Introduction

What are the Fibonacci Numbers?

The Fibonacci Numbers are a sequence of numbers that were named after Leonardo of Pisa who originally introduced the numbers in a book Liber Abaci.

The first number of the sequence is 0, and the second number is 1. The third number is the sum of the previous two numbers of the sequence, therefore 1 again. The fourth number is the sum of the two numbers previous to that, so the fourth number is 2. The sequence goes on so that:

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F0

F1

F2

F3

F4

F5

F6

F7

F8

F9

F10

F11

F12

F13

F14

F15

F16

F17

F18

F19

F20

0

1

1

2

3

5

8

13

21

34

55

89

144

233

377

610

987

1597

2584

4181

6765


Why are the Fibonacci Numbers important?

The Fibonacci numbers have many applications in the real world, especially in nature. Also, the sequence has many imaginary applications, such as Phi, the golden ration. The rest of the applications will be explained throughout the site.

How do you find a specific Fibonacci Number?

You can find any Fibonacci number by counting them, which takes some time if you don't have the list of Fibonacci numbers listed at the end of this page, but you can also use the Binet Formula. (Bin-eh)

Before using the Binet Formula, you must understand two concepts.

1.The golden ratio is known as phi, but can be expressed as:

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(see phi proof)

Or about 1.6; the golden ration will be further explained on other pages of the website. Press this link.

2.If you divide Fn by Fn-1 with incredibly large values for N, the ratio will even out to be approximately the golden ration.


The Binet Formula (To find the Nth number in the Fibonacci Sequence):

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