it to explain the pentagonal form of ...
The Fibonacci sequence is constant-recursive: each element of the sequence is the sum of the previous two. Hasse diagram of some subclasses of constant-recursive sequences, ordered by inclusion In mathematics , an infinite sequence of numbers s 0 , s 1 , s 2 , s 3 , … {\displaystyle s_{0},s_{1},s_{2},s_{3},\ldots } is called constant ...
Virahanka (Devanagari: विरहाङ्क) was an Indian prosodist who is also known for his work on mathematics.He may have lived in the 6th century, but it is also possible that he worked as late as the 8th century.
François Édouard Anatole Lucas (French pronunciation: [fʁɑ̃swa edwaʁ anatɔl lykɑ]; 4 April 1842 – 3 October 1891) was a French mathematician.Lucas is known for his study of the Fibonacci sequence.