Assessment of the incisor angles as a function of golden proportion and lower facial height

Mathematical models to determine diverse parameters in biological systems have been a challenging and interesting topic for the scientific community. This work aimed to determine the angles of the lower and upper incisor teeth as a function of the angle of the lower facial height and the golden proportion. The cephalometric parameters reported by Ricketts like the lower facial height angle, the axis of the mandibular body (Xi-Pm), the line that forms the mandibular geometric center with the anterior nasal spine (Xi-ENA), the occlusal plane, the dental line, and the upper and lower incisors lines and some cephalometric constraints were used to determine the proposed models.The analysis of several values for the lower facial height in the Ricketts range showed that both the model for the upper incisor (A) and lower incisor (B) provide functional values for these angles, which are within the statistical range reported by Ricketts with a maximum mean deviation of 1.58° and a maximum percentage difference of up to 10.40%. Outside of the Ricketts range, a maximum mean deviation of 5.15° and a maximum difference of up to 49.72% was found regarding the mean values. As a first approximation, the proposed models let us determine and personalize the target angle for orthodontic treatment of the upper and lower incisors based on the lower facial height of each patient and the golden proportion. These models can be a starting point for further research in this area, considering other parameters to be added to the proposed models.