As a circles radius (what the compass is set to) scribes 6 times around the circles circumference, the three corners of the 1st equilateral triangle (iteration 1) can be produced, and the apex of the 2nd triangle (iteration 2) can also be marked. With the compass still at this 1st setting, a segment of the Koch Spiral - from apex 1 to apex 2 (iteration 1 to iteration 2) - is created. The apexes of every triangle in the iteration series are the tangent points of the spiral.
Find the centre the 2nd triangle, and repeat the process. The process can be repeated - both zooming in or zooming out - to infinity.
|Asymmetric circles developing the Koch Spiral.|
More to come, and refer back to my entry on wave particle duality.
I would like to dedicate this entry to my Technical Drawing teacher Mr. D Pethig, Southland Boys´ High School, NZ
The figure below is the Koch Snowflake Spiral developed using Nspire software.