The use of golden proportion in dentistry: a integrative review

a Department of dentistry, Fundação Universidade Regional de Blumenau (FURB), Blumenau, Brazil ABSTRACT OBJECTIVE: The purpose of this integrative review was assembling information about the golden ratio, improving a different sight to the theme. METHODS: Original articles were retrieved on databases Scielo, PubMed, Lilacs and Web of Science selecting proper articles published between the years of 20062017. RESULTS: 55 articles were included, in which 42% of the findings corresponded to aesthetic perception and 40% to golden ratio and ethnical groups. CONCLUSION: The findings suggest that there’s no relationship between golden ratio and natural teeths and this ratio isn’t a decisive factor to ensuring the smile attractiveness, however, if this proportion were individually applied for each patient, can become a useful guide.


INTRODUCTION
In our current society, aesthetics is overvalued and primarily related to how well individuals are accepted in social groups.People are routinely exposed to countless amounts of information and methods to achieve the beauty standard found in celebrities or digital influencers, who, in turn, disclose through social media the many procedures they have followed to reach the aesthetic goal.As a result, several people are encouraged to seek the same kind of treatment or procedures.
The ease of access to information which was previously restricted to plastic surgery and dentistry professionals, the XXI century patient arrives at the clinic knowing details of the procedures.Therefore, there is a demand for professionals with deep technical/scientific knowledge to explain the limitations and particularities of each technique.Dentistry is a key tool in the search for the ideal smile; hence, several procedures are now widespread to that end, such as dental laminates and bichectomy.
According to Schubert (2009) [1], the pursuit of beauty is as ancient as human kind.Many cultures over time have shown their preferences and tastes through their beauty standards.In the tribal period, procreation and breastfeeding were the aesthetic requirements that defined a beautiful woman.Men needed to be strong and intelligent to be portrayed as handsome, as those were essential requirements to defend the offspring.During the medieval period, beauty was related to the devotion to God.Men should take care of his family and women ought to be a good mother, raising their children according to the Christian principles.These traits defined survival and became values influencing the cultural context [1].
According to Tatarkiewicz (1991) [2], to the Greeks the human body was based in mathematical proportions, which could be reproduced in artistic endeavors.To them, beauty was all about the details, mainly in the face.Always based on mathematical standards or references, the Greek built some of the most gorgeous and magnificent temples, such as Partenon and the most beautiful sculptures, such as Venus de Milo or Apollo of the Belvedere.These masterpieces were built following the Golden Ration principle [2].
According to Huntley (1985) [3], it is most certain the usage of this ration in the Greek works.Phidias, a famous Greek sculptor, was used as reference to indicate the golden ratio with the first letter of his name, phi (φ).The gold number (or phi number) is 1.61803.Later in history, this value was described in Math by Fibonacci, in which the value of a term is the sum of the previous two terms (ex.: 1+1 = 2; 1+2 =3; 2+3 = 5 and so forth) and the ration between these two factors is 0.618, which explains the ration of 1 to 1.618 [4].Some of the oldest references about this ratio are linked to the Greek philosopher Pythagoras.To him, nature presented relations and combinations that could only be explained with the science of numbers [3].In nature, this proportion can be observed in some flowers, such as Azalea, petunia and sunflowers, as well as in some shells and clams [4].
The golden ratio was introduced in several fields of study and in Dentistry it was no different.The first apparition in aesthetic dentistry was in the 70's, through Lombardi (1973) [5].In 1978, Levin [6] wrote about some of the many forms that the golden ration appears in nature and how it applies to aesthetic dentistry.In the field of facial analysis, Ricketts (1982) [7] had great prominence by measuring some attractiveness parameters against the golden ration.Preston (1993) [8] also deserves recognition for his work on golden ratio in aesthetic dentistry.He assessed several aspects of the smile and concluded that the golden ration was present only between the central and lateral incisors.
Although there are some studies about the usage of golden ratio in dentistry, it is noticeable the absence of relevant information on how to put this concept to practice, which causes a sense of doubt about its purpose.Therefore, this paper aims to consolidate information about the golden ratio, summarizing several studies and researches, offering deeper insight on the subject to dental surgeons, supporting them on the choice of techniques for aesthetic procedures.

