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2006
The relationship between geometry and architectural design are described and discussed along some examples. Geometry is the fundamental science of forms and their order. Geometric figures, forms and transformations build the material of architectural design. In the history of architecture geometric rules based on the ideas of proportions and symmetries formed fixed tools for architectural design. Proportions were analyzed in nature and found as general aesthetic categories across nature and art. Therefore proportions such as the golden section were seen as the power to create harmony in architecture as well as in art and music. According Pythagoras there were general principles for harmony. They were also applied in architecture and they found a further development especially in the renaissance. Leon Battista Alberti integrated such general harmonic proportion rules in his theory of architecture and realized them in his buildings. To find general principles of harmony in the world w...
2017
Roman Architect Vitruvius has state three conditions for good building i.e. commodity (usefulness), firmness (solidity or strength) and delight (beauty). Proportion plays very important role in all three as it provide guidelines for useful spaces, for creating good structural system and creating aesthetically pleasing environment. Since ages the humans have experimented the proportions of built mass by using mathematical principles. The Greece has used the geometric proportion in Parthenon by using the golden ratio in the façade of building, also used the correction of optical illusion by changing the proportion of building elements. The Roman Architect Vitruvius written that principles of proportion and symmetry used in architecture are in fact derived from symmetry found in shape of human body and he quoted "Therefore, since nature has designed the human body so that its members are duly proportioned to the frame as a whole, it appears that the ancients had good reason for th...
International journal of engineering research and technology, 2013
Architecture has its unique relationship with mathematics, incorporating the study of such mathematical concepts as ratio, proportion, scales and symmetry. Put up definitions and explanations of the mathematical concepts of elementary geometry, stating their connection to architecture and ratio and proportion relate to architectural plan with mathematical accuracy in measuring. In this paper showing the connections between geometry and architecture with what appears to be an obvious example from various styles, architectural works which are also derived from basic geometric figures.The aim is to re-search the age old geometrical principles applied in Indian architecture. Deriving ancient principles of interrelationship between ‘Geometry & Architecture’ in three major branches of Indian architecture, particularly, Hindu Architecture and Islamic Architecture. Historically, architecture was part of mathematics, and in many periods of the past, the two disciplines were indistinguishable...
International Journal of Research -GRANTHAALAYAH
The uniqueness of His creation is reflected in different fields of life by the great masters throughout the ages that have born with the formation of the universe, from the big bang, till times still to come. Special ratio that can be used to describe the proportions of everything from nature’s smallest building blocks, such as atoms, to the most advanced patterns in the universe, such as unimaginably large celestial bodies. One of the key evidences presented for creation is the recurring appearance of the Divine proportion, or golden section, throughout the design of the human body and other life forms. An attempt has been made to relate Sri yantra and golden ratio and the various forms that seem to exemplify in the plan and elevation of the Indian temple. The yantra which is a complex geometry has been perfected to be used for the development of temple forms of different eras. The following paper will be a tool for the researchers to use the yantra in deriving the spaces of Indian...
The buildings will have an extreme influence on one’s health and divine and our psychic state of being. The combination of euphony and stability, colour and light, connection with ecological footprint, and geometric guise are contributing factors of shelter which aspires to be stimulating. The relationship between architecture and geometry has frequently been a median issue in architectural theory and practice. Since the historic architecture, to the modern era architecture; the constructive, metaphysical, and aesthetic roles or geometry in architecture have been accurately used. As different kinds of geometry were evolved through the centuries, its perceived use to architecture developed equivalently from Vitruvius's early use of Euclidean ruler and compass constructions for architectural plans to the use of modern geometry to describe the structure of architectural forms. Apart from these and other surveillance about building forms, the relevance of geometry to architecture is demonstrated importantly by directing to occurrences of geometric forms in nature, space, architecture and other designs. In precise to the context, geometry is omnipresent in all the spheres of life.
