This is a curve formed as the intersection of a radius and a line segment moving at corresponding rates. A square and a circle are drawn so that one corner of the square is the center of the circle, and the side of the square is the radius of the circle. The idea is this. A radius falls over from the side of the square to the base at a constant rate. At the same time, a line segment falls from the top of the square at constant rate. Both start moving at the same time, and both hit the bottom at the same time.
Thus, the ratio, change in arc length/ displacement of falling cross piece, represents the speed of the sweeping radius relative to the falling cross piece. Since both move at constant speeds, this ratio is always the same value. With some knowledge of "modern" trigonometry, it can then be calculated. The length of the arc swept out from beginning to end is pi/2 radians(90 deg.) time radius length. The distance the cross piece falls is simple the length of the square's side. But, since the length of the square's side is equal to the length of the radius, (pi/2) times radius length/side length= pi/2. Thus, the curve is a pictorial representation of the irrationality of pi.