Download The Golden Proportion in Dentistry

Middle East J Rehabil Health. Inpress(Inpress): e34020.
doi: 10.17795/mejrh-34020
Review Article
Published online 2016 March 01.
The Golden Proportion in Dentistry: A Literature Review
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Amir Ali Karamifar, Mohammad Sadegh Nazari, Ali Hasani, Maryam Davari,
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Kousha, Ali Mokhtar, and Isa Safari
1Orthodontics Department, Dental School, Semnan University of Medical Sciences, Semnan, IR Iran
2Tehran Dental Branch, Islamic Azad University, Tehran , IR Iran
3Oral and Maxillofacial Surgery Department, Tehran Dental Branch, Islamic Azad University, Tehran, IR Iran
4Prosthodontics Department, Dental School, Semnan University of Medical Sciences, Semnan, IR Iran
5Dental School, Semnan University of Medical Sciences, Semnan, IR Iran
6Orthodontics Department, Tehran Dental Branch, Islamic Azad University, Tehran, IR Iran
7Orthodontics Department, Dental School, Shahid Sadoghi Yazd University of Medical Sciences, Yazd, IR Iran
*Corresponding author: Maryam Davari, Prosthodontics Department, Dental School, Semnan University of Medical Sciences, Semnan, IR Iran., E-mail: [email protected]
Received 2015 November 8; Revised 2015 December 30; Accepted 2016 January 2.
Abstract
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Context: In the last 2 decades, several studies have questioned the application of the rule of the golden proportion in dentistry. Therefore,
the purpose of this review study was to assess the dental use of the golden proportion.
Evidence Acquisition: We performed MEDLINE and Cochrane searches for English language literature published through 2015 using
the following terms: golden proportion, golden ratio, and dentistry. Additional articles were then retrieved through hand searching the
reference lists of the above articles. The manuscripts selected included review articles, systematic reviews, and meta-analyses.
Results: The findings showed that the mean ratio of the relative widths of the central incisors, lateral incisors, and canines was 1.6:1:0.85 on
both sides. The ratios were not influenced by either sex or previous orthodontic treatment.
Conclusions: The results suggest that the rule of the golden proportion should not be used for treatment planning without observing
individual modifying factors. Moreover, orthodontic treatment does not change the dentition toward the golden proportion.
Keywords: Golden Proportion, Golden Ratio, Dentistry
1. Context
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Aristotle pointed out the value of proportion in esthetics as early as the fourth century BC. The golden proportion was described by the Pythagoreans in the sixth
century BC, and a little later by the Greek geometrician
Euclid. However, long before the Greeks, the Egyptians
had found and set up the golden number (1.618), and
the width to length ratio in the Egyptian rectangle was
0.6 (ɸʹ) (1). The golden proportion was used in ancient
Greek architecture to design the Parthenon, and can also
be seen in da Vinci’s classical drawings of the human
anatomy. This ratio is approximately 1.61803:1; that is, the
smaller section is about 62% of the size of the larger. The
uniqueness of this ratio is that the ratio of the smaller
part to the larger part is the same as the ratio of the larger
part to the whole (2).
The golden proportion is also evident in the arts (3). Renowned artists such as Michelangelo, Raphael, and Leonardo da Vinci made use of this concept (4). For example,
da Vinci drew the “ideal man” using the golden proportion, and the head of the Mona Lisa was drawn using this
relationship. Moreover, evidence suggests that the classical music composed by Mozart, Beethoven, and Bach incorporated the golden proportion (5). Whether the use of
the golden proportion by these artists and musicians was
by design, intuition, or accident is not known.
Ricketts devised a golden proportion caliper to establish and evaluate the ratios between various elements of
the attractive face (6). Moreover, Lombardi was the first
to propose the application of the golden proportion in
dentistry, but he also stated, “it has proved too strong
for dental use” (7). In addition, he defined the idea of a
repeated ratio, which implies that in an optimized dentofacial composition from the frontal aspect, the lateral to
central width and the canine to lateral width are repeated in proportion (7). Levin pointed out that “the width of
the maxillary lateral incisor is in the golden proportion
to the width of the central incisor and also the width of
the maxillary canine to the lateral incisor when viewing
from the front” (8).
Preston measured 58 computer-generated images of
dental casts with an image-measurement program, and
evaluated the frequency of the golden proportion (considered to be in the range of 0.61 - 0.63) in the ratios of the
perceived maxillary lateral to central incisors and canine
to lateral incisors (9). He found that natural teeth were
rarely in the golden proportion (17% maxillary lateral to
central and 0% canine to lateral). He also reported that
the mean perceived maxillary lateral to central incisor ra-
Copyright © 2016, Semnan University of Medical Sciences. This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/) which permits copy and redistribute the material just in noncommercial
usages, provided the original work is properly cited.
Karamifar AA et al.
were studies concerning the golden proportion that were
currently in progress. The papers were read by a team of
researchers containing 2 orthodontists and a dentist,
and the appropriate papers were accepted (Figure 1). The
more reliable and more statistically significant studies
from these papers are included in Table 1. This table also
contains the historical development of the golden proportion in dentistry.
