106 results on '"Golden rectangle"'
Search Results
2. Maxillary Anterior Teeth Dimensions and Relative Width Proportions: A Narrative Literature Review.
- Author
-
Cinelli, Francesca, Piva, Francesco, Bertini, Fabio, Russo, Daniele Scaminaci, and Giachetti, Luca
- Subjects
INCISORS ,LITERATURE reviews ,GOLDEN ratio ,COSMETIC dentistry ,ETHNIC groups ,INTERDENTAL papilla - Abstract
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]
- Published
- 2024
- Full Text
- View/download PDF
3. Maxillary Anterior Teeth Dimensions and Relative Width Proportions: A Narrative Literature Review
- Author
-
Francesca Cinelli, Francesco Piva, Fabio Bertini, Daniele Scaminaci Russo, and Luca Giachetti
- Subjects
teeth dimensions ,teeth proportions ,golden proportions ,golden percentage ,RED proportions ,golden rectangle ,Dentistry ,RK1-715 - Abstract
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.
- Published
- 2023
- Full Text
- View/download PDF
4. The Geometry of Beauty
- Author
-
Curcio, Liliana, Kacprzyk, Janusz, Series Editor, Gomide, Fernando, Advisory Editor, Kaynak, Okyay, Advisory Editor, Liu, Derong, Advisory Editor, Pedrycz, Witold, Advisory Editor, Polycarpou, Marios M., Advisory Editor, Rudas, Imre J., Advisory Editor, Wang, Jun, Advisory Editor, Magnaghi-Delfino, Paola, editor, Mele, Giampiero, editor, and Norando, Tullia, editor
- Published
- 2021
- Full Text
- View/download PDF
5. The Divine Proportion
- Author
-
Innocenzi, Plinio and Innocenzi, Plinio
- Published
- 2019
- Full Text
- View/download PDF
6. FINITE BLASCHKE PRODUCTS AND THE GOLDEN RATIO.
- Author
-
ÖZGÜR, Nihal and UCAR, Sumeyra
- Subjects
- *
GOLDEN ratio , *FINITE geometries , *FINITE, The , *TRIANGLES - Abstract
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]
- Published
- 2021
- Full Text
- View/download PDF
7. Comparation between golden rectangle and ideal facial height proposed by the Silva Cephalometric Method (MCS) through digital analysis (NemoStudio 2022) in a university population
- Author
-
Encalada, Manolo Esteban Bravo, Dominguez, Diego Alejandro Lima, Pacheco, Pablo Andrés Astudillo, and Calderón, Manuel Estuardo Bravo
- Subjects
General Medicine ,Golden rectangle ,Facial height ,Golden proportions ,Lateral cephalic x-ray - Abstract
Objective:The purpose of this work was to establish a statistical relationship of the results obtained with two different techniques. The comparison was made between the ideal facial height proposed in the Silva cephalometric method (SCM) and the facial height obtained using Euclid's rectangle or golden rectangle. Materials and Methods:38 cephalometric radiographs of dentistry students of Universidad de Cuenca, of both sexes, were used. All of these radiographs had suitable characteristics for cephalometric tracing in the NemoStudio 2022 software. Once the cephalometric tracing was made using these software tools, SCM was performed on each one of them to collect the data, and then we proceeded to overlap Euclid’s rectangle on all the images. The correlation of these two methods was established with Pearson’s correlation coefficient. Results:It was concluded that the Pearson correlation coefficient was [r]: 0.9271 Conclusions:5% of the patients presented compatibility with the logarithmic spiral of the golden ratio.
- Published
- 2023
8. المستطيل الذهبي في بيت صلاة بعض المساجد التلمسانية.
- Author
-
بن زغادي محمد
- Subjects
ISLAMIC architecture ,SPACE (Architecture) ,MOSQUES ,MODERN architecture ,BUILDING design & construction ,RECTANGLES - Abstract
Copyright of Journals Eduction for Girls is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2021
9. BRIDGE OF KNOWLEDGE: AN INTERNET PLATFORM FOR R2R AND R2B TRANSFER OF KNOWLEDGE AND PROMOTION OF COOPERATION
- Author
-
HENRYK KRAWCZYK and PAWEŁ LUBOMSKI
- Subjects
research to research cooperation ,knowledge to business transfer ,golden rectangle ,science gateways ,knowledge platforms ,Information technology ,T58.5-58.64 - Abstract
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.
- Published
- 2020
- Full Text
- View/download PDF
10. A Compendium of Fibonacci Ratio
- Author
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Priyanka Katyal, Pratima Gupta, Nikhita Gulati, and Hemant Jain
- Subjects
golden angle ,golden proportion ,golden rectangle ,phi concept ,Medicine - Abstract
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.
