The Effect of Phi on the Perception of Attractiveness

Abstract

The ratio Phi, equal to approximately 1.618, is an observable phenomenon that Greek mathematician Euclid defined this relationship as a line in two parts, in which the ratio of the longer part to the shorter part is equal to the ratio of the total length over the longer part. The ancient Greeks thought of Phi as a mathematical representation of physical beauty. Although many studies have shown a correlation between Phi and perceived attractiveness, other studies have displayed no/very weak, correlation. The question, “Does the expression of Phi play a significant role in the attractiveness of a face?” was investigated. It was hypothesized that if the features of a face closely fit the proportions of Phi, then survey respondents will give that face a higher attractiveness rating than a face whose features do not. Landmark localization data was calculated for images of 14 different faces. Individual and average facial ratios were calculated for each photograph, and a survey was conducted in which 100 participants were asked to rate the attractiveness of each face on a scale of 1-10. The average attractiveness rating of each face was then compared to the variance/distance of its average facial ratio away from the numerical value of Phi. Based on the analysis of the data, faces with features whose proportions closely fit the ratio of Phi are perceived as more attractive than faces with features that do not. Faces with average facial ratios closer to Phi received higher average attractiveness ratings.