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3. Results
Based on the results of this study, the following conclusions were drawn:
1) The rule of the golden proportion is not valid for the
examined populations. The mean ratio of the maxillary
anterior teeth in people is 1.6:1:0.85. The canine is markedly wider than predicted by the golden ratio (1.6:1:0.6).
2) No sex-dependent or side-dependent variations in the
width ratios of the maxillary anterior teeth were found.
3) In the examined population, the orthodontically
treated participants did not exhibit a significant difference in the width ratios of the maxillary anterior teeth,
when compared to the corresponding teeth of the untreated participants.
The findings showed that the mean ratio of the relative
width of the central incisors, lateral incisors, and canines
was 1.6:1:0.85 on both sides. Moreover, the ratios were not
influenced by either sex or previous orthodontic treatment. The rule of the golden proportion in dentistry is
defined as follows: after measuring the width of the maxillary anterior teeth from the frontal view, and considering the width of the lateral incisor as 1, the width of the
canine compared to that of the lateral incisor is 0.62,
while the width of the central incisor compared to that of
the lateral is 1.62 (9).
In the 1960s and 1970s, several studies were conducted
to find possible applications of the rule of the golden
proportion in dentistry. Ricketts (16) was the first to define the application of the rule for the anterior maxillary teeth, stating that the application of the formula
was indispensable in restorative and prosthetic dentistry. Magne et al. (18) also found a width/length ratio of
78% for the unworn central incisors; that is, the length
was related to the width according to the rule of the
golden proportion.
The width to height ratio of the maxillary central incisors
has been suggested to be significant in terms of the overall
dental appearance, because these teeth normally dominate in a person’s smile (7). For the golden proportion, the
width to height ratio of a maxillary central incisor crown
would be equal to 0.62. The golden proportion takes into
consideration the relative widths of the maxillary anterior
teeth, and assumes that in attractive dentition the ratio
of the apparent widths of the central incisor to the lateral
incisor is 1.62:1; similarly, the apparent width of the lateral
incisor is in the golden proportion to the width of the canine (i.e., 1:0.62) (8). The golden percentage is a modifica-
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tio was 0.66, and the mean perceived maxillary canine to
lateral incisor ratio was 0.84 (9). Gillen et al. in a study of
54 subjects, found that the golden proportion was rarely
seen (10); however, their measurements were made directly on the casts, rather than on the frontal images.
Snow stated that the concept of the golden percentage is a useful application in the diagnosis and development of symmetry, dominance, and proportion for
an esthetically pleasing smile (11). Some other authors
have also mentioned the use of this proportion in anterior esthetics (12, 13); for example, Rosenstiel et al. generated some computer images of the six maxillary anterior
teeth, which had been categorized according to different
tooth heights and proportions (14). The images were sent
via e-mail to dentists in 38 countries to determine their
esthetic preferences. It was reported that the dentists
preferred the golden proportion when viewing very tall
teeth, and that they considered this proportion less desirable for teeth of normal height or shorter teeth (14). Ward
believed that when the golden proportion was used, the
lateral incisor appeared too narrow, and the resulting canine was not prevalent enough (15). He preferred using
the 70% proportion, and he also recommended adhering
to the concept of the repeated ratio, which was defined
by Lombardi in 1973 (7).
In orthodontics, Ricketts (16) was the first to claim that
the analysis of a physically beautiful face should be approached mathematically, and he advocated the use
of the golden proportion in that respect. He observed
dozens of photographs of magazine models to select
pairs of distances representing the golden proportion
in those beautiful faces. On this basis, he performed a
small study using 10 beautiful faces and defined several
golden proportions in them. Although objections were
made against the study design (17), Ricketts’s articles (16)
appear to be key publications in orthodontics and oral
surgery for facial esthetics.
Based on the above information, the purpose of this review study was to assess the rule of the golden proportion in dentistry.
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2. Evidence Acquisition
C
We performed MEDLINE and Cochrane searches for English language literature published through 2015 using
the following terms: golden proportion, golden ratio,
and dentistry. Additional articles were then retrieved
through hand searching the reference lists of the above
articles. The manuscripts selected included review articles, systematic reviews, and Meta-analyses. The inclusion
criteria consisted of papers related to anterior esthetics
and mouth rehabilitation, while the exclusion criteria
consisted of papers not related to esthetic dentistry, such
as articles about architecture, painting, and in vitro studies. We found 15 papers in the first step of searching the
databases, but 2 papers were rejected. In addition, we
searched “clinicaltrials.gov” to determine whether there
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Middle East J Rehabil Health. Inpress(Inpress):e34020
Karamifar AA et al.
not depend on any particular feature of the dentition. In
a survey involving 301 dentists (21), it was found that the
dentists preferred other esthetic design principles to that
of the golden proportion.
More recently, Baker and Woods (22) and Shell and
Woods (23) were unable to establish significant correlations between changes in the golden proportion and
changes in the esthetic ratings after orthognathic treatment. Although most of the subjects were considered
to be esthetically improved after treatment, the proportions were equally likely to move away from or toward
the golden proportion. Therefore, they concluded that
the achievement of the golden proportion had little or
no influence on the overall esthetic scores.
