
ALT Fig. 1. 3.2radius² is the exact area of a circle. A circle is cut into quadrants. Each one is aligned to each vertices of a square. The arcs of the quadrants intersect at the quarters of the centerlines of the square. The ratio between the radius and the side of the square is calculable. r = √((side/2)² + (side/4)²) = side√5/4

ALT Fig. 1. 3.2radius² is the exact area of a circle. A circle is cut into quadrants. Each one is aligned to each vertices of a square. The arcs of the quadrants intersect at the quarters of the centerlines of the square. The ratio between the radius and the side of the square is calculable. r = √((side/2)² + (side/4)²) = side√5/4

ALT Fig. 2. 6.4radius is the exact circumference of a circle derived algebraically by subtracting the area of a circle from a larger one and dividing the result by the difference of their radii which is the theoretical width of the circumference, denoted as x. C = 3.2(r² - (r - x)²) / x = 6.4r - 3.2x The width of the circumference is just theoretical. It separates the circumference from the rest of the circle. Its value may approach zero. That makes the value of 6.4r - 3.2x rather exactly 6.4r.



























































