The golden ratio in facial symmetry

The ideas of beauty and, specifically, female facial beauty, are developed in depth in this paper, in light of the adjustment of facial beauty to the golden ratio according to the parameters defined for such purpose. An experimental design of our own is made, software for carrying out the experiments is developed and the experimental results are analyzed for both male and female population from the Computer Engineering Program of the Autonomous University of Zacatecas (UAZ) and the Psychology Department, also at UAZ. It is concluded that women are more sensitive than men to the aesthetics dictated by the conformance to the golden ratio. Also, we conclude that the golden ratio does play an important role in female facial beauty perception.

Indian Journal of Dental Research, 2014

The evolution of orthodontics during the 20 th century followed an interesting path in the assessment of facial esthetics and attractiveness. Facial aesthetics is an important concern of the current society. Social acceptance, psychological well-being, and self-esteem of an individual are all related to facial form and attractiveness. [1,2] Improvement of facial appearance is the most frequently reported subjective reason for seeking orthodontic treatment. [3-5] Prehistoric man rarely described facial features in the human representations he carved in stone or painted on a rock. [6] Artworks became more refined to depict facial features, proportions and resemblance in the ancient civilizations of Egypt, China, and Greece. Egyptian artists used simplified grid systems to draw figures to ideal proportions. [6] Ancient Greece formalized the study of beauty and developed intricate formulas for constructing human and godly representations. [4] The renaissance brought one of the most important axioms of facial esthetics, the golden proportion, into the limelight. Initially described by Euclid, it was later termed as the divine proportion by the mathematician

2019

Historically, mathematics and architecture have been associated with one another. Ratios are good example of this interconnection. The origin of ratios can be found in nature, which makes the nature so attractive. As an example, consider the architecture inspired by flowers which seems so harmonic to us. In the same way, the architectural plan of many well-known historical buildings such as mosques and bridges shows a rhythmic balance which according to most experts the reason lies in using the ratios. The golden ratio has been used to analyze the proportions of natural objects as well as buildings harmony. In this paper, after recalling the (mathematical) definition of the golden ratio, its ability to describe the harmony in the nature is discussed. When teaching mathematics in the schools, one may refer to this interconnection to encourage students to feel better with mathematics and deepen their understanding of proportion. At the end, the golden ratio has been statistically exam...

Pattern Recognition, 2008

Analysis of attractiveness of faces has long been a topic of research. Literature has identified many different factors that can be related to attractiveness including symmetry, averageness, sexual dimorphism and adherence to the Golden Ratio. In this research we systematically analyze the role of three factors: symmetry, conformance to Neoclassical Canons and the Golden Ratio in the determination of attractiveness of a face. Unlike many researchers, we focus on the geometry of a face and use actual faces in standardized databases for our analysis. Our results are in agreement with the literature in that males and females generally agree on which faces are viewed as attractive and which are not. However, there are some differences in the criteria used by males and females to determine attractiveness. Using statistical analyses, we have developed a model to predict the attractiveness of a face using its geometry. The results show that our model is accurate with low residual errors.

Journal of the Institute of Engineering

The Golden Ratio, mathematics and aesthetics are intricately related among each other. In this paper, we exhibit the presence of mathematics in aesthetic impression that appears in nature, classic art, architecture, logo design and much more. The divine proportion can be found in music, poetry and other forms of art, however our focus here is only in the visual ones. The Golden ratio is considered sacred due to its relationship to nature and even the construction of the universe and the human body. It has been used for centuries in the construction of architectural masterpieces by the great artists, who, being able to see its beauty used it in their designs and compositions. We explain how the applications of the Golden ratio in architectures, paintings and geometrical shapes create the mystery of beauty. Further we present the existence of the divine proportion in human body and natural flora and fauna. There are a diverse number of directions, paths and tangents to which the study...

Fig. 3 The Golden Ratio in art and nature.(a) The Parthenon: manmade beauty;(b) DNA: natural beauty. this claim with the use of the Golden Ratio, a concept going back to ancient times. The Golden Ratio, denoted by φ, is an irrational number, like π, which expresses a fundamental ratio that is almost as common as π and has the habit of appearing when least expected [2]. The geometrical meaning of φ is seen from the line segments of Fig. 2.

