Mathematical Tooth Proportions: A Systematic Review

Purpose The aim of this systematic review was to evaluate and compare three commonly used proportions that include the golden proportion, golden percentage, and Recurring Esthetic Dental (RED) proportion to identify which of the mathematical formulas, if any, can be used to provide predictable and repeatable esthetic clinical outcomes. Methods A comprehensive search of electronic databases that included EBSCO, ProQuest, SCOPUS, Science Direct, Wiley, Google Scholar and PubMed was conducted using the terms: golden proportion, golden percentage, and Recurring Esthetic Dental (RED) proportions alone or in concurrence with one or both ensuing terms: tooth proportions and esthetic tooth proportions. In addition, the following journals were hand searched for relevant articles: Journal of Prosthodontics, Journal of Prosthetic Dentistry and Journal of Esthetic and Restorative Dentistry. Related citations were also considered. Results Tooth proportions varied substantially in the natural dentition. No studies revealed findings that supported the use of one mathematical formula to predict esthetic success. The golden proportion is present between the central to lateral incisor in some cases, but rarely between the lateral incisor and the canine. When compared to the other proportions, the golden percentage provided better starting points for tooth shape and size, but only when values were adjusted to consider other factors such as ethnicity and/or facial proportions. Conclusion Mathematical formulas did not provide consistent results that would allow for their use as a standardized guide for esthetically pleasing smiles. Although the golden percentage may be a good starting point if the percentages are adjusted on a case-by-case basis, generalized esthetic ideals cannot be determined by a mathematical formula and are open to interpretation by both the clinician and the patient.

Automated summary

This systematic review evaluated and compared the effectiveness of three mathematical formulas – golden proportion, golden percentage, and RED proportion – in predicting esthetic clinical outcomes. Results showed significant variation in tooth proportions in the natural dentition, with the mathematical formulas not providing consistent results to guide aesthetically pleasing smiles.