### The Distribution of Natural Numbers Divisible by 2, 3, 5, 11, 13 a...

##### By: Harry K. Hahn; Harry K. Hahn

The Square Root Spiral ( or “Spiral of Theodorus” or “Einstein-Spiral” ) is a very interesting geometrical structure, in which the square roots of all natural numbers have a defined (spatial ) position to each other. The Square Root Spiral develops from a right angled base triangle with the two legs ( cathets ) having the length 1, and with the long side ( hypotenuse ) having a length which is equal to the square root of 2. The Square Root Spiral is formed by further...

From the image FIG 1 it is evident that the numbers divisible by 2 ( marked in yellow ) lie on defined spiral graphs which have their starting point in or near the centre of the square root spiral. These spiral graphs have either a positive or a negative rotation direction. A spiral graph which has a clockwise rotation direction shall be called negative (N) and a spiral graph which has an counterclockwise rotation direction shall be called positive (P). The gre...