International Dental Journal of Student's Research

The argument whether the well renowned composition – the golden section, a number approximate equal to 0.618 – holds the key to the secret of beauty, is an enigma which has existed from the time of ancient Greeks with Fechner being one of the first to conduct study on golden proportion in the 1980s. The normal human face was considered by Ricketts to be the most beautifully perfect structure in all of the animal kingdom. In an attempt to study the face, the “divine proportion” was explored in relation to the Dentofacial complex, claiming that a number of golden relationships existed in the faces, Cephalogram, and study casts of those considered having outstanding beauty. There has to be set protocols to assess facial profile analysis based on different criteria. Here, we have taken a call to review for assessment of craniofacial morphology in relation golden proportion.

Psychonomic Bulletin & Review, 1998

Evolutionary, as well as cultural, pressures may contribute to our perceptions of facial attractiveness. Biologists predict that facial symmetry should be attractive, because it may signal mate quality. We tested the prediction that facial symmetry is attractive by manipulating the symmetry of individual faces and observing the effect on attractiveness, and by examining whether natural variations in symmetry (between faces) correlated with perceived attractiveness. Attractiveness increased when we increased symmetry, and decreased when we reduced symmetry, in individual faces (Experiment 1), and natural variations in symmetry correlated significantly with attractiveness (Experiments 1 and lA). Perfectly symmetric versions, made by blending the normal and mirror images of each face, were preferred to less symmetric versions of the same faces (even when those versions were also blends) (Experiments 1 and 2). Similar results were found when subjects judged the faces on appeal as a potential life partner, suggesting that facial symmetry may affect human mate choice. We conclude that facial symmetry is attractive and discuss the possibility that this preference for symmetry may be biologically based. The question of what makes a face attractive, and whether our preferences come from culture or biology, has fascinated scholars for centuries. Variation in the ideals of beauty across societies and historical periods suggests that standards of beauty are set by cultural convention. Recent evidence challenges this view, however, with infants as young as 2 months of age preferring to look at faces that adults find attractive (Langlois et aI., 1987), and people from different cultures showing considerable agreement about which faces are attractive (Cunningham, Roberts, Wu, Barbee, & Omen, 1995; Jones & Hill, 1993; see Langlois & Roggman, 1990, for a review). These findings raise the possibility that some standards of beauty may be set by nature rather than culture. Consistent with this view, specific preferences have been identified that appear to be part of our biological rather than our social heritage (

Psicologica, 2016

espanolEn dos experimentos se evaluo el impacto de distintas desviaciones de la proporcion aurea sobre la percepcion de la belleza. Como estimulos se utilizaron adaptaciones en blanco y negro de pinturas de Mondrian ajustadas a la proporciones aurea, 1/6 y 1/2. En cada ensayo se presentaron a los participantes dos versiones del mismo estimulo. Los participantes dispusieron de 1500 ms para seleccionar el estimulo que consideraban mas bello. En los ensayos experimentales una de las pinturas mantuvo la proporcion aurea, mientras que la otra se ajusto a la proporcion 1/2 o 1/6. En los ensayos de control las proporciones de los estimulos fueron identicas. Los participantes, estudiantes universitarios sin formacion en arte, seleccionaron como mas bellos los estimulos con proporcion aurea en comparacion con la proporcion 1/6, pero no en comparacion con la proporcion 1/2. Estos resultados fueron consistentes tanto con un diseno intrasujeto (Experimento 1) como en un diseno entregrupos (Expe...

Empirical Studies of the Arts, 2018

Scientific disciplines as diverse as biology, physics, and psychological aesthetics regard symmetry as one of the most important principles in nature and one of the most powerful determinants of beauty. However, symmetry has a low standing in the arts and humanities. This difference in the valuation of symmetry is a remarkable illustration of the gap between the two cultures. To close this gap, we conducted an interdisciplinary, empirical study to directly demonstrate the effects of art expertise on symmetry appreciation. Two groups of art experts—artists and art historians—and a group of non-experts provided spontaneous beauty ratings of visual stimuli that varied in symmetry and complexity. In complete contrast to responses typically found in non-art experts, art experts found asymmetrical and simple stimuli as most beautiful. This is evidence of the effects of specific education and training on aesthetic appreciation and a direct challenge to the universality of symmetry.