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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. [ABSTRACT FROM AUTHOR]

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.

Geometric properties of finite Blaschke products have been intensively studied by many different aspects. In this paper, our aim is to study geometric properties of finite Blaschke products related to the golden ratio α = 1 + √ 5 /2 . Mainly, we focus on the relationships between the zeros of canonical finite Blaschke products of lower degree and the golden ratio. We show that the geometric notions such as "golden triangle, "golden ellipse" and "golden rectangle" are closely related to the geometry of finite Blaschke products. [ABSTRACT FROM AUTHOR]

Currently, the European Commission puts emphasis on supporting collaboration between universities and business. There are many possible ways to create a strong relationship between both these parties. Positive results of such cooperation lead to increased competitiveness of the global market and, in consequence, bring significant growth of innovation. The cooperation between research to-research (R2R) and research-to-business (R2B) is analysed. The paper shows how the IT technology can be used to support and stimulate it. In our University we proposed a two-step strategy. Firstly, we tried to improve collaboration among scientists in order to develop R2R activities. Secondly, we focused on R2B projects that stimulate promising scientists to take part in various innovative activities carried out in cooperation with the industry representatives. Based on some well-known good practices a special Internet platform was designed and implemented to support such a strategy. Its name is the “Bridge of Knowledge”. The platform architecture, its functionality and some other aspects of the development process are described. The platform was developed and introduced at the Gdańsk University of Technology. It has been available online for nearly 2 years now and it has been attracting increasing numbers of new visitors and returning users. Several use cases of cooperation between R2R and R2B were analysed and described with the use of advanced analytic tools and on the basis of the organisation’s resources. The idea of the Bridge of Knowledge platform is to gather and share resources not only from one university. The architecture of the platform focuses on a wide and easy interoperability. Other universities can share their resources without any additional cost.

The Fibonacci sequence of numbers is known since the ancient past. It is considered as a proportion which can be frequently appreciated in nature. The associated ratio, called as the golden ratio is manifested in the works of art, nature, galaxies, monuments etc. Many famous mathematicians, philosophers, and artists have used this ratio in their work. Humans distinguish this proportion as pleasing, as it enlightens beauty when applied in living or non living entities. The ideal proportion is directly related to golden proportion. It ranges from 1 to 1.618. Moreover, the proportion can be applied in facial aesthetics also. Studies have showed that the beautiful faces have facial measurements close to golden ratio. Thus, the treatment following the standard will help in obtaining optimal facial aesthetics. The review is written with an aim to highlight the historical perspectives, its varied applications in the past and present; and further scope of research in future.

Our goal is to prove that the golden section, however important, is not the only key to understand a mathematical-formalizing approach to the idea of beauty. Having developed, from this point of view, reading keys linked to the post-modern, it is necessary to link together the multiple rivulets of knowledge that gather in this direction. Moreover the canons of the approaches presented up to now are very indicative for the understanding of many aspects of beauty, which however depends on the historical moment and the cultures created in the various civilizations. Therefore we can affirm that there is no effective definition of "beauty" that can be codified through fixed canons, but that the concept is expressed by a series of stratifications and interpretations that tend to link several major variations, expressing the various answers given by man to the question: what is the beauty?

The Fibonacci sequence of numbers is known since the ancient past. It is considered as a proportion which can be frequently appreciated in nature. The associated ratio, called as the golden ratio is manifested in the works of art, nature, galaxies, monuments etc. Many famous mathematicians, philosophers, and artists have used this ratio in their work. Humans distinguish this proportion as pleasing, as it enlightens beauty when applied in living or non living entities. The ideal proportion is directly related to golden proportion. It ranges from 1 to 1.618. Moreover, the proportion can be applied in facial aesthetics also. Studies have showed that the beautiful faces have facial measurements close to golden ratio. Thus, the treatment following the standard will help in obtaining optimal facial aesthetics. The review is written with an aim to highlight the historical perspectives, its varied applications in the past and present; and further scope of research in future. [ABSTRACT FROM AUTHOR]

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.

It can be found quite often in the literature that many well-known architects have employed either the golden rectangle or the Fibonacci rectangle in their works. On contrary, it is rare to find any specific reason for using them so often. Recently, Shekhawat (2015) proved that the golden rectangle and the Fibonacci rectangle are one of the best connected rectangular arrangements and this may be one of the reasons for their high presence in architectural designs. In this work we present an algorithm that generates n-4 best connected rectangular arrangements so that the proposed solutions can be further used by architects for their designs.

It is often found in the literature that many researchers have studied or documented the use of golden rectangle or Fibonacci rectangle in architectural design. In this way, a lot of well-known architects in the history, knowingly or unknowingly, have employed either the golden rectangle or the Fibonacci rectangle in their works. Using some mathematical tools, this paper tried to approach one of the properties of the golden rectangle (or the Fibonacci rectangle) and its significance to architectural design, which could lead to state one hypothesis about why architects have used them so often. This work begins with an algorithm which constructs a Fibonacci rectangle and a golden rectangle. Then adjacency among the squares (which are arranged inside them) is defined, by considering each square as a room or an architectural space. At the end, using some tools of the graph theory, it has been proved that they are one of the best arrangements of squares (or rectangles) inside a rectangle, from the point of view of connectivity.

