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Today is Fibonacci Day and to those not familiar with Fibonacci and the Fibonacci Sequence, below you’ll find some useful information including the Fibonacci Sequence formula and an amazing although slightly inaccurate representation of the Fibonacci Spiral.

From Wikipedia:

The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci (a contraction of filius Bonacci, “son of Bonaccio”). Fibonacci’s 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence may have been previously described in Indian mathematics.

Fibonacci numbers are used in the analysis of financial markets, in strategies such as Fibonacci retracement, and are used in computer algorithms such as the Fibonacci search technique and theFibonacci heap data structure. The simple recursion of Fibonacci numbers has also inspired a family of recursive graphs called Fibonacci cubes for interconnecting parallel and distributed systems. They also appear in biological settings, such as branching in trees, arrangement of leaves on a stem, the fruit spouts of a pineapple, the flowering of artichoke, an uncurling fern and the arrangement of a pine cone.

The Sequence is represented below:

0,1,1,2,3,5,8,13,21,34,55,89,144,…

Observing the sequence more closely you’ll notice that each number is the sum of the 2 numbers before it. You can start a Fibonacci Sequence with any 2 numbers, for instance starting with 5 and 6 the sequence would resemble something like this: 5,6,11,17,28,45,…

The Mathematical formula for the Fibonacci Sequence is below:

Below You’ll see A tiling with squares whose sides are successive Fibonacci numbers in length

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The next image will represent A Fibonacci spiral created by drawing arcs connecting the opposite corners of squares in the Fibonacci tiling; this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34

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Now for the grand finale, below if you will take the time to observe this amazing although slightly inaccurate representation of a Fibonacci Spiral. Try to pay attention to the spiral and how it doesn’t complete at the very end… :)

To learn more about Fibonacci and the origin and uses of the Fibonacci Sequence please refer to the following Wikipedia entry http://en.wikipedia.org/wiki/Fibonacci_number