- Published
- 2019
- Full Text
- View/download PDF
11. Is the Golden Section a Key for Understanding Beauty? - Part I
- Author
-
Franco Eugeni and Luca Nicotra
- Subjects
Golden section, golden number ,beauty ,golden rectangle ,fractals ,Philosophy. Psychology. Religion ,Social Sciences - Abstract
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?
- Published
- 2018
- Full Text
- View/download PDF
12. A Compendium of Fibonacci Ratio.
- Author
-
KATYAL, PRIYANKA, GUPTA, PRATIMA, GULATI, NIKHITA, and JAIN, HEMANT
- Subjects
- *
GOLDEN ratio , *FIBONACCI sequence , *MATHEMATICIANS , *OUTLINES , *PHILOSOPHERS - Abstract
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]
- Published
- 2019
- Full Text
- View/download PDF
13. The Infinitude of Primes
- Author
-
Fine, Benjamin, Rosenberger, Gerhard, Fine, Benjamin, and Rosenberger, Gerhard
- Published
- 2016
- Full Text
- View/download PDF
14. Old Shoes, New Feet, and the Puzzle of the First Square in Ancient Egyptian Architecture
- Author
-
Schneider, Peter, Williams, Kim, editor, and Ostwald, Michael J., editor
- Published
- 2015
- Full Text
- View/download PDF
15. Best connected rectangular arrangements
- Author
-
Krishnendra Shekhawat
- Subjects
Adjacency ,Algorithm ,Architectural design ,Fibonacci rectangle ,Floor plan ,Golden rectangle ,Engineering (General). Civil engineering (General) ,TA1-2040 - Abstract
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.
- Published
- 2016
- Full Text
- View/download PDF
16. Finite Blaschke products and the golden ratio
- Author
-
Sümeyra Uçar, Nihal Yılmaz Özgür, and Fen Edebiyat Fakültesi
- Subjects
Finite Blaschke Product ,Golden Ellipse ,Physics ,Matematik ,Golden Triangle ,Mathematics::Complex Variables ,General Medicine ,Combinatorics ,Finite Blaschke product,golden ratio,golden triangle,golden ellipse,golden rectangle ,Golden Ratio ,Mathematics::Metric Geometry ,Golden ratio ,Mathematics ,Sonlu Blaschke Çarpımı,altın oran,altın üçgen,altın elips,altın dikdörtgen ,Golden Rectangle - Abstract
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 $\alpha =\frac{1+\sqrt{5}}{2}$. 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.
- Published
- 2021
17. Rectangles and spirals
- Author
-
J. N. Ridley
- Subjects
Combinatorics ,General Mathematics ,Diagonal ,Regular polygon ,Golden rectangle ,Rectangle ,Circumscribed circle ,Logarithmic spiral ,Inscribed figure ,Mathematics ,Incircle and excircles of a triangle - Abstract
Every reader knows about the Golden Rectangle (see [1, pp. 85, 119], [2, 3]), and that it can be subdivided into a square and a smaller copy of itself, and that this process can be continued indefinitely, converging towards the intersection point of diagonals of any two successive rectangles in the sequence. The circumscribed logarithmic spiral passing through the vertices and converging to the same point is also familiar (see [3, 4]), and is analogous to the circumcircle of a regular polygon or a triangle. The approximate logarithmic spiral obtained by drawing a quarter-circle inside each of the squares is equally well known [3, p. 64]. Perhaps slightly less familiar is the inscribed spiral, which is tangential to a side of every rectangle, like the incircle of a triangle or a regular polygon. It does not (quite) coincide with the spiral passing through the point of subdivision of each side, as discussed in [3, pp. 73-77]. The Golden Rectangle, its subdivisions, and the circumscribed and inscribed spirals are illustrated in Figure 1.
- Published
- 2021
18. Why golden rectangle is used so often by architects: A mathematical approach
- Author
-
Krishnendra Shekhawat
- Subjects
Algorithm ,Architectural design ,Connectivity ,Fibonacci rectangle ,Floor plan ,Golden rectangle ,Engineering (General). Civil engineering (General) ,TA1-2040 - Abstract
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.
- Published
- 2015
- Full Text
- View/download PDF
19. Algebra and Analysis
- Author
-
Andreescu, Titu and Gelca, Răzvan
- Published
- 2009
- Full Text
- View/download PDF
20. APPLICABILITY OF GOLDEN RECTANGLE IN FAÇADE OF BUILT FORM
- Author
-
Harshika Sahay Ar. and Neelam Kushwah Ar.
