Dental arch form, a new proposal based on an integral mathematical model
Date
2025-09-26
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad CES
Abstract
Introduction: The purpose of this study was to represent a mathematical model of dental arch geometry based on four intra-arch variables, representing a mandibular dental arch of triangular, oval, and square shapes, and to identify quantifiable parameters for classifying the geometry of these arches. Methods: Employing two parabolas, a mathematical formula was created that describes two curves; equations were developed for the anterior zone, delimited by the canines, and the posterior zone. The model was fed by canine and molar depth and width. Data reported in the literature were used to validate the model, and curves representing oval, triangular, and square arcs were created. Results: This study demonstrates that it is possible to plot the dental arch form in the three geometries and indicate a consistent aspect ratio between the three arch types, where the anterior zone represents the arch geometry. Conclusions: An equation can be derived from four intra-arc measurements to create a curve of the mandibular dental arch. This curve can provide an aspect ratio in the anterior region of the dental arch, enabling a more reliable geometry classification as square, triangular, or oval.
Description
Keywords
Arch form, Dental model, Mandibular arch, Mathematical model