Figure 2

2D view of the relationship between difference and ratio. Equation 2 at v = 300 (lower scale for values of x/y) or v = 1 (upper scale for values of x/y). Slices through x = –128, –64, –32, –16, –8, –4, –2, –1, 1, 2, 4, 6, 8, 16, 32, 64, 128 are shown and labelled in colour code. Datapoints were generated using y = –16 to –0.0001 and 0.0001 to 16. The orthogonal asymptotes of all hyperbles are u = x – v·y = ± ∞ for x/y → 0 and u = x – v·y = x for x/y → ± ∞. The only root of the function, thus, the saddle point formed by all hyperbles (cf. Fig. 1) is always x/y = v.