- Subjects
business.industry ,Computer science ,Golden rectangle ,Facade ,Structural engineering ,business - Abstract
All of us want to promote pleasing architecture but is there a clear theory that explains what makes a design good. Why do some buildings look pleasing to us while the others not so much? Why do a few of them give us a sense of wellbeing whereas a few of them make us feel out of place. Architecture never has a single answer and is very subjective. It is evident that there could be a tangible relationship between the visual aspect of a building and the intangible that is the way we feel about it. This research tries to understand these tangible characteristics of a built form and tries to objectify aesthetics by analyzing it through the lens of scale and proportion. “Geometry existed before creation” - Johan Kepler “Nature seems to be written in the language of mathematics” - Galileo Galilei These statements form the basis of this research. It will start with the study of the relationship of aesthetics of façade and their proportions by overlaying the guiding principles attached to these attributes on several built forms. Once established as to how through history buildings have related to different simple and complex equations the research moves on to perceive a certain number of buildings in current scenario. These buildings may or may not have been built on some geometrical guiding principles. Later through survey the research will try and identify whether or not an aesthetically pleasing building has some relationship with scale. It will try and identify the exact equation that guided the form of the building. The relationship between proportion and aesthetics will be established by running experiments, overlaying and calculating proportion theories on to the façade of that particular built form.
- Published
- 2020
21. A geometria aplicada à Évora romana: da malha urbana às termas
- Author
-
de Morais Sarmento, Ricardo
- Subjects
architecture ,arqueologia ,rectángulo áureo ,archeology ,Portugal ,golden rectangle ,arqueología ,arquitectura ,rectângulo de ouro ,Flavian ,Flávio - Abstract
The Roman baths in the city of Évora, discovered in 1987 and integrated into the current building of the Paços do Concelho, proved to be one of the most important examples of this typology at the national level. This structure was located close to the Forum and asserted itself as one of the most important public buildings in the city. Thanks to the archaeological intervention of 2019, it was possible to record and study new structures in the complex. Several researches suggest that the architecture of this period uses a vast set of geometric and spatial rules in order to make the space harmonious and sensorially pleasant to human experience. In this sense, the present study proposes to analyze this thermal complex by using geometry with the aim of better understanding its spatial and volumetric organization and also the way in which the aforementioned complex was related to the coeval urban context. Las termas romanas de la ciudad de Évora, descubiertas en 1987 e integradas en el edificio actual de los Paços do Concelho, resultaron ser uno de los ejemplos más importantes de esta tipología a nivel nacional. Esta estructura estaba ubicada cerca del Foro y se afirmó como uno de los edificios públicos más importantes de la ciudad. Con la intervención arqueológica de 2019, se lograron registrar y estudiar nuevas estructuras en el complejo. Varias investigaciones sugieren que la arquitectura de este periodo utiliza un vasto conjunto de reglas geométricas y espaciales para hacer que el espacio sea armonioso y sensorialmente agradable para la experiencia humana. En este sentido, el presente estudio se propone analizar este conjunto termal, utilizando la geometría para tratar de comprender mejor su organización espacial y volumétrica y también la forma en que dicho conjunto se relacionaba con el contexto urbano de la época.[pt] As termas romanas da cidade de Évora, descobertas em 1987 e integradas no actual edifício dos Paços do Concelho, revelaram-se um dos mais importantes exemplares desta tipologia a nível nacional. Esta estrutura localizava-se próximo do Forum e afirmava-se como um dos mais importantes edifícios públicos da cidade. Com a intervenção arqueológica de 2019, foi possível registar e estudar novas estruturas do complexo. Várias pesquisas sugerem que a arquitectura deste período utiliza um vasto conjunto de regras geométricas e espaciais de forma a tornar o espaço harmonioso e sensorialmente agradável à vivência humana. Nesse sentido, o presente estudo propõe-se fazer uma análise deste complexo termal, utilizando a geometria para tentar compreender melhor a sua organização espacial e volumétrica e também a forma como o referido complexo se relacionava com o contexto urbano da época.
- Published
- 2022
- Full Text
- View/download PDF
22. A deduction of the Golden Spiral equation via powers of the Golden Ratio ϕ.
- Author
-
Zahn, Maurício
- Subjects
- *
POLAR coordinates (Mathematics) , *GOLDEN rectangle (Mathematics) , *GOLDEN ratio , *FIBONACCI sequence , *CELESTIAL reference systems - Abstract
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]
