Comment by lainga
What privileges the square root over any other fractional power?
What privileges the square root over any other fractional power?
Indeed. Related is the Ammann-Beenker tiling and it's connections to the 'Silver Ratio' of sqrt(2) + 1.
* https://en.wikipedia.org/wiki/Silver_ratio
* https://en.wikipedia.org/wiki/Ammann%E2%80%93Beenker_tiling
Finding intersection points of a circle with a line is equivalent to solving a system of equations, where one equation is that of a circle, (x-a)^2 + (y-b)^2 = r^2, and the second is that of a line, Ax + By = C. To solve it, you’ll be taking square roots, and not other roots. Similarly, to find intersection of two circles, you’ll be taking square roots, and not other roots.