Sir, I thank Dr A. Astakhov for contributing to the discussion on the golden proportion (BDJ 2008; 205: 61). It must be agreed that if good reference points like contact points or incisal edges are lost it makes the task a little more difficult and 0.5 mm makes a big difference to the aesthetics of the anterior teeth.

Dr Astakhov emphasises a main point that I cannot repeat often enough, that the golden proportion can only be evaluated when looking at the patient face on. It is erroneous to try to determine this with the gauge on the curve of the arch, as the parallax error can be very large. Figure 1 shows the gauge accurately superimposed on the golden proportion lines between the teeth, but also that the line of vision can give a huge parallax error. I have to disagree, however, about using the golden mean gauge on photographs where the gauge is extremely accurate giving remarkable aesthetic diagnostic information, because here the curve of the arch is reduced to the flat plane on the photograph.

Figure 1: The erroneous use of the golden mean gauge due to parallax.
figure 1

The golden mean gauge is erroneously superimposed on the golden proportion lines between the central and lateral incisor teeth. The gauge shows a grossly distorted enlargement of the bicuspid. The more the arch is tapered the worse the effect

Full size image

The easiest way to solve the problem clinically and in the laboratory is to use cheap, hygienic, disposable paper grids. Figure 2 shows the grid being used with natural teeth and demonstrates how well they fit the grid spaces irrespective of curvature and irrespective of whether the arch is broad or narrow. These grids in the golden proportion will help to solve most proportional problems. I find the formula suggested by Radlinsky hard to understand and I could not find any written reference to it. However, the formula does suggest that the widths are symmetrical, although perfect symmetry is very rare in nature and indeed when the teeth are constructed totally symmetrically (which the patient always requests), there is a distinct loss of naturalness and charm.

Figure 2
figure 2

The paper grids in the golden proportion showing how perfectly the teeth fit the spaces in a natural dentition

Full size image