swastika7

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As you can see, by attaching an arc from each "special case" in point in the above diagram (depicting the very small square circle areas), one forms two spirals, one spiral arm whose angle of inclination (36 degrees) is determined by the angle of the Pythagorean triangle (let this spiral be called PHI), and one spiral arm whose angle of inclination (45 degrees) is determined by the other angle, of the "equiangular" triangle (let this second spiral be called PI).

Here is a diagram depicting the complete two spirals for up to area 256 (square circle sixteen):