square roots as points of intersection of two circles.

Credit to whoever cast this mathemagical spell at Perspective Infinity. 

A circle of radius r₃ lies on the plane.


Within the circle are inscribed six others: three white ones of radius 1/r₃, which is the curvature of the white circle; two orange ones of radius (r₃² + 2)/2r₃; and a red one of radius . The point at which the red intersects the orange is the square root of r₃.