METHODS
Considering the various research methods that aim to obtain summarized information about a given topic, the method of choice for this paper is integrative review, as it allows an in-depth methodic approach, enabling the integration of experimental and non-experimental studies [9].According to Baldini Soares et al. (2014) [10], integrative review seems to be useful in the creation and formulation of research problems in new theories and define this approach as a complex review, which requires systematic and methodological rules in order to obtain the appropriate level of accuracy for scientific researches.It also compiles data from theoretical and empirical literature, aggregating several resolutions, such as theory and evidence review, analysis of methodological problems and definition of concepts.The integrative review establishes the current perception of a given theme, supporting the quality of delivered services to the patients, rating protocols, procedures and critical thinking required for the daily routine [11].
The integrative review is part of the field called Evidence Based Research (EBR), which aims to reinforce the importance of research for clinical practice.It assesses the available evidence from studies and proposes solutions to the decisions; hence, it provides aid for health procedures based on scientific knowledge [12].The goal of literature integrative review is to enable the meaningful comprehension of a given theme, based on preview studies.To that end, precise standards of methodology are followed, as well as appropriate interpretation of results, enabling the reader to determine the quality of the studies used in the review [12].The integrative

Golden proportion in dentistry | Tridapalli & Steinbach
review allows the reader to access all the information from a given study and not only the main results, enabling a clearer and more complete reading of the theme [10].
The integrative review is organized in phases recommended by Ganong (1987) [13].The first phase is completed by formulating one objective and one question for the theme of study; the second phase consists of specifications to include studies; the third phase comprehends selecting the studies; the fourth phase develops a questionnaire to gather data, which for this paper was done by a categorization to separate similar information regarding the theme; the fifth phase assesses the studies with the questionnaire, analyzing the methodology and conclusions of each study; the sixth phase evaluates the information found and the seventh and eighth phases are for discussion and interpretation of the findings.
This paper was started with the question: How can the golden ration be used in dentistry?To answer these questions, a bibliographic review was done in the following data bases: Lilacs, SciElo, Pubmed/MedLin, Web of Science, in the months from April 2017 to October 2017, searching the themes "golden proportion and dentistry" and "golden proportion and teeth" and "golden proportion and aesthetic".As part of the second phase of the integrative review, articles in any languages were considered, as long as fully available online, as well as published between January 2006 and September 2017 (due to the high amount of articles in the period).Editorials, letter to readers, theses, partially available online studies and duplicate articles were dismissed.The identified articles were pre-selected based on the title and summary, and those which met the selection criteria were read and recorded.After the selection, the articles were categorized as such: articles related to aesthetic perception, golden ration in different ethnic groups, golden ration and dentistry, clinic cases of golden ratio, among others.Afterwards the studies were deemed valid, the agreements and disagreements between different authors were noted so that readers would have a quick access to relevant results of the studies, based on different approaches to the golden ratio.

RESULTS AND DISCUSSION
The research was carried out in the data bases, identifying 93 articles under "Golden proportion and aesthetic", 83 under "Golden proportion and dentistry" and 87 under "Golden proportion and teeth", totaling 263 articles.Based on the summaries, titles and publication year (from January 2006 to September 2017), 188 articles were pre-selected, out of which 117 were duplicates.Hence, the final amount was 71 papers.To analyze the papers, all of them were read and 16 articles were deemed out of the desired scope, leaving a total of 55 valid articles.The findings were grouped by theme similarity, being: dentistry/malocclusion, aesthetic perception, clinic cases, ethnic groups and agenesis of upper lateral incisors.Table 1: found articles per title, author and publication year.In the selected period, the year 2015 presented the highest number of publications (8-14.54%)followed by 2016 (7-12.72%)and 2013 (7-12.72%).The Figure 1 represents articles per year.The publications in general are from parts of the world, such as Asia, Europe, Latin America and North America.The grouping of articles correspond to 2 articles about agenesis of upper lateral incisors, 3 clinic cases, 5 dentistry/ malocclusion, 22 ethnic groups and 23 aesthetic perception (Figure 2).This paper considers aesthetic perception those articles that relate the perception of a group of individuals to attractive smiles.
These facts indicate that the standardization of a single concept to establish ideal measurements for attractiveness is not real.This integrative review demonstrates that studies performed in a population have divergent results in India, Korea, China and Malaysia.

