Today, more than any other era in history, there is an overwhelming pre-occupation with beauty. For centuries, poets and artists have been unsuccessful in creating a consistent definition of “beauty”. There have been many artistic interpretations, yet a reproducible mathematical definition is absent and clearly needed find more .
Historically, previous attempts at evaluating attractive biological standards have created good tools, but not good definitions. According to the Pythagoreans of ancient Greece, “Everything is arranged according to the numbers.” It was hypothesized that mathematics was the unifying force between life, art, the gods, and the universe. By studying the numbers and the theorems of Pythagoras, it was believed that perfection, harmony, and balance would be revealed.
Leonardo Fibonacci, a mathematician in 13th century Italy, charted the population of rabbits and discovered a number series from which the Golden Ratio is derived. The number sequence in the series is the sum of the two preceding numbers. The number series starts with the sequence “0, 1, 1, 2, 3, 5…” and continues to infinity. From this sequence, the Golden Ratio is produced by dividing each number in the series by the number that precedes it. The ratio continues and eventually converges to what is known as Phi (1.618…), named after Phidias, the Greek sculptor.7,8 The mathematical concept of the Golden Ratio has had a great influence on aesthetics because it provides a rational basis for analysis. It does not, however, provide a definition of facial beauty.
Regardless of age or ethnicity, there is in every beautiful face, a certain proportion and harmony between facial segments. The proper balance of position and proportion between facial features is very pleasing to the eye. Consider the positioning of the brow, eyes, cheek, nose, lip and chin in relation to the facial height. According to R.M. Ricketts, D.D.S, the ratio of the distance from the eyes to the nasal base, and the distance from the labial commissure to the chin, is 1:1 in a normal face. The ratio of the distance from the nasal base to the labial commissure, and one of either of the two previous distances is (0.618…) This is an example of the golden facial relationships. This Golden Ratio can also be used for aesthetic relationship analysis of the face. Stephen Marquardt, D.D.S., has used the Golden Ratio to create a pentagram-based overlay in which facial features are positioned, as an analytical tool, according to this ratio.