The dental arch form revisited

Recently, the beta function has been shown to be an accurate mathematical model of the human dental arch. In this research, we tried to find the equation of a curve that would be similar to the generalized beta function curve and at the same time could represent tapered, ovoid, and square dental arches. A total of 23 sets of naturally well-aligned Class I casts were selected, and the depths and widths of the dental arches were measured at the canine and second molar regions. Using the mean depths and widths, functions in the form of Y = AXm + BXn were calculated that would pass through the central incisors, canines, and second molars. Each function was compared with the generalized beta function with the use of root mean square values. It was shown that the polynomial function Y = AX6 + BX2 was the nearest to the generalized beta function. Then the coordinates of the midincisal edges and buccal cusp tips of each dental arch were measured, and the correlation coefficient of each dental arch with its corresponding sixth order polynomial function was calculated. The results showed that the function Y = AX6 + BX2 could be an accurate substitute for the beta function in less common forms of the human dental arch.