Esthetic Smile Analysis of Maxillary Anterior Tooth Width: The Golden Percentage

STEPHEN R. SNOW, DDS*

ABsTRAcr With increasing application of cosmetic dental treatment comes the need for a greater under- standing of esthetic principles. Scientific analysis of beautiful smiles has revealed repeatable, objective principles that can be systematically applied to evaluate and improve dental esthetics in predictable ways. Symmetry across the midline, anterior or central dominance, and regressive proportion are three composition elements required to create unity and esthetics in a smile. The Golden Proportion has been suggested as one possible mathematic analysis tool for assessing dominance and proportion. in the frontal view of the arrangement of maxillary teeth. It has proven to be controversial in developing esthetically beautiful smiles and cumbersome for evaluating symmetry. CLINICAL SIGNIFICANCE This article considers a bilateral analysis of apparent individual tooth width as a percentage of the total apparent width of the anterior segment and proposes the concept of the Golden Percentage as a more useful application in diagnosing and developing symmetry, dominance, and proportion for esthetically pleasing smiles.

( J Esthet Dent 11:177-184,1999)

s dental decay decreases,' as A public desire for improved dental esthetics increases; and as dental restorative materials and techniques improve,g9 the nature and scope of dental treatment is evolving to emphasize elective cos- metic treatment. Because esthetics embraces the study of beauty and emotional responses to it,l0 cos- metic dental treatment involves artistic and subjective components designed to create the illusion of beauty. With the increasing appli- cation of cosmetic treatment

comes the need for a greater under- standing of esthetic principles. Careful scientific analysis of beautiful smiles has shown that repeatable, measurable, objective principles can be systematically applied to evaluate and improve dental esthetics in predictable ways.11*li Smile line placement, minimized negative space, axial inclination graduation, incisal embrasure gradation, and gingival frame contour are examples of some of the esthetic principles considered and used in smile design.

SYMMETRY, DOMINANCE, AND PROPORTION

Lombardi described the importance of composition and unity for the perception of a pleasing smile.I3 Just as the arrangement of individual objects within a painting contributes to its composition and unity, the arrangement of individual teeth in a smile determines their esthetic impact as well.

An esthetically pleasing smile tends to exhibit a high degree of symmetry across the midline (Figure 1). Teeth

Presented at the UCLA Center for Esthetic Dentistry, Esthetic and Contemporary Restoratiue Pact Graduate Program, Lac Angeles, California, October 17,1997. *Private Practice Emphasizing Cosmetic Restoratiue Dentistry, Dandle, California; Visitin Professor, UCLA Center for Estbetic Dentistry, Los Angeles, California; Faculty, Esthetic Professiona&, Woodbnd Hills, orlifornia

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E S T I I E T I C S M 1 I . E A N A I , Y S I S O F M A X I L L A R Y A N T E R I O R T O O T H W I D T H : T H E G O L D E N P E R C E N T A G E

G O L D E N P R O P O R T I O N

The apparent width differences cre- ated by a perspective view of fence boards, an arch of teeth, or any other regressive series of objects can be analyzed mathematically. Formulae can be generated to predict a con- stant ratio in the apparent diminish- ing size of the repeated elements.

Figure 1 . Esthetically pleasing smile with balanced symmetry, dominance, and proportion.

evenly positioned in a balanced arrangement within the arch indi- vidually contribute to the appear- ance of a unified whole. By contrast, an asymmetrical arrangement of teeth appears irregular, imbalanced, or haphazard (Figure 2).

A perspective view of a fence pro- vides additional insight into smile composition principles (Figure 3). The fence boards are an example of a regressive series. Each individual fence board appears proportionally smaller in the distance. A frontal perspective view of an arch of teeth also represents a regressive series. The curvature of the dental arch reveals less and less of each tooth toward the distal. The less a tooth is visible, the smaller and less important it appears within the display. Maxillary central incisors, by virtue of their position in the front of the arch, should appear to be the widest, whitest, and therefore,

the most predominant teeth when viewed from the frontal aspect.

