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The name he is commonly called, Fibonacci, was made up in 1838 by the Franco-Italian historian Guillaume Libri [9] [10] and is short for filius Bonacci ('son of Bonacci'). [11] [c] However, even earlier, in 1506, a notary of the Holy Roman Empire, Perizolo mentions Leonardo as "Lionardo Fibonacci". [12]
The Fibonacci numbers are the best known concept named after Leonardo of Pisa, known as Fibonacci. Among others are the following. Among others are the following. Concepts in mathematics and computing
The number in the n-th month is the n-th Fibonacci number. [20] The name "Fibonacci sequence" was first used by the 19th-century number theorist Édouard Lucas. [21] Solution to Fibonacci rabbit problem: In a growing idealized population, the number of rabbit pairs form the Fibonacci sequence.
The n-Fibonacci constant is the ratio toward which adjacent -Fibonacci numbers tend; it is also called the n th metallic mean, and it is the only positive root of =. For example, the case of n = 1 {\displaystyle n=1} is 1 + 5 2 {\displaystyle {\frac {1+{\sqrt {5}}}{2}}} , or the golden ratio , and the case of n = 2 {\displaystyle n=2} is 1 + 2 ...
A Fibonacci word is a specific sequence of binary digits (or symbols from any two-letter alphabet). The Fibonacci word is formed by repeated concatenation in the same way that the Fibonacci numbers are formed by repeated addition. It is a paradigmatic example of a Sturmian word and specifically, a morphic word.
Name First elements Short description OEIS Mersenne prime exponents : 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... Primes p such that 2 p − 1 is prime.: A000043 ...
That is to say, the Fibonacci sequence is a divisibility sequence. F p is prime for 8 of the first 10 primes p; the exceptions are F 2 = 1 and F 19 = 4181 = 37 × 113. However, Fibonacci primes appear to become rarer as the index increases. F p is prime for only 26 of the 1229 primes p smaller than 10,000. [3]
Fibonacci instead would write the same fraction to the left, i.e., . Fibonacci used a composite fraction notation in which a sequence of numerators and denominators shared the same fraction bar; each such term represented an additional fraction of the given numerator divided by the product of all the denominators below and to the right of it.