A Mathematical Study of Anterior Dental Relations: Part II, Incisor and Canine Overjet

A mathematical model of anterior inter-arch relations was described in a previous article.¹ This model is modified and manipulated and, using hypothetical dental measurements, results are generated and presented. The present work continues the two-dimensional examination of anterior dental relations in the first article, the emphasis remaining on incisor and cauine overjet.

Other authors have started by observing ideal occlusions, then have worked backwards to gain ratios of preferred maxillary to mandibular teeth widths; this restricts their studies to Class I occlusions with complete anterior dentitions and similar anterior form of both arches. This paper has no premise of normal or initial ratios. Incorporation of multiple factors allows forming and testing of hypotheses of anterior dental relations. Many factors influence anterior dental relations in varying degrees. Some dental measurement changes examined here are: the sum of teeth widths in each arch; spacing; crowding; angle of the arc of each arch and the antero-posterior buccal relation. Summary tables are presented to aid the prediction of the direction of inter-arch response to change in a dental measurement. Some inferences are discussed and are presented as a series of principles considered valid for this model. The principles may warrant testing with other arch form models.