All three composition elements of symmetry across the midline, ante- rior or central dominance, and regressive proportion are created by the dentoalveolar arch curvature and are simultaneously required for ideal unity and esthetics in a smile.14

One such constant is the Golden Proportion. Like any constant factor used to determine the ratio between two parts, the Golden Pro- portion mathematically describes the ratio between a larger and a smaller length. The Golden Propor- tion, however, is unique in that the ratio of smaller length relative to the larger length is identical to the ratio of the larger length to the total length (Figure 4). The illustration demonstrates the presence of this ratio within the segments of a pent- agon. The ratio AB:BC = the ratio AC:AB. The ratio is 1.618:l.O.

Figure 2. Less pleasing smile with a haphazard tooth arrangement causing asymmetry and poor balance.

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Figure 3. Perspective view of a fence demonstrating a regressive series with each element appearing proportionally smaller in the distance.

This ratio has been used for cen- turies by artists, mathematicians, architects, and engineers to study and design proportionality in the beauty of art and nature. Dentists have proposed that the Golden Proportion is prevalent in a compar- ative analysis of the dimensional ele- ments of beautiful faces and beauti- ful smile~.’~J~ The Golden Proportion is considered a “starting point” in designing the relative width of teeth in a beautiful smile. Whether or not the Golden Propor- tion is absolutely and dogmatically required for a beautiful smile is still unclear. It is beyond the scope of this article to prove that strict adherence to the Golden Proportion in the width relation of anterior teeth is valid or even necessary for pleasing smile esthetics. A subse- quent article will address that ques- tion. But even if the Golden Propor- tion is not an absolute determinant of optional esthetics, it is unques-

tionably a useful tool for initially evaluating dominance and propor- tion in tooth arrangement and cos- metic dental treatment planning.

Classically, the application of a Golden Proportion analysis is based on the apparent mesiodistal width of the anterior teeth (from distal height of contour to distal height

of contour) when viewed from the frontal aspect (Figure 5) . Typically, the presence or absence of the Golden Proportion within a smile is evaluated by measuring the anterior teeth from the frontal aspect and then dividing the apparent mesio- distal width of the central incisor, lateral incisor, and canine by the apparent width of the lateral incisor. Usually the central incisor appears wider than the lateral, yielding a ratio greater than 1.0. The ratio of the width of the lateral to itself is always 1.0. If the arrangement of teeth is “in Golden Proportion,” then the 1.618:l.O ratio for anterior teeth yields the relative widths of 1.618:1.0:0.618 for the central incisor, lateral incisor, and canine, respectively (Figure 6).

Unfortunately, Golden Proportion analysis traditionally has been applied unilaterally-correlating the width of the canine and central

Figure 4. Golden Proportion as seen in the ratio of the lengths of the seg- ments within a pentagon.

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ESTHETIC SMILE ANALYS18 OF MAXILLARY ANTERIOR TOOTH WIDTH: THECOLDEN PERCENTAGE

incisor to the width of the lateral incisor on the same side. Unilateral analysis of a smile presents an obvi- ous difficulty: it allows for analysis of dominance and proportion but not symmetry.

Figure 7, A, shows how unilateral Golden Proportion evaluation may generate confusing computations if the mesiodistal width of the lateral incisors differs. In this circumstance, the central incisors can be measured to determine that they have identical widths. However, the lateral incisors appear to have different widths, owing to malalignment and overlap. As a result, differential numeric ratios are obtained for the relative proportion of the two central incisors, despite the fact that they are identical in width (Figure 7, B).

In Figure 8, A, the central incisors have measurably different widths.

However, Golden Proportion evalu- ation shows a larger ratio for the maxillary right central incisor than for the maxillary left central incisor, even though the left is obviously significantly wider than the right incisor (see Figure 8, B). Once again, the potentially confusing results arise from the differing widths of the lateral incisors used to unilater- ally calculate the ratios.

One final difficulty in applying the Golden Proportion analysis is that it requires a caliper and calculator to complete. It may be conceivable for a clinician to “eyeball” a ratio of 1.6 18:l .O, but it certainly is not convenient.

These examples demonstrate how unilateral calculations provide no meaningful numeric assessment of symmetry and, therefore, no quan- tifiable recommendation for the

development of unity and balance required for an esthetically pleasing smile. Clearly, for the Golden Pro- portion to be most useful in cosmetic dentistry, it must be adapted for easy bilateral analysis of the teeth.

