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Old 04-10-2014, 08:58 AM
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Clampy Clampy is offline
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Math Geek will like this
It's in the tool song lateralus but it's a nod to the never ending spiral of the Fibonaci Sequence



In mathematics, the Fibonacci numbers or Fibonacci series or Fibonacci sequence are the numbers in the following integer sequence:[1][2]


or (often, in modern usage):

(sequence A000045 in OEIS)
By definition, the first two numbers in the Fibonacci sequence are 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two.

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation


with seed values[1][2]


or[3]


The Fibonacci sequence is named after Fibonacci. His 1202 book Liber Abaci introduced the sequence to Western European mathematics,[4] although the sequence had been described earlier in Indian mathematics.[5][6][7] By modern convention, the sequence begins either with F0 = 0 or with F1 = 1. The Liber Abaci began the sequence with F1 = 1, without an initial 0.

Fibonacci numbers are closely related to Lucas numbers in that they are a complementary pair of Lucas sequences. They are intimately connected with the golden ratio; for example, the closest rational approximations to the ratio are 2/1, 3/2, 5/3, 8/5, ... . Applications include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings,[8] such as branching in trees, phyllotaxis (the arrangement of leaves on a stem), the fruit sprouts of a pineapple,[9] the flowering of artichoke, an uncurling fern and the arrangement of a pine cone.[10]



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