[ Back ]                     weblink to the PDF-Documents :         1.)     ►    The Ordered Distribution of Natural Numbers on the Square Root Spiral   

                                                      please also read  :      2.)    ►    The Distribution of Prime Numbers on the Square Root Spiral   

                                                                         and  :      3.)    ►    The distribution of numbers divisible by 2, 3, 5, 11, 13 or 17 on the square root spiral

  extract from the study :     

Abstract :

The most amazing property of the square root spiral is surely the fact, that the distance between the successive winds of the square root spiral quickly strives for the well known geometrical constant Pi.

All natural numbers, divisible by a certain prime factor, lie on defined spiral graphs on the Square Root Spiral ( or “Spiral of Theodorus”, or “Wurzelspirale” ). And the Square Numbers 4, 9, 16, 25, 36 … even form a highly three-symmetrical system of three spiral graphs, which divides the square root spiral into three equal areas.

A mathematical analysis shows that these spiral graphs are defined by quadratic polynomials.
The Square Root Spiral is a geometrical structure which is based on the three basic constants: 1, sqrt2 and pi , and the continuous application of the Pythagorean Theorem of the right angled triangle.
Fibonacci number sequences also play a part in the structure of the Square Root Spiral.

Fibonacci Numbers divide the Square Root Spiral into areas and angle sectors with constant proportions.

These proportions are linked to the “golden mean” ( golden section ), which behaves as a self-avoiding-walk- constant in the lattice-like structure of the square root spiral.

To learn more about these amazing facts, see my detailed introduction to the Square Root Spiral :

“ The ordered distribution of natural numbers on the Square Root Spiral “