- Published
- 2017
- Full Text
- View/download PDF
23. The Golden Rectangle
- Author
-
Kristy Fulton
- Subjects
Combinatorics ,Golden rectangle ,Mathematics - Published
- 2021
24. Best connected rectangular arrangements.
- Author
-
Shekhawat, Krishnendra
- Subjects
FIBONACCI sequence ,MATHEMATICAL proofs ,ALGORITHMS ,RECTANGLES ,ARCHITECTURAL design ,FLOOR plans - Abstract
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]
- Published
- 2016
- Full Text
- View/download PDF
25. Numerous Signs and Natural Objects
- Author
-
Spinks, C. W., Jr and Spinks, C. W., Jr
- Published
- 1991
- Full Text
- View/download PDF
26. The Geometry of Beauty
- Author
-
Liliana Curcio
- Subjects
Computer science ,media_common.quotation_subject ,Theory of Forms ,Beauty ,Perfection ,Golden rectangle ,Natural (music) ,Geometry ,Architecture ,Function (engineering) ,media_common ,Simple (philosophy) - Abstract
The inherent rules of Geometry, as well as the forms described by them, have always inspired artistic creation and suggested canons to achieve perfection in the creating of many works of art. Let us think about the beauty of some geometric shapes used in painting, architecture, sculpture. The natural forms have almost always inspired those built, where the aesthetic aspect is obtained through a deep dialogue between shape, function, materials, and technique. Everything tends to achieve a common goal; and thanks to this communion of knowledge the forms develop themselves differently, in relations with the historical period in which they are used within the various design choices. The dialogue between different fields is fundamental to find those optimal choices to achieve the beauty in each construction in progress. The aim of this work is to understand how it is possible to obtain even very complex three-dimensional surfaces starting from a simple geometric figure—such as a flat polygon—through synthetic processes and simple transformations. These surfaces, often described by structures of extraordinary beauty, are recognizable in the configuration of many natural growth’s forms, in some admirable architectural constructions characterized by perfect and futuristic shapes and, at last, in the description of some contemporary and delicate beauty sculptures where the light is added to the shape to mark its beauty.
- Published
- 2021
27. Why golden rectangle is used so often by architects: A mathematical approach.
- Author
-
Shekhawat, Krishnendra
- Subjects
MATHEMATICAL analysis ,FIBONACCI sequence ,ARCHITECTURAL design ,SPACE (Architecture) ,GRAPH theory ,GOLDEN rectangle (Mathematics) - Abstract
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]
- Published
- 2015
- Full Text
- View/download PDF
28. The golden ratio and Loshu-Fibonacci Diagram: Novel research view on relationship of Chinese medicine and modern biology.
- Author
-
Chen, Zhao-xue, Huang, Yun-kun, and Sun, Ying
- Subjects
CHINESE medicine ,DNA analysis ,BIOCHEMISTRY ,BIOLOGY ,CONCEPTUAL structures ,MATHEMATICAL models ,MATHEMATICS ,PHENOMENOLOGY ,PHYSIOLOGY ,ETHNOLOGY research ,THEORY - Abstract
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]
- Published
- 2014
- Full Text
- View/download PDF
29. Investigate, because of the golden rectangle
- Author
-
Susan D'Agostino
- Subjects
Combinatorics ,Golden rectangle ,Mathematics - Abstract
“Investigate, because of the golden rectangle” offers mathematics students and enthusiasts inspiration for mathematical play by way of a guided construction of the golden rectangle. The discussion is illustrated with numerous hand-drawn sketches. A golden rectangle is a rectangle whose side lengths are in the golden ratio, which is, where the Greek letter (pronounced “phi”) is approximately equal to. Readers learn that an indirect, even haphazard, approach in mathematical play may lead to unanticipated discoveries. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.
- Published
- 2020
30. A Compendium of Fibonacci Ratio
- Author
-
Pratima Gupta, Hemant Jain, Priyanka Katyal, and Nikhita Gulati
- Subjects
Combinatorics ,phi concept ,Fibonacci number ,golden angle ,Clinical Biochemistry ,golden rectangle ,lcsh:R ,lcsh:Medicine ,General Medicine ,golden proportion ,Compendium ,Mathematics - Abstract
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.
- Published
- 2019
31. The Church in The Hague by Aldo van Eyck: The Presence of the Fibonacci Numbers and the Golden Rectangle in the Compositional Scheme of the Plan.
