The biologic significance of the divine proportion and Fibonacci series

Abstract

This article shows the application of basic mathematical and geometric principles to the normal morphology of structures regularly involved in orthodontics and dentistry. For appreciation of beauty, it has been suggested that the human mind functions at the limbic level in attraction to proportions in harmony with the Golden Section. This is a proportion of 1.618 and its reciprocal 0.618 in geometry. Fibonacci numbers express precisely the same ratio and are mathematically unique and mysterious. Questions arose regarding these geometric and mathematical relationships in our living patients. Studies were conducted from measurements of models of the teeth of normal-occlusion subjects, the photographs of the faces of commercial models, and conditions found in lateral and frontal cephalometric head films. Variations of the beautiful photographic models were analyzed together with computerized composites of patients with ideal occlusions. Several key relationships were found. The investigation yielded useful relationships for all aspects of dentistry and particularly for orthodontics and orthognathic surgery. The normal face and the occlusion of the teeth have a majestic beauty. The study strongly suggests that esthetics can indeed be made scientific rather than the need to resort to subjective perceptions as in the past.