The form of the human dental arch

Abstract

The human dental arch form is shown to be accurately represented mathematically by the beta function. The average correlation coefficient between measured arch-shape data and the mathematical arch shape, expressed by the beta function, is 0.98 with a standard deviation of 0.02. Forty sets of casts--15 Class I, 16 Class II, and 9 Class III--were examined. A precision machine tool device was used to record the X-, Y-, and Z-coordinates of selected dental landmarks on all casts to 0.001 mm accuracy. The coordinates were processed through a computer curve-fitting program. The Class III mandibular arches had smaller arch depth and greater arch width (beginning in the premolar area) than the Class I arches. The Class II mandibular arches exhibited generalized reduced arch width and depth compared with the Class I arches. Maxillary arch depths were similar in all three groups. However, the Class III maxillary arch widths were greater from the lateral incisor-canine area distally compared with the Class I maxillary arch, and the Class II maxillary arch form was narrower than the Class I arch form from the lateral incisor-canine area distally. The beta function more accurately described the dental arch form than representations previously reported.