Assessment of divine proportion in the cranial structure of individuals with Angle Class II malocclusion on lateral cephalograms

INTRODUCTION: The study of the Divine Proportion (Φ = 1.618) began with the Greeks, having as main researchers the mathematician Pythagoras and the sculptor Phidias. In Dentistry, Ricketts (1981-82) was an early to study this issue. OBJECTIVE: This study proposed to evaluate how some cephalometric measures are presented in relation to the Divine Proportion, with the total of 52 proportions, formed by 28 cephalometric landmarks. METHODS: Lateral cephalograms of 40 Class II adults patients aging from 17 to 45 years (13 male and 27 female) were evaluated. The linear distances between the landmarks were measured using Radiocef Studio software. RESULTS: After statistical analysis, the data shown an average of 65,48% in the Divine Proportion, 17,5% in the relation Ans-Op/V1S-DM16 and 97,5% in the relations Na-Me/Na-PoNa e Na-PoNa/Na-Gn. CONCLUSION: Among all cephalometric measurements investigated, the lower facial third and the dental arches showed the smallest percentages of Divine Proportion.

Divine proportions and facial esthetics after manipulation of frontal photographs.

AIM: To investigate the relationship between divine proportion and facial esthetics in frontal photographs as well as whether any of the 4 ratios for manipulation provide more favorable facial esthetics. MATERIAL AND METHODS: The sample comprised 20 frontal photographs of Caucasian individuals (11 males and 9 females). The photographs were digitized and stored on a compact disk. A photometric analysis was created with 7 facial segments that were measured on Image Tool software and 4 ratios between 2 facial segments calculated using Microsoft Excel. This manipulation led to 5 different photographs of the same individual: one photograph with no manipulation and the others with 1 of the ratios manipulated in the Deformer 2.0 to very close or equal to 1.618. Thereafter, the 5 photographs of all individuals were evaluated by 12 examiners. The examiners selected those photographs that were esthetically more pleasant. CONCLUSION: After evaluation, a chi-square test revealed a relationship between divine proportion and facial esthetics. Among the ratios selected, R1 and R2 provided more favorable facial esthetics.