33 lines
1.7 KiB
Markdown
33 lines
1.7 KiB
Markdown
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title: Fibonacci Number
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---
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## Fibonacci Number
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Fibonacci Number is a term of the <i>Fibonacci sequence</i>, probably one of the most famous
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sequences out there. In this sequence, each new number is the sum of the previous two numbers:
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- F(n) = F(n - 1) + F(n - 2).
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So let's take it from the start, and it starts with 0. The next number will be the sum of the
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previous two numbers, which will be 1. Therefore the next number will also be 1.
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Then comes the third number, which will be the sum of 1 and 1, which is 2.
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Then comes 1 and 2, which is 3, 2 and 3, which is 5, 3 and 5, which is 8, and so on.
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This sequence is seen in many places in nature, like the shell of a snail or the
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spiral patterns of a sunflower.
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The initial values are :
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0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...
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If you desire to make a program which finds the fibonacci-number after x iterations, make sure you
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have a large enough boundary. The value grows exponentially quick, and will therefore take more
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space than expected.
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Something that is fascinating about the Fibonnaci sequence is its existence in nature. It can be found in flower petals, seed heads, pinecones, shells, hurricanes, and so much more.
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### More Information:
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* A lot of information about Fibonacci numbers, including the proof of Binet's formula, can be found [here](https://en.wikipedia.org/wiki/Fibonacci_number).
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* [The On-Line Encyclopedia of Integer Sequences: Fibonacci numbers](http://oeis.org/A000045)
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* [The Fibonacci sequence as it is found in the musical scale.](https://www.youtube.com/watch?v=2pbEarwdusc)
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* [The Fibonacci sequence in nature](https://io9.gizmodo.com/5985588/15-uncanny-examples-of-the-golden-ratio-in-nature)
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