This paper presents an interesting deduction of the Golden Spiral equation in a suitable polar coordinate system. For this purpose, the concepts of Golden Ratio and Golden Rectangle, and a significant result for the calculation of powers of the Golden Ratio ϕ using terms of the Fibonacci sequence are mentioned. Finally, various geometrical considerations that help us deduce the sought equation are presented. [ABSTRACT FROM AUTHOR]

It can be found quite often in the literature that many well-known architects have employed either the golden rectangle or the Fibonacci rectangle in their works. On contrary, it is rare to find any specific reason for using them so often. Recently, Shekhawat (2015) proved that the golden rectangle and the Fibonacci rectangle are one of the best connected rectangular arrangements and this may be one of the reasons for their high presence in architectural designs. In this work we present an algorithm that generates n - 4 best connected rectangular arrangements so that the proposed solutions can be further used by architects for their designs. [ABSTRACT FROM AUTHOR]

It is often found in the literature that many researchers have studied or documented the use of golden rectangle or Fibonacci rectangle in architectural design. In this way, a lot of well-known architects in the history, knowingly or unknowingly, have employed either the golden rectangle or the Fibonacci rectangle in their works. Using some mathematical tools, this paper tried to approach one of the properties of the golden rectangle (or the Fibonacci rectangle) and its significance to architectural design, which could lead to state one hypothesis about why architects have used them so often. This work begins with an algorithm which constructs a Fibonacci rectangle and a golden rectangle. Then adjacency among the squares (which are arranged inside them) is defined, by considering each square as a room or an architectural space. At the end, using some tools of the graph theory, it has been proved that they are one of the best arrangements of squares (or rectangles) inside a rectangle, from the point of view of connectivity. [ABSTRACT FROM AUTHOR]

Associating geometric arrangements of 9 Loshu numbers modulo 5, investigating property of golden rectangles and characteristics of Fibonacci sequence modulo 10 as well as the two subsequences of its modular sequence by modulo 5, the Loshu-Fibonacci Diagram is created based on strict logical deduction in this paper, which can disclose inherent relationship among Taiji sign, Loshu and Fibonacci sequence modulo 10 perfectly and unite such key ideas of holism, symmetry, holographic thought and yin-yang balance pursuit from Chinese medicine as a whole. Based on further analysis and reasoning, the authors discover that taking the golden ratio and Loshu-Fibonacci Diagram as a link, there is profound and universal association existing between researches of Chinese medicine and modern biology. [ABSTRACT FROM AUTHOR]

This paper analyses the presence of the Fibonacci numbers and the golden section within a characteristic project of one of the twentieth century's leading architects: the Pastoor Van Ars church in The Hague designed by Aldo van Eyck. By means of a thorough analysis of the building based on field work and consultation of unpublished documents, it is possible to show that the compositional scheme of the plan of the church seems to have been designed according to Fibonacci relationships and the golden rectangle. [ABSTRACT FROM AUTHOR]

There is substantial evidence that even in Pre-Civilization era; human beings were conscious and strongly aware of beauty. Crude cave paintings point out this fact and so does old civilizations across the globe eg. Mayan, Egyptian, Mesopotamian, Greek, Indian, and Chinese. Esthetics, proportion, form and function go hand-in-hand. This was realized by humans very early, since, the inception of civilization, and the very fact was appreciated by great artists like Leonardo da Vinci and Michelangelo. This mystical (1:1.618) proportion was, for long, termed as Magical/Divine Proportion and later on Golden Proportion, which was appreciated in nature, both in plants and animals. It was also used in architecture. Attention to existence of Golden Proportion in dental arches was drawn by Lombardi1 and Levin2 (1978). Marquardt discovered the Golden Rectangle i.e., height of central incisor is in Golden Proportion to the width of the two central incisors. This Golden Proportion is also used in reconstruction of maxillofacial defects eg., eye, ear, nose, and fingers. The Golden Proportion principle is also used to design implant supported prostheses. Ward3 demonstrated the Recurring Esthetic Dental Proportion (RED) claiming it to be more consistent and practical to use in prosthodontic rehabilitation. This paper traces the origin of the Divine Proportion and gives an overview of the adaptation of the Golden Proportion in art and architecture in the middle ages. The paper also gives us an insight of how the Golden Proportion has been used in dentistry, particularly Prosthodontics, in the fabrication of Removable, Fixed, Maxillofacial, and Implant supported prostheses; and also been adapted in newly developed electronic techniques like 3-D imaging and interactive software. [ABSTRACT FROM AUTHOR]

The golden proportion has been known since a long time and is considered a proportion often cited as occurring frequently in nature. It has been described by many artists, mathematicians, scientists and philosophers. The proportion encompasses both living and nonliving entities; even artificial components and structures appear to be directed to conform to the golden proportion. It appears that humans are genetically programmed to recognize this proportion as pleasing since it explains beauty and is related to the science of numbers. The ideal proportion is related directly to the golden proportion that ranges from 1 to 1.618. The golden proportion is considered a universal standard for facial beauty, and its use may help simplify the diagnosis of facial and dental disharmonies, and treatment using this standard will help restore optimal facial esthetics. [ABSTRACT FROM AUTHOR]