Central Luzon State University
College of Arts and Sciences
Department of Psychology

The Golden Ratio: Reference of Beauty

Submitted to:
Nixon Agaser

Submitted by:
Jam Shimei I. Gamboa
Jeanne R. Dadufalza
Eden Leigh Pagoso
Micah A. Montes

The Golden Ratio: Reference of Beauty

Beauty has been defined as a combination of qualities that give pleasure to the senses or to the mind. It is a philosophical concept, the aspects of which are studied under the term aesthetics, derived from the Greek word for perception (aisthesis). Aesthetics, therefore, is the study of beauty and, to a lesser extent, it’s opposite the ugly. It involves both the understanding and evaluation of beauty, proportions and symmetry. The assessment of facial beauty is immersed in subjectivity and therefore leans towards the world of art. Facial proportions and facial balance, however, can be measured and therefore fit somewhere between art and science.
Aesthetics itself is now essentially a science in the formation, although obviously with a very strong philosophical and artistic background (Naini, et al. 2008.) According to Jang (2014) it is becoming clear that there is a science to beauty. Extensive research has shown that we have similar ideas about what constitutes a beautiful face. When British researchers asked women to rate pictures of various men, their choices were identical. When a group including English, Chinese, and Indians were asked to choose a “good looking” face from a selection of racially diverse faces, individuals from 13 countries shared the same choices. In other words, regardless of ethnicity, age, or culture, people share a universal sense of what is attractive. The writer Margaret Wolfe Hungerford (1878) said “Beauty is in the eye of the beholder”. Perceptions of facial beauty have genetic, environmental and cultural foundations.
The origin of our perceptions of beauty and harmony is justly called a ‘sense’ since it involves no intellectual element, no reflection on principles and causes. Though not an understandable or quantifiable entity, everyone admires beauty and its unique balance in nature. This balance and perception of beauty has been attributed to the ‘golden’ number or the ratio that gives certain things their loveliness. The “divine proportion” is one of the several terms used to describe the division of a line such that the ratio of the smaller section to the larger section is the same as that of the larger section to the whole. Other names given to this ratio include the “golden proportion,” and the “golden section”. This ratio can be expressed mathematically as 1.618:1 or 1:0.618. There have been many claims that the divine proportion was used in Greek art and architecture by the sculptor Phidias. This has led to its nickname as the “Phi” ratio. The term “divine proportion” was first used by the Italian Renaissance mathematician Fra Luca Pacioli (Rupesh, Rekesh, et al. 2014.) This is a geometrical proportion in which a line AB is divided at a point C in such a way that AB/AC = AC/CB. That is, the ratio of the shorter section to the longer section of the line is equal to the ratio of the longer section to the whole line. This gives AC/AB the value 0.618, termed the Golden Number (Naini, Gill, 2008.) In recent studies (Saraswathi, 2007) The Golden proportion and its application to the human face, Seventy five first year dental students (37 males and 38 females) of 17-19 years of age in Saveetha Dental College at Chennai were used. Length of the face was the vertical length which was the vertical distance in the midline of the face between the hairline and lower border of the chin. The width of the face was the bizygomatic width of the face, which was the horizontal distance between the prominent points laterally on the body of both the zygomatic bones. These two parameters were measured in centimeters without parallax error using a sliding caliper. The size of the face was the ratio between the length of the face and the width of the face. The Golden proportion or phi was 1.6. The shape of the face was normal when its size was equal to 1.6; the shape of the face was long when its size was larger than 1.6, and was short when its size was smaller than 1.6. The study on seventy-five individuals, only fourteen (9 F, 5 M) (19%) had a normal shape of the face. Therefore, sixty-one (29 F, 32 M) individuals (81%) had abnormally shaped faces. Eleven individuals (15%) had a long face and fifty individuals (67%) had a short face. The sixty-one individuals with an abnormal size of the face may be at risk of developing maxillofacial, jaw, respiratory, occlusal, and sleep disorders due to disproportionate face size and tooth size. This simple technique of applying the golden proportion to the face and identifying individuals with any values larger or smaller than it in mass surveys in order to determine the individuals and the percentage in a given population at risk of respiratory and jaw disorders facilitates early preventive and corrective interventions so that the population can lead a healthy and normal life. In (Rupesh, Rekesh, et al. 2014.) Fifty female dental students with acceptable profiles between the ages of 18 and 20 years were invited to participate in this investigation. Subjects with gross facial deformity/ asymmetry, history of orthodontic treatment, or extraction of teeth, except for third molars or cosmetic surgeries on the face were excluded. The aim of this study was explained and informed consent was obtained from each participant. The average values for five facial profile proportions in 25 subjects with higher esthetic scores (Group A) are summarized in table 1. In Group A, the ratios R1 and R2 (with the mean of 1.58) were closer to the Divine Proportion. The average values for five profile proportions in 25 subjects with lower esthetic scores (Group B) are summarized in table 2. In Group B, none of the ratios approximated the divine proportion. However, none of the ratios had the mean of 1.618. Comparison of profile proportions in group A and group B (table 3) revealed statistically significant differences in ratios R1, R2, R3 and R5. On Sunilkumar, Jadhav, et al. 2010, The study sample consisted of photographs taken at the Department of Orthodontics and Dentofacial Orthopaedics at our institute. The sample consisted of 300 photographs; 145 males and 155 females. The age of the samples ranged from 18yrs – 28yrs. Sample included subjects who showed well balanced faces, had Class I skeletal and dental pattern and with lip competency. Only subjects belonging to the North Maharashtrian population were included in the study so as to achieve our primary aim and objective of assessing facial proportion in this given population. All landmarks were measured once per day for 3 days by an author. This was cross checked by the second author .Results were as seen in table 1. Subjects were similar to the golden proportion (100%) in the value of TR-ME:LC-ME. The three measurements of anterior facial height TR-LC: LN-ME:LC-CH [2.5, 2.4, and 2.8 respectively] showed proportionality with the total facial height. In addition, CH-ME:LC-CH, LN-CH: CH-ME had 90.2, and 92.1 %, respectively. The values of TR-LN: LN-ME (1.43, 88.4%), LN-ME: LC-LN (2.21, 136.6%) and LC-LN: LN-CH (1.14, 71.1%) deviated from the golden proportion as seen in the graph given in Fig: 4. The value of LC-ME:TR-LC was small (1.5, 93.9%) but close to the golden proportion. The face width parameters CH: LN [77.9%], LC: CH [121.1%], TS: LC [86.5%] showed deviations from the golden proportion. In the current study, the researchers measured and tested whether subjects consider individuals with facial measurements that come closest to the golden ratio to be most attractive. In recent studies, it focused more on the orthodontics or the branch of dentistry that deals with irregularities of the teeth and their correction, wherein the golden ratio is used as a guide in making the said deformities match the “ideal look”. This experiment will investigate whether the golden ratio can be used to predict people’s assessment of beauty in others.

