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Background This study aimed to evaluate dentist perceptions of attractive smiles in the Pakistani population, considering different dental proportions. Methods Maxillary casts and digital images were used to create symmetrical representations of anterior teeth. dentists’ preferences for good and bad teeth proportions, width/height ratios, and various dental proportions (golden, recurring esthetic dental (RED), golden percentage, Preston, and local/observed) were assessed using one sample and paired t-test. The Chi-square test was used to determine the gender disparities and factors affecting smile attractiveness. A p -value of ≤ 0.05 was taken as significant. Results The RED proportion emerged as the preferred choice for normal-sized teeth, with specialists and general dentists favoring it over the golden proportion. For tall teeth, the golden proportion was predominantly preferred. The golden percentage received limited preference for aesthetic smile construction. Conclusions The smiles created using the principles of RED proportion were opted as the most attractive by local dentists. Factors such as tooth arrangement, color, and midline were highlighted as essential considerations in aesthetic smile construction.

Predictable results in the aesthetic treatment of anterior teeth can be obtained by resorting to the concept of dental aesthetics and, in particular, defining the ideal tooth dimensions and proportions to obtain a harmonious smile. Considering the great variety of articles dealing with the topic, and the lack of updated reviews, this narrative literature review aims to evaluate current knowledge on anterior teeth dimensions and to verify the existence and the potential applications of the anterior teeth proportioning theories (Golden Proportion, Golden Percentage, RED Proportion, and Golden Rectangle). PubMed, Embase, Cochrane Library, and Google Scholar databases were comprehensively searched using different keywords and term combinations. The research includes articles published up to June 2023, no time limits were set, and only articles in English were included. Inclusion criteria comprehended reviews, clinical studies, and in-vitro studies. A total of 66 articles were selected. Two main topics were identified: “Anterior teeth dimensions”, “Golden Proportions, Golden Percentage, RED Proportions, and Golden Rectangle”. As far as tooth dimensions are concerned, different width ranges are recognized for men and women and for different ethnic groups. Perfectly symmetric contralateral elements are found in low percentages of subjects. The correlation between dental dimensions and facial parameters is not always present, and it strongly depends on the sample’s ethnicity and gender. Ideal tooth proportions were only partially identified.

Objectives To evaluate the validity of the Golden Proportion, Golden Percentage, and Recurring Esthetic Dental (RED) Proportion among Kenyans of African descent with naturally well‐aligned teeth. Materials and Methods Standardized frontal photographic images of the smiles of 175 participants aged 18–35 years were obtained, and Adobe Photoshop was used to analyze and measure the frontal widths of the maxillary central and lateral incisors and canines in triplicate. The average teeth widths were calculated to determine the existence of the Golden Proportion, Golden Percentage, and RED Proportion, and their validity using independent sample t‐tests to compare the differences in the mean teeth widths at α < 0.05. Results The number of male and female participants was 107 (61.1%) and 68 (38.9%), respectively. The Golden Proportion between the maxillary central and lateral incisors was found in 4.0% on the right and 2.8% on the left of all the participants, but between the maxillary lateral incisors and canines was found in only 0.6% on the right of male participants (p < 0.0001). The RED Proportion between the maxillary lateral and central incisors was in the range of 67%–70%, and between the canines and lateral incisors was 82%–84% (p < 0.0001). The proportion of RED was not constant, and gradually increased distally. The Golden Percentage of 15% was observed in the lateral incisors bilaterally; however, in the central incisors and the canines, the Golden Percentage was 22% and 12%, respectively. Conclusion The Golden and RED Proportions were invalid determinants of anterior teeth proportions. The Golden Percentage existed only in the lateral incisors. The Golden Proportion, RED Proportion, and Golden Percentage theories may not be applicable to all populations when designing smiles. Racial and ethnic backgrounds are important considerations to establish objective quantifiable values of anterior tooth proportions that are beneficial for esthetic restorations.