occurred in the decade and a half between the mid-1940s and late 1950s. 4 Architectural Principles, in fact, did not initiate research on proportions, but rather provoked a discussion revolving around it. 5 Proceeding from a study of the work of Alberti and Palladio, Wittkower based the genesis of the architecture of Humanism on a system of harmonic relationships that placed the proportions of the human body in relation to those of a building, that is, he established a bond between man, nature, and the universe that was legitimized by the authority of Vitruvius. 6 In short, as Manfredo Tafuri lucidly pointed out, he gave life to "a theoretical universal claims." 7 Wittkower tried to demonstrate how careful contemplation of geometry and mathematical ratios could be read behind the fifteenth-and sixteenth-century revival of all'antica architecture.
Procedia - Social and Behavioral Sciences, 2014
This paper presents an exercise which aims to stimulate architect students' creativity, raise awareness on architectures' formal possibilities based on geometric shapes and to illustrate how the theoretical knowledge can be practically applied on a certain architectural program. As basic information for this exercise, the types and the features of the main structural geometric forms are enumerated while student work exemplifies their use in a particular case.
Golden Proportion or Golden Ratio is usually denoted by the Greek letter Phi (φ), in lower case, which represents an irrational number, 1.6180339887 approximately. Because of its unique and mystifying properties, many researchers and mathematicians have been studied about the Golden Ratio which is also known as Golden Section. Renaissance architects, artists and designers also studied on this interesting topic, documented and employed the Golden section proportions in eminent works of artifacts, sculptures, paintings and architectures. The Golden Proportion is considered as the most pleasing to human visual sensation and not limited to aesthetic beauty but also be found its existence in natural world through the body proportions of living beings, the growth patterns of many plants, insects and also in the model of enigmatic universe. The properties of Golden Section can be instituted in the pattern of mathematical series and geometrical patterns. This paper seeks to represent a panoptic view of the miraculous Golden Proportion and its relation with the nature, globe, universe, arts, design, mathematics and science. Geometrical substantiation of the equation of Phi, based on the classical geometric relations, is also explicated in this study. Golden Ratio and its chronicle, concept of Golden Mean and its relations with the geometry, various dynamic rectangles and their intimacy with Phi, Golden Ratio in the beauty of nature, Phi ratio in the design, architecture and engineering are also presented in this study in a panoptical manner.
WIT Transactions on Ecology and the Environment, 2004
In human history research in geometry takes a central place between other scientific developments. A major content was clearly defined already around 300 B.C. in Euclid's book "Elements". This paper gives an overview of human handling of Complex Geometry, which reaches beyond the simple forms like square/cube and circle/sphere. Complex Geometry includes the cone and its sections, ruled surfaces and polyhedra. Cone sections and polyhedra are part of Euclid's knowledge, but geometricians and architects had a hard job to depict these forms well and thus to understand them, let alone to use them. People got interested in Complex Geometry, in order to copy "perfect" natural shapes like crystals. More important was, that simple geometry turned out to be not sufficient for establishing innovative design. By its hermetic structure, Complex Geometry has the power to generate surprising shapes along a logical path. A historic survey proves that only in cooperation with artists of superb handicraft (drawing, modeling, carving) could Complex Geometry be investigated fruitfully. It was not until the early 19 th C. that ruled surfaces were defined and illustrated in a sufficiently clear way (Monge, Leroy).
The actual trends in architecture show more and more complex, irregular and seemingly “non-geometric” forms. It seems that the digital tools seduce the users to create anything possible. The more spectacular a building appears, often without perceptible structures, the better and more innovative it is evaluated. Therefore we are asking for fundamentals for design processes, in order to escape from an arbitrary design and finding a rational basis for design processes. When we look back in the history of architecture, we can find the background of geometric structures as important fundaments for designing, for example in symmetry concepts or using transformations. There is a tradition of using structural thinking for design disciplines referring to a mathematical-geometric basis. Structural thinking can be seen as a method and tool, especially with the help of digital tools. It is also the background for an aesthetic foundation of design processes. This way gives the chance to create dynamic architectural design processes, working with the formulated relations and interactions between geometry, material, construction, and other components in multidisciplinary interrelations with an integrative role for geometry. This theoretical background for architectural design processes with an important role for geometry will be illustrated by examples and some experiments by our students.
