Fig. 2. A geometrical construction leading from x to 1: (1+x) and 1:(1+x). A line is drawn from the lower left hand corner of a rectangle to the point x = N/D on a number line superimposed on the top edge of the rectangle. At the point where this line crosses the diagonal draw a vertical line. The vertical line marks the number line at x/(1+x) = N/(N+D). Next rotate Figure 1 by a halfturn; the vertical line intercepts a number line on the rotated edge of the rectangle at 1/(1+x) = D/(N+D). | top of page | back to text |