complete

Here we can see that, by measuring the circle's radius as the hypotenuse of the "Golden Ratio" Pythagorean triangle, we can yield the larger areas of the base 8,10,12 squared circles.

Therefore, these are the two ways to yield a "square circle" from applying the Pythagorean triangle with its "Golden Ratio" of 3:4:5 to split the fifteen degree angle difference between 45/45 fractal expansion (base twelve hypotenuse) and the 30/60 gnomonic expansion (base ten hypotenuse).

These lengths for the hypotenuse/radius of the square/circle are derived by continuing to follow the gnomonic and fractal expansion rates up to base 12,13,16 areas.

Here are all the fundamental measures for the Pythagroean square/circle formula for any figure up to circle radius eight.