GOLDEN PERCENTAGE

Supposing that a specific tooth arrangement were in perfect Golden Proportion, the ratio between the perceived widths of the maxillary anterior teeth would be 0.61 8:l .O: 1.618:1.618:1.0:0.618. If all these width ratios were added together the total would be 6.472. Dividing the individual ratio values by the total yields the percentage of width that each individual tooth would occupy of the total canine-to-canine width, viewed from the frontal per- spective. The results are interesting (Table 1). The Golden Proportion has been applied to the total canine- to-canine width to become the

Figrtre 5. Differences in the apparent mesiodistal width of the maxillary right lateral incisor and the maxillary left lat- era1 incisor when viewed from the frontal aspect.

Figure 6. G o k Proportion as seen m the ratio of the mesiodistal widths of the maxiky viewed from the frontal aspect. (This illustration was digitally created to demonstrate the appearance of an esthetically pleasing smile that fits the Goldm Proportion exactly)

anterior teeth when

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Figure 7. A, Malaligned arch form displaying central incisors with identical widths. B, Unilateral Golden Proportion analysis produces different ratio results for the central incisors-even though they have the same width.

“Golden Percentage”: 10%: 15%: 25 %:25 YO: 15 YO: 10% (Figure 9).

The Golden Percentage clearly is more useful in analyzing esthetic properties of the smile:

It does not depend on the width of lateral incisors alone for its analy- sis. Instead, it evaluates the width of each tooth for its contribution to

symmetry, dominance, and propor- tion of the entire anterior segment.

generate identical percentages in the analysis. Asymmetry is clearly identifiable and quantifiable. Percentages of 25% of the canine- to-canine width for a single central incisor (or 50% for both central

Teeth with identical widths

incisors) can be readily analyzed chairside during routine examina- tion and are easily estimated without calipers or calculators.

Application of the Golden Percent- age analysis to the smile in Figure 7 now provides meaningful results (Figure 10). The maxillary right and left central incisors generate identical

Figure 8. A, lrregular tooth arrangement displaying central incisors of differing widths. B, Unilateral Golden Proportion analysis produces a larger ratio for the maxillary right central incisor, even though it is clearly narrower than the maxillary lefr central incisor.

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ESTHETIC SMILE ANALYSIS O F MAXILLARY ANTERIOR TOOTH WIDTH: T H E GOLDEN PERCENTAGE

TABLE 1 CONVERTING GOLDEN PROPORTION T O GOLDEN PERCENTAGE

Maxillary Tooth Golden Proportion Ratio Golden Percentage Calculation (Ratio)

Right canine 0.6 18 0.61816.472 (10%)

Right lateral incisor 1 .ooo 1.000/6.472 (15%)

Right central incisor 1.618 1.61U6.472 (25%)

Lett central incisor 1.618 1.6 18/6.472 (25%)) Left lateral incisor 1 .ooo 1.00W6.472 (15%))

Left canine 0.6 18 0.618/6.472 (10%)

Total 6.472 6.47Y6.472 ( 100%)

percentages (24%) reflective of their identical apparent widths. The true asymmetry of the lateral incisors, caused by the twisting and overlap of the maxillary left lateral incisor, is revealed. Further applica- tion of Golden Percentage analysis to the smile in Figure 8 provides useful results as well (Figure 11). The asymmetry of the central incisors is now confirmed and quantifiable.

DISCUSSION

The symmetry, dominance, and proportion of maxillary anterior teeth are affected by many factors. The position of the incisal edges and the gingival frame are factors that define the apparent height of teeth. Taller teeth naturally have increased light reflection and increased visibility.

In considering only the effect of apparent width on symmetry, dominance, and proportion, the relative width percentage of teeth is determined by individual tooth alignment within an arch form.

Several factors, including rotation, spacing, overlapping, and other forms of malalignment of teeth, all negatively affect the relative pro- portion of each anterior tooth seen in the frontal view. If the malalign- ment factors of rotation, diastemas, overlapping, buccoversion, and linguoversion are absent or elimi- nated, then the apparent width per- centages of teeth is determined by curvature of the arch form itself. If only evenly aligned archforms are considered, the relative differences in the frontal appearance of nar- rower arches compared to wider arches can be analyzed.