2006
There is always a mystery on pre-modern architecture practice on the relation between dimensions and ratios. The reasons of using certain proportions used on the design of religious buildings/ spaces are the result of the application of numerical symbolism and Pythagorean triangle. Thus, the paper will be focused on the unity of theory in premodern architecture practice via giving some special examples of pre-modern architecture through the human history, such as Antique Egyptian and Antique Greek temples, Roman churches, Gothic cathedrals, and so on.
Intentionally or unintentionally, from ages, architects, builders and construction experts have used mathematics as a very basic yet important tool for the soulful purpose of design, execution and finalization of building projects. In the history, architects were mathematicians and also some mathematicians were architect too. Vitruvius was a very well-known architect as well as famous mathematician. Mathematical readings of Pythagoras were later used in building proportions. Well known worker and user of golden ratio Leonardo Da Vinci along with many achievements was an architect too. The approach of this research paper is to come up with findings on importance of mathematics in architecture, as in geometry, from very important site analysis to final design of elevation or façade. Aim of the whole research is to come up with mathematical functions related to mensuration of building construction and Architectural Engineering. This paper is an initial part of the same research.
International Design Journal
The term proportion designates a mathematical concept which belongs to the Greek Pythagorean heritage and whose application extends to all quantifiable knowledge. In this paper, we will focus on the notion of proportion in visual arts and particularly in architecture where it is articulated to the notion of scale. "The choice of a regulating line is one of the decisive moments of inspiration, one of the capital operations of architecture," wrote Le Corbusier; but the ardor of those who - like Claude Perrault, the architect of the Louvre colonnade - want to deny the interest of proportion in architecture because of the optical distortions that the changing point of view of the spectators causes to the geometrical reality of the project and to which Vitruvius makes these corrections that he calls "temperaturae" should be explained all the same. Rather, it will be important for us here to define proportion as a specifically architectural concept, to give it an architecturological meaning. The major problem is then above all to distinguish the architectural proportion from the mathematical or musical proportion with which it is still in historical and epistemological confusion. Seeking to construct a concept that enters into a system of scientific knowledge of architecture, it would seem that the concept of proportion can only be enlightened by another concept that is external to it and encompasses it, that of scale. In the history of architecture, the notion of scale made its significant appearance in the 19th century, with the introduction of the metric system. Although it began to take shape and become a practical reality in Le Corbusier's Modulor, the latest system of proportions, it remains to be seen whether this notion can be given the status of a concept in a scientific theory of architecture. The questions of the existence of the mathematical reason for beauty and the validity of mathematical aesthetics will be asked here.
European Scientific Journal, 2013
The topic is the multilateral relationship established during the process of spatial perception between the space and the observer. Spatial perception is as varied as the number of people who are making the observation and evaluation, just as the evaluation in the person's systematizing is connected with the codes that the space physically provides (dimension, color, fabric, light, order…). Although the concept of proportion, one of the concurrences in spatial coding, dates to the ancient period, in this study the evaluations will be made using the example of a building from the Renaissance period. In Renaissance architecture which began in Florence at the beginning of the fifteenth century and spread from there to Europe by the end of the same century, religious architecture like churches, cathedrals and chapels continued and examples of civil architectural buildings like kiosks, palaces and mansions gained speed (in comparison with the buildings of the Middle Ages). While Renaissance architects took the arch, dome, column and decorative items from Greek and Roman art in organizing buildings, they remained attached to some shared values and old traditions; however, they found an opportunity to produce new and original styles. In this context the architect led the way himself in clarifying the arrangement that would be applied, the proportions and the details through the form and measurements of the building What was inescapable in Renaissance period buildings was a conceptual harmony that numbers and proportions achieved. We know that this concept that had progressed ever since Aristotle had acquired the definition that "all the elements of the universe are the elements of numbers and in this context the number of the universe is a ball of numbers and harmony." 1 1 It is observable that in the buildings of Renaissance era architects tried to establish acoustic harmony and optical harmony as an extension of the ancient period.
