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What are Fibonacci numbers?

6 Answers
What is a Fibonacci number sequence? What is the significance of Fibonacci numbers and what are they used for?
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The Fibonacci numbers are integers found in the following sequence:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...

Each number in the sequence is the sum of the previous two numbers.

The sequence is named after Leonardo of Pisa, who was also known as Fibonacci. The numbers are used in the following areas:

Art: The relationship between the Fibonacci numbers and the golden ratio, in relation to body proportions.

Mathematics: Used to analyze Euclid's Algorithm to determine the highest common divisor between two integers.

Nature: The branching of trees, the number of leaves on a pinecone, leaf arrangements on a stem, and spiral shells are just a few examples of the Fibonacci numbers at work in nature. The reproduction of honeybees has rules that are based around the Fibonacci numbers.

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The Fibonacci number sequence starts off with

0, 1, 1, 2, 3, 5, 8, 13, ?

The next number is calculated by adding the two previous values together. So the next number would be

8 + 13 = 21

It is named after a guy called Leonardo Fibonacci (not da Vinci), who attempted to calculate the population growth of rabbits.

Nowadays it can be used as an algorithm for expanding a rectangle purely by adding squares (see attached image) in an outward spiral fashion. Other than that the only other uses I can think of are of purely academic nature...

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A

Fibonacci numbers or Fibonacci sequence is a sequence of numbers starting with 0 and 1 and following the general rule that every number in the sequence is a sum of the previous two numbers.

Thus the third number in the Fibonacci series is 0 + 1 = 1, the fourth number is 1 + 1 = 2, fifth number is 1 + 2 = 3, sixth is 2 + 3 = 5, then seventh is 3 + 5 = 8, eighth number is 5 + 8 = 13, ninth number is + 13 = 21, tenth number is 13 + 21 = 34 and so on..

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T

Fibonacci series starts with 0 then 1 and next elements are obtained by adding the previous two elements of the series.
i.e
0,1,1,2,3,5,8,11,23,34, and so on ..
This series has a wide range of applications..

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Fibonacci numbers are a sequence of numbers where the next is added. 1 1 2 3 5 8 13 21... And so forth.

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(duplicate answer)

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