Fibbonacci Numbers

Fibbonacci sequence is 1/2(5**-2 -1) = 1/1, 1/2, 2/3, 3/5, 5/8, 8/13, 13/21, 21/34, ... (more available here) converges after the 13th upon the golden ratio of 1.618.

fractions U/V representing screw like arrangement angle of rotation of the operation "s" is a fraction "u/v" of the full angle 360 degrees every "v"th point of the sequence "P sub n" lies on the same vertical, and "u" full turnings of the screw are necessary to get from P sub n to P sub (n+v) above it.

A similarity in one dimension that is not a mere translation has a fixed point "O" and is a dilation "s" form "O" in a certain ratio "a":1 where a <> 1. It is no essential restriction to assume a>0. Indefinite iteration of this operation generates a group SIGMA consisting of the dilations s**n (n=0,+-1,+-2,...).

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