- Author
-
Fernández-Llebrez, José and Fran, José
- Subjects
FIBONACCI sequence ,GOLDEN rectangle (Mathematics) ,MATHEMATICS & architecture ,TWENTIETH century ,MATHEMATICAL analysis - Abstract
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]
- Published
- 2013
- Full Text
- View/download PDF
32. ZLATNI REZ.
- Author
-
Zlatić, Sanja
- Subjects
MATHEMATICAL programming ,MATHEMATICAL models ,ACCURACY ,INDUSTRIAL engineering ,CHAOS theory - Abstract
Copyright of Technical Journal / Tehnički Glasnik is the property of Polytechnic of Varazdin and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2013
33. GOLDEN PROPORTION IN PROSTHODONTICS PART-1.
- Author
-
Singh, Parul, Rai, Manish, and Singh, Ajay
- Subjects
PROPORTION ,PROSTHODONTICS ,DENTISTRY ,PROSTHETICS ,COSMETIC dentistry ,AESTHETICS - Abstract
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]
- Published
- 2012
34. The golden proportion - God's building block for the world.
- Author
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Singh, Ravudai and Datta, Kusum
- Subjects
AESTHETICS ,PROGNOSIS ,CLINICAL medicine ,PHILOSOPHERS ,MEDICAL care - Abstract
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]
- Published
- 2008
- Full Text
- View/download PDF
35. A deduction of the Golden Spiral equation via powers of the Golden Ratio ϕ
- Author
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Maurício Zahn
- Subjects
Discrete mathematics ,Fibonacci number ,Applied Mathematics ,05 social sciences ,050301 education ,020206 networking & telecommunications ,02 engineering and technology ,Education ,Square root of 5 ,Combinatorics ,Mathematics (miscellaneous) ,Golden spiral ,0202 electrical engineering, electronic engineering, information engineering ,Golden rectangle ,Golden ratio ,Polar coordinate system ,Mathematics instruction ,0503 education ,Mathematics - Abstract
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.
- Published
- 2017
36. Aesthetics in a Mathematics for Liberal Arts Project
- Author
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Carol Gee and Jason Callahan
- Subjects
Liberal arts education ,010102 general mathematics ,05 social sciences ,Golden rectangle ,Mathematics education ,050301 education ,Rubric ,Golden ratio ,0101 mathematics ,0503 education ,01 natural sciences ,Mathematics - Published
- 2017
37. Shrinkage Points of Golden Rectangle, Fibonacci Spirals, and Golden Spirals
- Author
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Jun-Sheng Duan
- Subjects
Physics ,0303 health sciences ,Fibonacci number ,Article Subject ,lcsh:Mathematics ,030303 biophysics ,Mathematics::History and Overview ,Geometry ,Astrophysics::Cosmology and Extragalactic Astrophysics ,lcsh:QA1-939 ,Curvature ,03 medical and health sciences ,Modeling and Simulation ,Golden spiral ,Golden rectangle ,Polar ,Polar coordinate system ,Constant (mathematics) ,Astrophysics::Galaxy Astrophysics ,030304 developmental biology ,Shrinkage - Abstract
We investigated the golden rectangle and the related Fibonacci spiral and golden spiral. The coordinates of the shrinkage points of a golden rectangle were derived. Properties of shrinkage points were discussed. Based on these properties, we conduct a comparison study for the Fibonacci spiral and golden spiral. Their similarities and differences were looked into by examining their polar coordinate equations, polar radii, arm-radius angles, and curvatures. The golden spiral has constant arm-radius angle and continuous curvature, while the Fibonacci spiral has cyclic varying arm-radius angle and discontinuous curvature.
- Published
- 2019
- Full Text
- View/download PDF
38. Study on the Mathematical Relationship between the Fibonacci Sequence and Luoshu
- Author
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Lian Jiang and Zhao-Xue Chen
- Subjects
Algebra ,Sequence ,Fibonacci number ,Series (mathematics) ,Distribution (number theory) ,business.industry ,Golden rectangle ,Rectangle ,Modular design ,Orientation (graph theory) ,business ,Mathematics - Abstract
In researches of basic theory of TCM, the Luoshu has direct relationship with the Jiugong bafeng theory. In this paper based on analysis of mathematical relations among the Fibonacci sequence, the Fibonacci rectangle and golden rectangle, according to geometric properties of the golden rectangle as well as numeric distribution rules implied in Luoshu, relationship between the Fibonacci sequence including its modular series by 10 and Luoshu is studied, and inherent and consistent mathematical relationship between them is found in spatial orientation, digital running sequence, numeric grouping and generating rules, etc. The study results of this paper can help to build up close mathematical association between Luoshu and the Fibonacci sequence, which can lay key theoretical foundation for the ultimate breakthrough for scientific mysteries containing in Luoshu and the Jiugong bafeng theory in TCM.