Clinic cases and agenesis of upper lateral incisors
When used in clinic cases, 100% of the studies concluded that for size and proportion dental discrepancy, aesthetics can be reestablished with support from the golden ratio [33] and the usage of this simple and predictable technique in surgeries and dental facet placement achieves pleasant aesthetic results [34].Therefore, the golden ratio can be used as a guideline for harmonization and remodeling of smiles [35].
Pini et al. ( 2012) [36] and Bukhary et al. (2007) [37] concluded that the golden ratio is not necessary in the recreation of smiles with agenesis of lateral incisors and that there are no evidences to support that golden ratio should be considered an ideal standard in replacement of lateral incisors.

Aesthetic perception
In the book Molly Bawn, written in 1879 by Margaret Hungerford, is the classic sentence "the beauty is in the eyes of the beholder".Despite of its age, the sentence remains true and exemplifies the view of Akan; Torgut and Oktay (2017) [38] about beauty; to them, the beauty is determined by the judgement of the beholder and it changes according to the culture and individuals.This view has been true in this paper, in which several ethnicities were evaluated and achieved various results.In the population of India, Niranjan et al. (2016) [15], Sunilkumar et al. (2013) [16] and George et al. (2010) [17] found a relationship between this population and the golden ratio, while Anand et al. (2015) [39], Sandeep et al. (2015) [40] and Chander; Kumar and Rangarajan (2012) [41] did not find relation between the population and the golden ratio.This fact is due to the different criteria used to determine which part of the face had the golden ratio.
The main results found during the data gathering process related to aesthetic perception.Saha et al. (2017) [42] concluded that an individual numeric parameter does not define the beauty of a smile, supporting the findings of Basting; Trindade and Florio (2006) [43], which state it is not possible to establish single criterion to define adequate aesthetics.This proportion is not a defining factor in dental aesthetics [44] because when assessing the smiles of celebrities or common individuals of the general population, both showed divergences in relation to the golden ratio [45], indicating that this is not a valid method to determine the attractiveness of a smile [46].Corroborating with these studies, Murthy; Bv and Ramani (2008) [47] concluded that only 14% of individuals of their research showed the golden ratio in the natural anterior teeth.With the exception of the study by Koidu; Chatzopoulos and Rosernstiel (2017) [45], that evaluated several smiles only by measuring photos of celebrities and regular people, the other studies mentioned in this paper used assessment methods based in the particular opinion of each jury.In the research of Nikgoo et al. ( 2009) [46], for example, the jury was composed by one orthodontist, one prosthetist, one photographer and one painter.As well as the calibration might have been done, the individual opinion and ideology of each background remains unique, possibly interfering in the final results.
In spite of the golden ratio have been expressed as an aesthetical standard for decades, it is not routinely used [48] and is not commonly found in natural smiles [49].However, it can be useful to meet both patients and dentists expectations for aesthetic rehabilitation, if used considering the particularities of each individual [14,35,50,51,52].Petričević et al. (2008) [53] concluded that Golden ratio should not be used in clinic practice as a guide to achieve the ideal aesthetic, however, Solozzi; Momjjan and Courvoisier (2011) [54] quoted the golden ratio has shown effective in correcting the inferior third part of the face and Ward (2007) [55] that it can be used to plan smiles with high teeth.

