Comparative Evaluation of Golden Proportion and Recurring Esthetic Dental (RED) Proportion in Natural Dental Esthetics

This study explores the differences between the distribution of Golden Proportion and Recurring Esthetic Dental (RED) Proportion in natural maxillary anterior teeth. Photographs of the subject’s anterior teeth were taken from the frontal view. The width ratios of canine to lateral incisor and lateral incisor to central incisor were calculated. The existence of the Golden Proportion was considered when the width ratios between canine to lateral incisor or lateral incisor to central incisor were within the range of 0.55–0.66. To evaluate the existence of RED proportion in each subject, the width ratio of canine to lateral incisor was compared with the width ratio of lateral incisor to central incisor. The distribution of the Golden proportion was observed in 66.7% and the RED proportion was observed in 22.2% of the natural dentition of the study population. The existence of the Golden proportion was significantly higher than the existence of the RED proportion in well-aligned natural dentition in the study population (P < 0.05). Clinicians may choose the Golden proportion over the RED proportion during the maxillary anterior esthetic treatment procedure.

Introduction

In cosmetic dentistry, it is crucial to achieve a pleasing proportion when restoring or replacing anterior maxillary teeth. Different proportions have been proposed to characterize the appropriate connection between maxillary anterior teeth in the quest to create beautiful restorations [1]–[3]. The Recurring Esthetic Dental (RED) and Golden proportions have frequently been proposed as the foundation of smile design theory [4]–[6].

Lombardi was the first to propose using the Golden ratio in dental practice. The golden proportion is roughly 1.61803:1 in ratio [7]. This idea states that the maxillary lateral incisor’s width, when viewed from the front, should be approximately 62% of the maxillary central incisor’s width. In a similar fashion, the breadth of the maxillary canine, when viewed from the front, should be approximately 62% of the width of the resultant lateral incisor according to Bhuvaneswaram et al. [8]. Researchers found that by keeping this Golden ratio between the teeth in the maxillary anterior section, we could produce an aesthetically acceptable repair and grin.

Golden proportion appears to be an ideal ratio for controlling dental esthetics, however many studies that looked into its occurrences and clinical consequences in natural dentition have referred to it as a theoretical ratio and questioned its applicability [9], [10]. As a result, Ward developed the Recurring Esthetic Dental (RED) proportion concept, which allowed practitioners to choose their own proportion as long as it was consistent and moved distally in the arch [11], [12].

In contrast to the Golden Proportion, which is constant at roughly 62%, the values of the Red Proportion are often between 60% and 80%. This gives us more freedom to adapt tooth characteristics to facial proportions [13]. The width of the central incisor is multiplied by the required RED proportion to arrive at the required width of the lateral incisor after the ideal size of the central incisor has been calculated. To match the intended canine frontal appearance, the lateral incisor width is also multiplied by the same RED proportion. Nevertheless, the RED proportion, according to some experts, may not be the best way to relate the consecutive width of the maxillary anterior teeth in the natural dentition [14], [15].

For a few years, theories have been put out to produce harmony among the anterior teeth, such as the Golden proportion and the RED proportion based on the width ratio. Even though these hypotheses have not yet been thoroughly tested, they are among the most popular analytical tools for developing proportionate smiles. So, we must measure their distribution in people with natural, well-aligned dentitions and attractive smiles in order to support the use of the Golden and RED proportion to build esthetic anterior restoration. Therefore, it’s crucial to determine whether these strategies may be employed as accepted approaches to building beautiful smiles or not, as well as whether these methodologies are well suited to develop appropriate harmony to the frontal teeth.

According to numerous research, the typical tooth size on which these proportionate ideas were founded varied depending on race, age, and sex. In order to establish a harmonious grin design for suitable treatment planning, it is required to compare the distribution of the Golden and RED proportions and their gender and age variation in the Bangladeshi population.

Materials and Methods

Purposive sampling was used in this cross-sectional study, which had 108 participants total, including BSMMU staff members, postgraduate students, and patients. The subjects who participated in the study gave their consent, had a complete set of healthy well aligned natural teeth, and were excluded if they had any of the following: congenital defect in the maxillary anterior teeth, history of orthodontic or orthognathic treatment, and obvious asymmetry in the anterior region. A DSLR camera (CANON 700D) was used to capture a picture of each subject from the frontal perspective, as seen below: people sitting with their heads in their natural positions. The operating distance between the camera and the subject was set at 15 cm. The maxillary anterior teeth’s visibility was improved by the application of cheek retractors. Throughout the investigation, photographs were taken by the same investigator alone under the same lighting conditions.

These images were transferred to a computer. One study measured the width (the distance between the most mesial and distal contact sites) of each canine, lateral incisor, and central incisor of the maxilla using a software named Digimizer (Fig. 1). People stand with their heads in their natural positions. The operating distance between the camera and the subject was set at 15 cm.

Fig. 1. Measurement of each tooth width using software named Digimizer.

To get an accurate result, the investigator had to repeat each measurement and take a mean value. Sometimes, the measurement was repeated if it varied by more than 0.2 mm from the previous.

The width of each canine was divided by the width of the adjacent lateral incisor as seen from the front, and the width of each lateral incisor was divided by the width of the adjacent central incisor to determine whether the Golden Proportion existed. The existence of the Golden proportion between two adjacent anterior teeth was taken into consideration when the ratio was in the range of 0.55 to 0.66. When the width ratios of three neighboring anterior teeth were consistent, the existence of the RED proportion was taken into consideration; a difference of 0.05 or less was regarded as acceptable for the ratio in the case of RED proportion.