- Published
- 2018
39. Analysis of geometric proportions on maxillary anterior teeth for esthetic smile design: An In vivo study
- Author
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Binsu Sukumaran, Basil M Jacob, Pinky Varghese, Vighnesh Varma Raja, Babu Cherian, and Sreena Anu
- Subjects
Orthodontics ,education.field_of_study ,QD71-142 ,Dentition ,analysis ,esthetic smile ,geometric proportions ,maxillary anterior teeth ,Population ,Adobe photoshop ,Bioengineering ,General Biochemistry, Genetics and Molecular Biology ,RS1-441 ,stomatognathic diseases ,Pharmacy and materia medica ,Computer analysis ,Golden rectangle ,Original Article ,Maxillary central incisor ,General Pharmacology, Toxicology and Pharmaceutics ,education ,Analytical chemistry ,Anterior teeth ,Mathematics - Abstract
Background and Objectives: The maxillary central incisor is the dominant element of anterior dental composition and hence should be restored or replaced with proper proportion of width and length for better aesthetic results. However, the literature is not clear regarding verifiable guidelines for the determination of proportions of the teeth. The aim of this study was to investigate the existence and suitability of Golden Rectangle, Recurring Aesthetic Dental Proportion, and Golden percentage between the widths of maxillary anterior teeth in individuals with natural dentition, with the aid of digital photographs and computer analysis. Material and Methods: Frontal full-face digital photographs of the subjects (in smile) were made under standardized conditions using a digital camera and a tripod stand was used to place and orient the camera in the standardized position (camera was positioned 1 meter away from the patient; and the lens of the camera was adjusted at the patients' lip level). Imaging software (Adobe Photoshop CS5; Adobe Systems, Inc, San Jose, Calif.) was used to mark the anatomic landmarks and to digitally analyze the photograph. The entire process of proportion analysis was done by a single observer. Results: The RED proportion was not found to exist between the six maxillary anterior teeth. The values suggested in the golden percentage were not applicable on the subjects of this study. However, a slight modification of these percentages can be adopted taking into consideration the ethnicity differences of the subjects in this study. The values obtained were 24%, 15%, 11% in males and 23%, 15%, and 11% in females. Golden rectangle concept can be used for choosing dimensions of maxillary central incisors which are esthetically pleasing. Conclusion: RED proportion is an unsuitable methods to relate the successive widths of the maxillary anterior teeth. The golden percentage theory seems to be applicable to relate the successive widths of the maxillary anterior teeth if percentages are adjusted taking into consideration the ethnicity of the population. Golden rectangle concept is suitable for choosing dimensions of maxillary central incisors which are esthetically pleasing.
- Published
- 2021
40. Study on the Relationship between the Display and the Visibility of Humanbeing
- Author
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Dongho Kim
- Subjects
Aspect ratio ,business.industry ,Visibility (geometry) ,Golden rectangle ,Field of view ,Computer vision ,Artificial intelligence ,business ,Mathematics - Published
- 2016
41. The Golden Ratio and Jewelry Design
- Author
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Claudia Regina Batista and Adhemar Maria do Valle Filho
- Subjects
Combinatorics ,Pentagon ,business.industry ,Golden rectangle ,Golden ratio ,Jewelry design ,business ,Mathematics - Abstract
The golden ratio has universal application and provides maximum performance in an artistic composition. This article discusses how knowledge about golden ratio can be used in jewelry design. The golden rectangle and golden pentagon were used as grids to generate jewelry with harmonic proportions.
- Published
- 2018
42. The Divine Proportion
- Author
-
Plinio Innocenzi
- Subjects
symbols.namesake ,Sociology of scientific knowledge ,Close relationship ,media_common.quotation_subject ,Beauty ,Golden rectangle ,symbols ,The Renaissance ,Golden ratio ,Distinctive feature ,media_common ,Epistemology ,Archimedean solid - Abstract
The close relationship between art and science is a distinctive feature of the Renaissance, and, as we have observed again and again, Leonardo represents one of the highest points of this synthesis. The scientific knowledge that he obtained via his studies became a fundamental instrument also for his work as an artist and vice versa. As discussed in the previous chapter, it was thanks to his dear friend Luca Pacioli that Leonardo was able to fully appreciate the beauty of geometry and arithmetic. Luca Pacioli’s support was also critical, more generally, in enabling him to achieve a satisfactory knowledge of mathematics.
- Published
- 2018
43. The Five Angles of the Golden Rectangle: Tomas Venclova
- Author
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John Taylor
- Subjects
Combinatorics ,Golden rectangle ,Mathematics - Published
- 2017
44. Golden Rectangle Treemap
- Author
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Mao Lin Huang, Shiliang Fan, Weidong Huang, Ruolan Yang, and Liangfu Lu
- Subjects
File system ,History ,Theoretical computer science ,Hierarchy (mathematics) ,Computer science ,Golden rectangle ,computer.software_genre ,computer ,Hierarchical database model ,Computer Science Applications ,Education ,Visualization - Abstract
© Published under licence by IOP Publishing Ltd. Treemaps, a visualization method of representing hierarchical data sets, are becoming more and more popular for its efficient and compact displays. Several algorithms have been proposed to create more useful display by controlling the aspect ratios of the rectangles that make up a treemap. In this paper, we introduce a new treemap algorithm, generating layout in which the rectangles are easier to select and hierarchy information is easier to obtain. This algorithm generates rectangles which approximate golden rectangles. To prove the effectiveness of our algorithm, at the end of this paper several analyses on golden rectangle treemap have been done on disk file system.
