# Fibonacci Number _ Which is often used and accurate.

Fibonacci Number _ Which is often used and accurate.

Fibonacci Number  In mathematics, the Fibonacci numbers are sequences defined recursively as follows:

F(n)= egin{cases} 0, & mbox{if }n=0; 1, & mbox{if }n=1; F(n-1)+F(n-2) & mbox{if not.} end{cases}

What are the Fibonacci numbers?

Image result for fibbonancci numbers The Fibonacci number series is a simple series of numbers whose order of numbers is the sum of the two previous numbers (0,1,1,2,3,5,8,13,21,...etc) The formula for the Fibonacci series can be written as follows Un = Un-2 + Un-1, meaning that the nth term is the sum of the previous two terms.

Explanation: this sequence starts from 0 and 1, then the next number is obtained by adding the two previous consecutive numbers. With this calculation, the first sequence of Fibonacci numbers is therefore:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946....

The Fibonacci number sequence can be expressed as follows:

Fn = (x1n – x2n)/ sqrt(5)

with

Fn is the nth Fibonacci number
x1 and x2 are solutions to the equation x2 – x – 1 = 0.

The ratio between Fn+1 and Fn is almost always the same for any value of n and starting from a certain value of n, this ratio is constant. This comparison is called the golden ratio, which is close to 1.618.
Floor setting with Fibonacci number sized squares
Origin

read also     what is the  fibonacci sequence? which one is the most accurate?

Based on Donald E. Knuth's book The Art of Computer Programming, this sequence was first described by Indian mathematicians Gopala and Hemachandra in 1150, when investigating various probabilities of stuffing things into pockets. In the western world, this sequence was first studied by Leonardo da Pisa, also known as Fibonacci (c. 1200), when discussing the ideal growth of the rabbit population.

Also read from the source

1. What are the next 3 numbers from the Fibonacci number pattern 4 7 11 18 29?
4, 7, 11, 18, 29, term 6, term 7, term 8. So, the next 3 numbers from the Fibonacci pattern are 47, 76, 123.1.

2. What are Fibonacci numbers used for?
Image result for Use of Fibonacci numbers
Fibonacci First developed by Leonardo di Pisa, otherwise known as Leonardo Fibonacci, a mathematician in the thirteenth century who published the book "Liber Abaci", the Fibonacci number sequence is now used in various disciplines, such as biology, astronomy, geology, music, architecture , and financial

3. When were the Fibonacci numbers invented?
However, before this sequence was discovered in the West by Leonardo da Pisa, based on Donald E. Knuth's book The Art of Computer Programming, this sequence was first described by Indian mathematicians Gopala and Hemachandra in 1150, while investigating various possibilities for inserting goods. -goods

4 Who invented the number pattern?
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Leonardo da Pisa or Leonardo Pisano (1175 – 1250), better known as Fibonacci, was an Italian mathematician best known as the discoverer of the Fibonacci numbers. Leonardo was instrumental in introducing the Arabic numeral writing and calculation system to the European world.