Aim: This study aimed to investigate the existence of the golden proportion, recurring esthetic dental (RED) proportion and golden percentage between the frontal view widths of the maxillary anterior natural dentition among students of Indian origin by the aid of digital photography. Materials and Methods: This study was conducted with 80 dental students (41 female and 39 male), with ages ranging from 20 to 23 years. Students whose natural smile did not develop any visual tension with regard to the study′s and their own criteria were selected as having an esthetic smile. Photographs were taken, and the mesiodistal widths of six maxillary anterior teeth were measured digitally using software. Once the measurements were recorded three different theories of proportion were applied and statistical analysis was done. Results: The golden proportion, i.e., 62% RED proportion and golden percentage were not observed in the subjects. According to the subjects evaluated, the average width of the maxillary lateral incisor was 72% of the frontal view width of the central incisor. The average width of the canine was 84% of the frontal view width of the lateral incisor. Conclusion: The golden proportion and RED proportion were not observed in the natural smiles of subjects who were deemed to have an esthetic smile. The values proposed for the golden percentage theory were not observed in subjects with an esthetic smile. Average frontal view percentage widths of the maxillary anterior dentition exist and can be useful in predicting naturally occurring widths in smiles deemed to be esthetic in a specific population.

The anterior maxillary tooth proportions are an important component of anesthetic smile. Harmonization of the face and the observed proportions affect the acceptability of a smile's esthetics. Many concepts have been proposed as guidelines for esthetic dental proportions, such as the golden proportion and the golden percentage. However, no study has yet investigated the proportions of the maxillary anterior tooth widths in the Deutero-Malay race, the largest population in Indonesia. The aim of this study was to evaluate the maxillary anterior tooth width proportions among students of Deutero-Malay origin in the Faculty of Dentistry, Universitas Indonesia (FKG UI) and to verify whether these proportions match the golden percentage. Methods: This descriptive study was conducted on 100 FKG UI students of Deutero-Malayorigin. Subjects were queried regarding their satisfaction with the overall appearance of their smiles (harmonization of face, mouth, and teeth). Study models were made for all subjects from maxillary impressions. The outermost point of the maxillary anterior tooth width, from the frontal aspect, were projected onto millimeter-block paper and measured. The percentage was obtained by dividing the width of each anterior tooth by the total anterior tooth width and the data were then tabulated and analyzed statistically. As a results, the proportions of the maxillary anterior tooth widths were 12, 16, 22, 22, 16, and12%. These proportions were considered esthetically satisfying to 97% of the study subjects. It was conclude that the maxillary anterior tooth widths among FKG UI students of Deutero-Malay origin showed a specific proportion that does not follow the golden percentage proposed in earlier studies on subjects of different origins. However, the observed proportion was considered esthetically satisfying by the study subjects.

This book combines practical guidance and theoretical background for analysts using empirical techniques in competition and antitrust investigations. Peter Davis and Eliana Garcés show how to integrate empirical methods, economic theory, and broad evidence about industry in order to provide high-quality, robust empirical work that is tailored to the nature and quality of data available and that can withstand expert and judicial scrutiny. Davis and Garcés describe the toolbox of empirical techniques currently available, explain how to establish the weight of pieces of empirical work, and make some new theoretical contributions. The book consistently evaluates empirical techniques in light of the challenge faced by competition analysts and academics--to provide evidence that can stand up to the review of experts and judges. The book's integrated approach will help analysts clarify the assumptions underlying pieces of empirical work, evaluate those assumptions in light of industry knowledge, and guide future work aimed at understanding whether the assumptions are valid. Throughout, Davis and Garcés work to expand the common ground between practitioners and academics.

Some results are given of a study of phytoplankton in lake if Osbysjon in the town of Djursholm, near Stockholm. This is a small shallow lake, pond-like in character, with little or no influx of water. The principal species are chrysophytes, with cyanophytes, desmids and diatoms of secondary importance in the standing crop. During the winter of 1958 there was a marked reduction in oxygen concentration, with formation of hydrogen sulphide in the deeper layers. Sulphur bacteria and some iron bacteria began to develop in January, but by April chlorophytes and dinoflagellates had appeared and during May the normal algal population was restored. During the period of break-up of ice there was a reduction in the total volume of standing crop. The various species observed are listed and their distribution is shown in tables and diagrams.