- Published
- 2017
45. Overview
- Author
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Kenneth S. Schmitz
- Subjects
Scientific law ,Theoretical physics ,Recursion ,Mathematical model ,Simple (abstract algebra) ,Golden rectangle ,Calculus ,Golden ratio ,Statistical mechanics ,Hypothesis ,Mathematics - Abstract
The objectives of Physical Chemistry: Concepts and Theory are presented. The book is organized in accordance with the mathematics used: continuum for thermodynamics; discrete for quantum theory; statistics and probabilities for statistical mechanics; and the mathematics for potential-driven changes at short and long times for kinetics. The Reader is presented with material developed from the fundamental mathematical form of differential equations rather than integrated expressions to provide a better understanding of the interrelationships between subfields within the area of physical chemistry. This approach reveals how experimental conditions and a judicious choice of theoretical expressions can reduce the equations to a suitable form for the system at hand. The introduction of how mathematics describes the world we experience is at three levels: Nature is Patterns, Nature is Numbers, and Nature is Recursion Relationships. Many objects in Nature are related to the Golden Ratio, such as apple seeds, spiral galaxies, and mollusk shells. Numbers give a quantitative description of Nature and the power of prediction. The complexity of Nature is embraced in the relationships between the numbers as manifested in recursion relationships, in which a few numbers can be used to generate a more complete description of Nature. The study of prime numbers is an example of how a scientific study on a system evolves through the use of mathematical models. It is through mathematics that information is gained about a system, which leads to a simple understanding as reflected in movies and television series such as Star Trek.
- Published
- 2017
46. Mathematics in Tiwanaku-The gold number in the gate of the sun
- Author
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J.Willam Ariel Muñoz F., Michael Carlos Gonzales V., and Marco Antonio Cabero Z.
- Subjects
Combinatorics ,03 medical and health sciences ,0302 clinical medicine ,Component (UML) ,Golden triangle (mathematics) ,Golden rectangle ,Nanotechnology ,030206 dentistry ,030217 neurology & neurosurgery ,Mathematics ,Gold number - Published
- 2017
47. Automated Best Connected Rectangular Floorplans
- Author
-
Krishnendra Shekhawat and José Pinto Duarte
- Subjects
Discrete mathematics ,Fibonacci number ,Computer science ,021105 building & construction ,Architectural design ,0211 other engineering and technologies ,Golden rectangle ,020101 civil engineering ,02 engineering and technology ,Rectangle ,Space allocation ,Frequent use ,0201 civil engineering - Abstract
As part of a larger research aimed at developing design aids for architects, this paper presents the “automated” generation of the “best connected” rectangular floor plans, satisfying given topological and dimensional constraints. It has been seen that architects, knowingly or unknowingly, have often used either the golden rectangle or the Fibonacci rectangle in their works throughout history. But it was hard to find any specific reason for such use, other than aesthetic. In 2015, Shekhawat showed that they are among the best connected rectangular arrangements (dimensionless rectangular floor plans) and that this may well be another reason for their frequent use in architectural design. In this work, an alternative algorithm is presented which generates n − 3 best connected rectangular arrangements, being n the number of rooms. Then, this concept is further extended for constructing the best connected dimensioned rectangular floor plans. The goal is to provide an optimal solution for the rectangular space allocation problem, while satisfying given topological and dimensional requirements.
- Published
- 2017
48. Many L-Shaped Polyominoes Have Odd Rectangular Packings
- Author
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Michael Reid
- Subjects
Combinatorics ,Polyomino ,Coprime integers ,Largest empty rectangle ,Golden rectangle ,Discrete Mathematics and Combinatorics ,Rectangle ,General family ,Mathematics - Abstract
A polyomino is called odd if it can tile a rectangle using an odd number of copies. We give a very general family of odd polyominoes. Specifically, consider an L-shaped polyomino, i.e., a rectangle that has a rectangular piece removed from one corner. For some of these polyominoes, two copies tile a rectangle, called a basic rectangle. We prove that such a polyomino is odd if its basic rectangle has relatively prime side lengths. This general family encompasses several previously known families of odd polyominoes, as well as many individual examples. We prove a stronger result for a narrower family of polyominoes. Let L n denote the polyomino formed by removing a 1 × (n−2) corner from a 2 × (n−1) rectangle. We show that when n is odd, L n tiles all rectangles both of whose sides are at least 8n 3, and whose area is a multiple of n. If we only allow L n to be rotated, but not reflected, then the same is true, provided that both sides of the rectangle are at least 16n 4. We also give several isolated examples of odd polyominoes.