Narrower arch forms curve back rapidly through the lateral incisors and canines as the transition occurs into the posterior segments. From the frontal aspect, the lateral incisors and canines in MITOW arches are necessarily “tucked back” to form the relatively quick turn. In a MITOW

curvature, the lateral incisors and canines would display a more oblique orientation when viewed

from the frontal aspect. Narrower arches would predictably display lateral incisors and canines that comprise a smaller percentage of the perceived canine-tocanine width relative to the central incisors. There- fore, these arches would appear to have more dominant central incisors. Arches with width percentages that approximate the Golden Percentage would have more dominant central incisors and would imply a dental arch that is relatively narrower.

Wider arch forms curve back slowly in a “delayed” transition into the posterior segments. From the frontal aspect, the lateral incisors and canines in wide arches are necessarily ‘flattened out” to form the relatively gentle tum. In a wide curvature the lateral incisors and canines would display a more facial orientation when viewed from the frontal aspect. Wider arches would predictably display lateral incisors and canines that comprise a larger percentage of the perceived canine- tocanine width relative to the

182 J O U R N A L OF ESTHETIC DENTISTRY

SNOW

Figure 9. Bilateral analysis of the Golden Percentage. (The identical illustration as Figure 6 digitally created to demon- strate the appearance of an esthetically pleasing smile that fits the Golden Percentage exactly)

central incisors. Therefore, these arches would appear to have less dominant central incisors. Arches with symmetric width percentages that deviate from the Golden Percentage (with central incisor percentages significantly less than 25%) would have less dominant central incisors and imply a dental arch that is relatively wider.

In the clinical application of smile design, the final relative width proportion of anterior teeth is ulti- mately dependent upon the arch form. In comparing two hypothetic arches that have teeth with identical mesiodistal widths, the wider arch form would have relatively narrower central incisors and relatively wider canines, less closely imitating the

Golden Percentage relation (Figure 12). The narrower arch of the two would have relatively wider central incisors and relatively narrower canines, more closely approximating the Golden Percentage (Figure 13). The curvature of the arch form may be the most critical factor in deter- mining the esthetics of maxillary tooth width proportions.

Figure 10. Bilateral Golden Percentage analysis of this arch arrangement now produces percentages that reflect the identi- cal widths of the maxillary left and right central incisors.

Figure 11. Bilateral Golden P ~ c ~ ~ g e a ~ l Y s i s O f this arch now produces percenWeS that qwntib' the diffm-

ence in widths of the maxillary left and right central incisors.

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ESTHETIC SMILE ANALYSIS O F MAXILLARY ANTERIOR TOOTH WIDTH: THE GOLDEN PERCENTAGE

Figure 12. Relatively wide arch form with relative width pro- portions that deviute from the Golden Percentage.

Figure 13. Relatively narrow arch form digitally created fiom the same image used in Figure 12 to compare the effect of arch form on two bypothetic arches with teeth of identical mesio- distal width. Golden Percentage is followed in this example.

CONCLUSION

Although the precise percentages of 10%:15%:25%:25%:15%:10~0 are required for anterior tooth width ratios to be “in Golden Propomon,” further studies are required to vali- date if those exact percentages are required to create the most subjec- tively beautiful smiles. Possibly, society maintains slightly different percentages to define the most beautiful smiles in different cul- tures. Future studies with carefully designed methods that objectively determine quantifiable width ratios in subjectively beautiful smiles will undoubtedly determine exactly what percentages are truly “golden.”

Nevertheless, the analysis of appar- ent anterior tooth width as a per- centage of total canine-to-canine width is more useful and applicable in diagnosing and creating symme- try, dominance, and proportion for esthetically pleasing smiles. The

principle of the Golden Percentage in evaluation and treatment plan-

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Reprint r e v & : S hen R. Snow, DDS, S n o w Dental Gare,%9 San Ramon Valley Blvd, (Y216, Dnville, CA 94526; e-mail: -&.?let 81999 B.C. Decker 1%.

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