Introduction
The study of the face and the ability to alter its form has fascinated mankind for thousands of years. The clinical ability to alter dentofacial form, whether through facial growth modification, orthodontics or surgery, requires an understanding of facial beauty, including the evaluation of facial esthetics, proportions and symmetry.
Many guidelines, norms, and standards have been proposed to describe ideal proportions in the human face, and for a long time, golden proportions have supposedly been apparent in the ideal human face.[1] The golden proportion was described geometrically in the 4th century BC by Euclid as the unique division of a line (AB) into 2 parts (AC and CB) in such a way that AB:AC=AC:CB.
Although Euclid is the oldest known writer to describe the construction of this golden proportion, the proportion was probably already known by the ancient Egyptians, since this ratio can be recognized in the large Egyptian pyramids from the 3rd millennium BC. A more accurate mathematical approach came from Fibonacci in the 12th century, in which the golden proportion was defined as phi, and was found to be equal to 1.618. The golden proportion is often associated with esthetics and harmony in many fields such as architecture, sculpture, music, poetry, the morphology of flowers, sea shells, mammals, and the human face.[2]
In orthodontics, Ricketts[3,4] was the first to claim that the analysis of a physically beautiful face should be approached mathematically, and he advocated the use of golden proportions in that respect.
The apparent widths of the maxillary anterior teeth on smile, and their actual mesio-distal width, differ because of the curvature of the dental arch. Particularly, only a portion of the canine crown can be seen in a frontal view. For best appearance, the apparent width of the lateral incisor should be 62% of the width of the central incisor, the apparent width of the canine should be 62% of that of the lateral incisor, and the apparent width of the first premolar should be 62% of that of the canine. This ratio of recurring 62% proportions appears in a number of other relationships in human anatomy, and is referred to as the “golden proportion.”[5]
Huntley rightly considers that the divine proportion-the golden rectangle, triangle, cuboid, and ellipse represents mathematical beauty and harmony.[6]