Method
Participant
Thirty young adults (15 men, 15 women) between the age range 16-19 years, studying in Central Luzon State University were randomly selected and randomly assigned to each treatment in the experiment.

Materials and Procedure The visual presentations that were used were 2x2 pictures of 3 individuals, given that the faces were measured in accordance to the golden ratio. The first “face” or treatment had a score nearest to the golden ratio, the second “face” or treatment had a score quite near to the golden ratio and the third “face” or treatment was a bit far from the golden ration. Without the participant’s knowledge of the scores of the pictures presented to them, 10 participants evaluated the first face, 10 other participants also evaluated the second face, and the other 10 participants assigned in the third face also evaluated and rated the picture.

Statistical Design The researchers made use of the two-by-three factorial ANOVA to determine if there are interactions between the golden ratio and gender variables or factors considered. An interaction implies that differences in one of the attractiveness factors depend on differences in another factor.
Results and Discussion

Tests of Between-Subjects Effects | Dependent Variable:Attractiveness | Source | Type III Sum of Squares | Df | Mean Square | F | Sig. | Corrected Model | 10.667a | 5 | 2.133 | .934 | .477 | Intercept | 1526.533 | 1 | 1526.533 | 668.555 | .000 | Face/Treatment | 6.067 | 2 | 3.033 | 1.328 | A .284 | Gender | .133 | 1 | .133 | .058 | B .811 | Face * Gender | 4.467 | 2 | 2.233 | .978 | C .391 | Error | 54.800 | 24 | 2.283 | | | Total | 1592.000 | 30 | | | | Corrected Total | 65.467 | 29 | | | | a. R Squared = .163 (Adjusted R Squared = -.011) | |
From A the table, the p-value for the main effect of treatment is .284 and therefore the effect of the face/treatment is not significant. We can conclude that on average, the attractiveness level of the individuals are the same. From B, the p-value for gender is .811; we can therefore conclude that how male and female rate attractiveness are the same, fail to reject the null hypotheses. From C, the p-value for the interaction is .391; the interaction is not significant and we can conclude that the effects of gender and treatment on rating the individual picture are the same.

References
Rupesh, S., Rakesh, S., Winnier, J.J., Kaimal, A., John, A., Prasannan, M., Jeyaprakash, V. (2014). The role of divine proportion in the perception of beauty: A cross sectional study. Amrita Journal of Medicine, Vol. 10, No: 1 Jan - Jun 2014. Page 1 – 44
Meenai, Y.A., Abbas, M.H. (2010). Beauty measuring system based on the Divine Ratio (AN EXPLORATORY RESEARCH). International Conference on User Science and Engineering.
Jang, F. (2014). What is beauty? The answer may lie in math!. Facial assessment consultation and treatment by skinworks. Volume 1 Skinworks ultimate skin health.
Sunilkumar, L.N., Jadhav, K.S., Nazirkar, G.,Singh, S., Nagmode, P.S., Ali, F.M. (2013). Assessment of Facial Golden Proportions among North Maharashtrian Population. J Int Oral Health 2013; 5(3):48-54.
Naini, F.B., Gill, D.S. (2008). Facial Aesthetics: 1. Concepts and Canons. Dent Update 2008; 35: 102-107
Saraswathi, P. (2007). The golden proportion and its application to the human face. Eur J Anat, 11 (3): 177-180 (2007)