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  Open main menu Fibonacci S  Sequence in Nature  In mathematics, the  Fibonacci numbers , commonly denoted  F n , form a sequence , called the  Fibonacci sequence , such that each number is the sum of the two preceding ones, starting from 0 and 1.    Fibonacci numbers are strongly related to the golden ratio;   Binet 's formula   expresses the  n th Fibonacci number in terms of  n  and the golden ratio, and implies that the ratio of two consecutive Fibonacci numbers tends to the golden ratio as  n  increases. Fibonacci numbers are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci. In his 1202 book Liber Abaci , Fibonacci introduced the sequence to Western European mathematics,  although the sequence had been described earlier in Indian mathematics,  as early as 200 BC in work by Pingala   on enumerating possible patterns of Sanskrit poetry formed from ...

                        FRACTAL GEOMETRY                  The formal mathematical definition of fractal geometry is by Benoit Mandelbrot. It says that a fractal is a set for which the Haudorff Besicovitch dimension strictly exceeds the topological dimension .However, this is a very abstract definition. Generally, we can define a fractal as a rough or fragmented geometric shape that can be subdivided in parts,  each of which is (at least approximately) a reduced -size copy of the whole. Fractals are generally self -similar and independent of scale.                   Fractal geometry is recent synthesis of old mathematical constructs. It is a misunderstood idea that is quickly becoming buried under grandiose terminology that serves no purpose. Its essence is induction using simple geometric constructs to transform initiating objects...