- Published
- 2014
49. Golden Rectangle Ratio – How Precious Is It? : A Clinical Study
- Author
-
Sagar C. Chaudhari, Smita A. Khalikar, and S. P. Dange
- Subjects
Orthodontics ,Dentition ,business.industry ,medicine.medical_treatment ,Restorative Procedures ,Crown (dentistry) ,Clinical study ,stomatognathic diseases ,stomatognathic system ,medicine ,Golden rectangle ,Crown length ,Maxillary central incisor ,business ,Dental esthetics - Abstract
Maxillary central incisors are of critical value in the dental esthetics. The golden rectangle ratio concept may play a role in selecting the optimum width and length of this tooth. The aim of this study is to investigate the existence of this ratio among individuals with natural dentition and routinely used acrylic denture teeth sets and to validate its role in dental esthetics. The clinical crown length of maxillary left and right central incisor (CI) is measured, mean is calculated and combined crown width of left and right central incisors is measured. Crown width to crown length ratio of natural dentition and acrylic denture teeth sets of different manufacturers was calculated and compared with the Golden Rectangle ratio and statistically analysed. Golden rectangle was found to have a significant relationship with esthetic appearance of maxillary central incisors. The results of this study will help in proper selection of teeth for all restorative procedures.
- Published
- 2014
50. Jardín xerófito para divulgación científica
- Author
-
Arcadio Monroy-Ata and Balbina Vázquez-Benítez
- Subjects
Irrigation ,plantas crasas ,science popularization ,Biología ,Soil surface ,golden section ,lcsh:Chemistry ,Mexico city ,lcsh:Zoology ,divulgación científica ,sección áurea ,lcsh:QL1-991 ,succulent plant ,lcsh:QH301-705.5 ,Atmospheric water ,xerophytic garden ,Cactus ,Archaeology ,Garden design ,Pentagon ,Geography ,lcsh:Biology (General) ,lcsh:QD1-999 ,Plant species ,Golden rectangle ,Cacti ,jardín xerófito ,Cartography - Abstract
ResumenEn este trabajo se diseñó y estableció un jardín xerófito con fines de divulgación científica. Ésto se realizó en las áreas verdes del Campus I de la Facultad de Estudios Superiores Zaragoza, de la Universidad Nacional, al oriente de la Ciudad de México. El diseño del jardín consistió en trazar y dibujar, en la superficie del suelo, una espiral logarítmica, una estrella de Vitrubius, un pentágono fractal y un rectángulo áureo. Se utilizaron estacas de 10 cm de alto, pintadas de blanco, para delimitar las curvas y plantas crasas para remarcar las figuras geométricas. Se trasplantaron 29 especies vegetales, con 144 individuos en total, y se instaló un atrapanieblas como modelo de cosecha de agua atmosférica para riego vegetal. La divulgación científica de los conceptos geométricos se ha realizado mediante visitas guiadas. Se concluye que es factible establecer un jardín urbano de cero riego en el Oriente de la capital mexicana, sin embargo, es necesario reforzar las estructuras de las curvas geométricas. También, se requiere establecer páneles informativos sobre las figuras dibujadas sobre el suelo y cédulas con datos técnicos de las especies vegetales, para facilitar la divulgación de los conceptos científicos del diseño base del jardín y la explicación de la función del atrapanieblas.AbstractIn this work, a xerophytic garden was designed and established for science popularization purposes. This was made on a green area of the Facultad de Estudios Superiores Zaragoza of the National University, at the East of Mexico City. The garden design was outlined by drawing on the soil surface, a logarithmic spiral, a Vitrubius star, a fractal pentagon and a golden rectangle. For this, white painted 10 cm high stakes were buried to delimit the curves, and succulent plants were planted to remark the geometric figures. Twenty nine plant species were transplanted, with 144 total individuals, and a catch-fog mesh device was installed with a view to exhibit an atmospheric water harvesting model for plant irrigation. The science popularization of geometric concepts was made by means of guided visits. It was concluded that it is feasible to establish an urban garden without irrigation in the East of Mexico City. Nevertheless, it is necessary to strengthen the structure of geometric curves. Also, it is required to install information panels about the soil drawings and technical fact sheets on plant species in order to facilitate popularization of the underlying scientific concepts of garden design and the explanation of catch-fog device function.
- Published
- 2014
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