................................MERKURIUSZ

phiboncci sequence
Number phi (Φ = 1,618) is a very special number. Evidences of existence are everywhere.  That all is based on phibonacci sequence .Before I will say more about occurrence, I want to teel you something about history and about great italian mathematician.

fibonacci1

Leonardo phibonacci
(1175 r. – 1250 r.)
That is basic phi model

 frac{a+b}{a} = frac{a}{b} equiv varphi,

and it equals:

varphi = frac{1+sqrt{5}}{2} = 1,61803,39887ldots

Number phi has been discovered by Leonardo from Piza (caled phibonacci) also owing to him we are using arabic number system.
1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 …
1/1= 1 13/8= 1.625
2/1= 2 21/13= 1.615384615
3/2= 1.5 34/21= 1.619047619
5/3= 1.66666667 55/34= 1.617647059
8/5= 1.6 89/55= 1.618181818
(phi)= 1.61803398874988…
Golden angle
That is 137.51*.
360-360*2/3=120, 360-360*5/8=144, 360-360*8/13=138.4615, …

Golden Spiral
Golden spiral is graphic interpretation of phiboncci sequence. phirst and second number are one. So ther is drown…

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