Golden Proportion in Maxillary Anterior Teeth Revisited

The golden ratio is widely cited as an ideal for maxillary anterior tooth proportions, yet studies report inconsistent conformity, and prevalence figures are almost always presented without a chance baseline against which “conformity” can be judged. The objective of this work was to determine whether the central-to-lateral incisor (CI/LI) and lateral-incisor-to-canine (LI/Can) apparent-width ratios of the maxillary anterior segment converge on a pre-specified proportional tolerance zone more often than chance, and to estimate the value on which these ratios actually center. In this cross-sectional analytical study, 100 young adults (20–30 years) attending the College of Dentistry, University of Baghdad, were consecutively screened; 50 with intact, unrestored, non-rotated maxillary anterior teeth were measured from standardized frontal intraoral photographs, and 41 remained after data verification excluded 9 records with duplicated values. Apparent widths of the central incisor, lateral incisor and visible canine were measured bilaterally by a single examiner using a purpose-built, cue-free landmarking application; a ratio was classified as convergent within 1.4–1.8. Convergence was benchmarked against a chance baseline (π₀ = 22.9%) derived from a log-uniform reference distribution, and the empirical center of each ratio was estimated by bootstrap geometric mean. CI/LI (mean 1.554 ± 0.114) converged within the tolerance zone in 36/41 participants (88%; 95% CI 74–95%), far exceeding chance (p < 0.001), whereas LI/Can (mean 1.344 ± 0.201) converged in only 12/41 (29%; 95% CI 18–44%), statistically indistinguishable from chance (p = 0.211). Both ratios lay significantly below Φ (Wilcoxon p ≤ 0.001). The bootstrap geometric mean of CI/LI was 1.55 (95% CI 1.517–1.585), an interval that excludes Φ. Maxillary CI/LI proportions cluster within a bounded interval centered near 1.55 rather than at Φ, and this clustering is real rather than a chance artefact; the LI/Can relation shows no such property. Smile-design guidance should treat the golden proportion as a range-based tolerance zone rather than a fixed target and reported “conformity” rates should always be benchmarked against a chance baseline.