Faces

This is where the algebraic portion comes in. Let us say that there is a circle with a radius whose value is an element in the set of positive integers, or Z+. 

Let us say that the value of the circle's radius is 8. 

At every integer value, one could draw a triangle from the preceding point of integer values (i.e. if the point in question is (4, 0), then the point (3, 0) will have a line drawn to it). Then, a straight line will be draw from (4, 0) to circumference, parallel to the y-axis. At this point (circumference intersection with the line x=4), a straight line segment is drawn to the point (3, 0). 

The value of the line x=4 from (4, 0) to the circumference of the circle is the 48^(1/2).

This exercise can be done for a circle with the value of the radius as an element of Z+.

The following are derivations of the proof listed above.