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tion of the golden proportion rule, and it was proposed as
a simple and objective tool to assess such dental esthetic
measures as anterior dominance, symmetry across the
midline, and the regressive proportion (11).
The largest study (19) conducted on this topic involved
376 dental students in Jordan. The authors found that the
average ratio of the maxillary central incisor, the lateral
incisor, and the canine was 1.53:1:0.8. Dimensions that
corresponded to the rule of the golden proportion were
found in only 31.3% of the women and 27.1% of the men
(19). In addition, Ong et al. (20) conducted a survey with
a selected sample of individuals who had to assess 60 different smiles on a 5-point Likert-type scale. Their results
demonstrated that the overall dental attractiveness did
Literature Published to 2015
Using Key Words: Golden
Proportion, Golden Ratio, Dentistry
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Hand Search From the Reference
Lists of the Above Articles for
Additional Articles
Selected Including Review
Articles, Systematic Reviews
and Meta-analysis
re
Inclusion Criteria: Papers
Related to Anterior Esthetic and
Mouth Rehabilitation
2 Papers Rejected
or
Found 15 Papers in the First
Step of Searching the Database
Exclusion Criteria: Paper not
Related to Esthetic Dentistry,
Such as Articles Main Concept
About Architecture, Painting
and Also in Vitro Studies
Searched in the ‘Clinicaltrials.
gov’ to Find Whether There are
Studies Currently in Progress
C
Read Papers by Team Research
Containing 2 Orthodontist and
a Dentist
Accepted the Appropriate
Papers by Them
Figure 1. Literature Review Procedure
Middle East J Rehabil Health. Inpress(Inpress):e34020
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Karamifar AA et al.
Table 1. Studies of the Golden Proportion
Reference
Outcome
Levin (8)
In attractive dentition, the ratio of the apparent widths of the central incisor to the lateral incisor is 1.62:1;
similarly, the apparent width of the lateral incisor is in the golden proportion to the width of the canine,
that is, 1:0.62.
Preston (9)
Considering the width of the lateral incisor as 1, the width of the canine compared to that of the lateral incisor is 0.62, while the width of the central incisor compared to that of the lateral is 1.62.
Snow (11)
Magne et al. (18)
Ali Fayyad et al. (19)
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The assigned values for the six anterior teeth were added (assigning 1.6 to the central, 1 to the lateral, and
0.62 to the cuspid).
The width/length ratio was 78% for the unworn central incisors; that is, the length was related to the width
according to the rule of the golden proportion.
The average ratio of the maxillary central incisor, the lateral incisor, and the canine was 1.53:1:0.8.
Acknowledgments
The authors would like to thank the implant research
center at the dental branch of the Islamic Azad University.
Footnote
Authors’ Contribution:Study concept and design:
Amir Ali Karamifar, Maryam Davari, and Ali Hasani; acquisition of data: Mohammad Sadegh Nazari; analysis and
interpretation of data: Mohammad Sadegh Nazari and
Isa Safari; drafting of the manuscript: Mohammad Sadegh Nazari; critical revision of the manuscript for important intellectual content: Ali Mokhtar; statistical analysis:
Mohammad Sadegh Nazari; administrative, technical,
and material support: Sina Kousha; study supervision:
Amir Ali Karamifar and Maryam Davari.
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A variation of the golden proportion was suggested
by Snow (11), who proposed that the golden proportion
could be used to develop symmetry, dominance, and
proportion for aesthetically pleasing smiles. To simplify these proportions, the assigned values for the six
anterior teeth were added (assigning 1.6 to the central,
1 to the lateral, and 0.62 to the cuspid). Then, the assigned width of each tooth was divided by the total to
determine the relative percentage. The resulting percentages were: central incisor 25%, lateral incisor 16%,
and cuspid 9%. These percentages illustrate the dominance of the central incisors, which are 50% of the cuspid to cuspid width.
In fact, several studies have indicated that wide variation exists for patients and dentists with regard to the
ideal anterior tooth proportions (14, 24, 25). In a study
by Rosenstiel et al. (14), 549 dentists evaluated computer images of the same six maxillary anterior teeth.
Those dentists preferred 80% proportions when viewing short or very short teeth, and the golden proportion (62%) for very tall teeth. There was no identifiable
preference for teeth of normal length or tall teeth, and
the choices could not be predicted based on gender,
specialist training, experience, or patient volume. The
results of a similar study by Kokich et al. (25) demonstrated that orthodontists, general dentists, and lay
people detect specific aesthetic discrepancies at different levels of change. In the case of the golden proportion, the lay people did not discern a lateral incisor narrowing until the deviation reached 4 mm.
4. Conclusions
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It is likely that patients who present for cosmetic rehabilitation will not be comfortable with some of the wide
deviations identified in the previous studies. Nevertheless, these studies demonstrate that no single rule or
formula can be used to generalize across a population.
Overall, the results suggest that the rule of the golden
proportion should not be used for treatment planning
without observing individual modifying factors. Furthermore, orthodontic treatment does not change the dentition toward the golden proportion.
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