Geometric and mathematical proportions and their relations to maxillary anterior teeth

One of the critical aspects of esthetic dentistry is creating geometric or mathematical proportions to relate the successive widths of the anterior teeth. The golden proportion, the recurring esthetic dental (RED) proportion, and the golden percentage are theories introduced in this field. The aim of this study was to investigate the existence of the golden proportion, RED proportion, and the golden percentage between the widths of the maxillary anterior teeth in individuals with natural dentition.

Standardized frontal images of 376 dental student smiles were captured. The images were transferred to a personal computer, the widths of the maxillary anterior teeth were measured, and calculations were made according to each of the above mentioned theories. The data were statistically analyzed using paired student T-test (level of significance P<0.05).

The golden proportion was found to be accurate between the width of the right central and lateral incisors in 31.3% of men and 27.1% of women. The values of the RED proportion were not constant, and the farther the one moves distally from the midline the higher the values. Furthermore, the results revealed the golden percentage was rather constant in terms of relative tooth width. The width of the central incisor represents 23%, the lateral incisor 15%, and the canine 12% of the width of the six maxillary anterior teeth as viewed from the front.

Both the golden proportion and the RED proportion are unsuitable methods to relate the successive widths of the maxillary anterior teeth. However, the golden percentage theory seems to be applicable to relate the successive widths of the maxillary anterior teeth if percentages are adjusted taking into consideration the ethnicity of the population.