The statistical package of social science (SPSS) version 25 (SPSS Inc. Chicago, USA) was used to analyze the collected data. Data was presented as a percentage proportion and a mean SD. To examine the differences between males and females and various age groups, the chi-square and paired t-tests were used. To compare the Golden and RED proportions, the Z test was used. The testing level of significance followed a 95% confident interval (p-value 0.05).

Results

It was determined that 72 out of the 108 participants had the Golden proportion on at least one side. 66.7% of the population had the Golden proportion between their maxillary anterior teeth. On the other hand, 24 people out of 108 showed a RED proportion on at least one side. In 22.2% of the population, there was an incidence of the RED proportion between the maxillary anterior teeth. According to the Z-proportion test, there was a significant difference between the proportions of Golden and RED in the sample population. In the study population, the incidence of the Golden Proportion was noticeably higher than the RED Proportion (Tables I–V). For the distribution of the Golden and RED percentages, there was no discernible variation between the various age and sex groups (P > 0.05) (Tables I–V).

Table I. Distribution of Golden Proportion within the Range 0.55–0.66 in Maxillary Anterior Teeth According to Sex (n=108)

Gender	n	Golder proportion		p-value
		Canine/Lateral	Lateral/Central
Male	62	12 (9.7%)	50 (40.3%)	0.090
Female	46	3 (3.3%)	38 (41.3%)
Total	108	15 (6.9%)	88 (40.7%)

Table II. Distribution of Golden Proportion within the Range 0.55–0.66 in Maxillary Anterior Teeth According to Age (n=108)

Age (in years)	N	Golder proportion		p-value
		Canine/Lateral	Lateral/Central
20-29	53	11 (10.4%)	42 (39.6%)	0.182
30-39	42	3 (3.6%)	37 (44.0%)
40-49	13	1 (3.8%)	9 (34.6%)
Total	108	15 (6.9%)	88 (40.7%)

Table III. Distribution of RED Proportion in Maxillary Anterior Teeth According to Sex (n=108)

Gender	N	RED proportion		p-value
		Yes	No
Male	62	16 (25.8%)	46 (74.19%)	0.380
Female	46	8 (17.4%)	38 (82.6%)
Total	108	24 (22.2%)	84 (77.7%)

Table IV. Distribution of RED Proportion in Maxillary Anterior Teeth According to Age (n=108)

Age (in years)	N	RED proportion		p-value
		Yes	No
20–29	53	16 (30.2%)	37 (69.8%)	0.075
30–39	42	7 (16.7%)	35 (83.3%)
40–49	13	1 (7.69%)	12 (92.3%)
Total	108	24 (22.2%)	84 (77.8%)

Table V. Comparison of the Distribution Between Golden Proportion and RED Proportion (n=108)

	No. of participants	Percentage (%)	Z-proportion test
Golden proportion	72	66.7	Z = 4.314
Red proportion	24	22.2	p < 0.001

Discussion

The current study’s findings revealed that, with a 95% confidence interval, Golden proportions exist in 40.7% of lateral to central incisors and 6.9% of canine to lateral incisors in the maxilla. The outcome of the current study is comparable to that of a study conducted by Mashid et al. [16] in 2004 in which the Golden proportion, which ranges from 0.5 to 0.64, was present between the central and lateral incisors in 34.9% of subjects and between the canine and lateral incisor in 6.2% of subjects.

However, the results of the current study were more significant than those of investigations by Azimi et al. [14] and Preston et al. [17]. Differences in the range in the present study, research methods, and subject ethnicities may account for variations in the values found in this study as opposed to the previous studies [14], [17], [18]. In line with earlier studies, there were no appreciable differences between the various age and sex groups (P > 0.05).

22.2% of the individuals had the RED proportion, which had a value of 0.70 ± 0.05. This number was rather close to the 70% RED proportion as Ward et al. [11]. The values for the presence of the RED proportion were in line with those from the study by Azimi et al., which revealed that the RED proportion was present in an 18.5% sample and had a value of 0.73 ± 0.05. Neither of these investigations found the presence of the RED proportionin the majority of the sample populations [14]. In line with earlier studies, no statistically significant difference was discovered between the various age and sex groups (P > 0.05).

In this study, 72 people out of 108 showed the Golden proportion on at least one side. 66.7% of the population had the Golden proportion between their maxillary anterior teeth. On the other hand, 24 people out of 108 showed RED proportion on at least one side. In 22.2% of the population, there was an incidence of the RED proportion between the maxillary anterior teeth. According to the Z-proportion test, there was a significant difference between the proportions of Golden and RED in the sample population.

Golden proportion incidence was noticeably higher than RED proportion incidence. Furthermore, 33% of the patients had bilateral presence in their native maxillary anterior dentition if they had the Golden proportion. However, only 7.2% of participants with RED percentage in their native maxillary anterior teeth had bilateral presence.

Two popular theories that have been taken into consideration for many years to achieve an aesthetically pleasing anterior restoration are the Golden and RED proportions. Even though some researchers in their studies disputed the presence of the Golden and RED proportions in the natural dentition, both are widely used by smile designers in various clinical settings throughout the world. However, in this study, in well-aligned natural dentition, the presence of the Golden proportion was substantially higher than the presence of the RED proportion.

Conclusion

In the research population’s well-aligned natural dentition, the presence of the Golden proportion was substantially higher than the presence of the RED proportion. As a result, during the maxillary anterior esthetic treatment technique, the practitioner may opt for the Golden proportion rather than the RED proportion.