Dentistry and malocclusion
Lukez et al. (2015) [56], assessed the elements of the aesthetic smile and their contribution to the well-being of teenagers.In the end of the research, concluded that the aesthetic concern with the golden ratio standard was responsible for only 2% of the results, being the severity of malocclusion the most important factor (18%).On the other hand, Akan; Torgut and Oktay (2017) [38] demonstrated that malocclusion is not related to the individual's attractiveness as well as the golden ratio is not tied to the beauty of a person.Bragatto et al. (2016) [57], sought to identify whether the cephalometric standards approximate to the golden ratio after orthognathic surgery in Angle's Class II and III patients.The analysis showed out of the 13 standards defined by Ricketts, only one came close to the golden ratio after the surgery, demonstrating that the golden ratio was not present.Supporting these results, Marconato et al. (2015) [50] concluded that the golden ratio was verified in 67.56% of patients at the end of dental treatment, showing it can be applied to ensure a harmonic and aesthetic smile.This result goes in line with the findings by Mayumi et al., (2012) [58] in which 62% of analyzed patients presented a standard that during the treatment became closer to the golden ratio value, being called regressive golden ratio.It also goes in line with the study by De Andrade Brum et al. (2010) [59], in which most parts of facial proportions do not relate to the golden ratio, however, at the end of the dental treatment, the values became closer to the ones established by the golden ratio, confirming the findings in the study by Prokopakis et al. (2013) [60], that dentists can use the golden ratio if they are looking for attractive, symmetric and standardized aesthetic values.
When the golden ratio is assessed and used in accordance to the particularities of each individual, and not in a frantic pursuit to achieve the exact values, the results are encouraging, harmonic, natural and real.

Gender differences
The prevalence of golden ratio is different between genders, to Kanaparthy et al. (2017) [14], in Saudi Arabia,

Golden proportion in dentistry | Tridapalli & Steinbach
the proportion has been found between the central and lateral incisors of women and between lateral incisors and the canine tooth in men.Some studies found higher prevalence of golden proportion in women [18,23,32].As opposite, other studies demonstrated the golden ratio was more common in men than women [19,15,61,62].To Condon et al. (2011) [20] there was no significant differences in the values found for both gender.
In adulthood, cephalometric evaluation differs between genders, whilst in puberty it is almost impossible to determine the sex of the individual analyzing the skull.In women, the supraorbital margins are sharper and the paranasal sinuses are smaller than in men.Similarly, the jaw structure is thinner, and the glabella is less developed.The zygomatic bone has the lower edge irregular and rough in men and smooth and regular in women [63].These differences illustrate that when assessing facial structures, the gender of the patient must be taken into account, not excluding anatomic differences, but adapting to them.

CONCLUSION
The findings in this integrative review identified the possibility of using the golden ratio as a guide in aesthetic rehabilitation as long as the characteristics of each individual are taken into account, because the reading of articles revealed that, as an isolated factor, the golden ratio is not decisive in dental aesthetic.In this paper did not find significant evidence that the proportion is naturally present in populations, since several factors must be equally analyzed.
In order to the benefits of the golden ration surpass the particularities of the techniques, the dentist surgeon must keep in mind that the proportion should not be deemed as a general rule to be applied deliberately to standardize smiles, but as a harmonization tool to be individually applied to each case.All the concepts that create the harmony between smile and facial aesthetics must be taken into account, analyzing the individual inwards, understanding the patient's desires, needs and expectations.

Table 1 .
Represents the evaluated articles Year Title/Autor 2017 Effects of malocclusions on facial attractiveness and their correlations with the divine proportion -AKAN, Seden; TORGUT, Ayse Gul; OKTAY, Hüsamettin 2017 Perception of Acceptable Range of Smiles by Specialists, General Dentists and Lay Persons and Evaluation of Different Aesthetic Paradigms -SAHA, Mainak Kanti et al.

Figure 2 .
Figure 2. Provision of themes