Katona, V. (2018) Symmetries and Proportions in Architecture. Symmetry: Culture and Science, vol. 29, no. 3, pp. 325–327., 2018
On 18 August 1418, the Florentine Arte della Lana announced an architectural competition for building the dome of Santa Maria del Fiore Cathedral using Neri di Fioravanti's design. The two main competitors were two master goldsmiths, Lorenzo Ghiberti (by whom the concept of symmetry was first explained in vulgar Italian) and Filippo Brunelleschi. Lifelong competition between the two remained sharp, but Brunelleschi received the commission, and completed the dome in 1436. It was the first "octagonal" dome in history to be built without a temporary wooden supporting frame, and was one of the most impressive projects of its time.
Riset Arsitektur (RISA)
In terms of history, proportion, composition and geometry have been applied as design elements since long ago, way before the era of modern architecture. The existence of these three elements enables numerous variations and produces freedom of expression. Unfortunately, in current design processes, these visual principles are often overlooked. In fact, they play a role as one of the indicators of aesthetics of a building, as well as exerting influence on human perception in capturing and perceiving a given space. The purpose of this research is to study the application of proportion and composition principles to one of the creations of the Indonesian modern architect Frederich Silaban. The BNI 46 Building design by Silaban acts as the research object, displaying a façade which is crammed with modern thoughts, different on each side but remaining harmonious and visually attractive. The theory of proportion, composition, geometry and structuring principles provide the basis for analyzing the existing object. This research uses the descriptive analytical method with the qualitative approach to data collection of the research object. The next step is the vertical and horizontal analysis of the building enclosure in relation to the implementation of geometric proportion and composition principles in the building. This research is expected to be beneficial in terms of enriching the knowledge and study of geometric proportion and proportion in architecture, adding to the consideration of implementing visual principles for professionals, as well as adding to the archive/portfolio concerning Silaban as one of Indonesia's pioneering modern architects.
Jurnal Teknologi, 2016
Mathematics and architecture are interrelated. A building with the appropriate mathematical elements in its design will be impressive in its appearance. One of the most widely used mathematical proportions in architecture is divine proportion, or better known as φ (618. 1 1 n F n F n lim = = ∞ → with Fn the n-th Fibonacci sequence). This type of proportion exists everywhere in nature, including in human body, shapes, artworks, music, paintings and even in the universe. In this study, we investigate the existence of divine proportion in modern architecture. In identifying the divine proportion, geometrical analysis was applied by measuring the dimensions of parts on the floor plan of a building in a higher learning institution in Malaysia. The length, width, height and angles of the floor plan were examined. The results show that the divine proportion, which was obtained from the proportion of length and width, exists in 33% of parts of the first and ground floors of the building examined.
works of Ernst Haeckel and D'Arcy Thompson ViewProject
The term "Composition" deals with the arrangement and alignment of ideas to emphasize and balance an entity. Architectural Composition has further to deal with elaborate design. Understanding the Composition in architecture begins with space development and their relations. Composition of spaces and functions is called design. Looking into the compositions, geometry plays the major role in it. The essential study of forms, shapes and spaces, and their order along with their algebra contributes to the process of composition and designing of any element of architecture. Geometry is one of the main features in configuration of architecture. Mathematics, is one of the oldest subjects which followsgeometry in different manner and its application. Mathematical Connotations and Arithmetic Progression gives the different form generation when it relates to the Architecture. Architectural composition with its geometrical configuration gives the proportionate system of the Structure. The design element-geometry, deals with the art and architecture of expressing ideas and conceptual methods.
Civil Engineering and Architecture, 2020
In this paper, the author investigates the role and contribution of pure and applied mathematics to architecture and fine arts in a unified manner. To this end, a thorough and explanatory historical overview of this diachronic and interdisciplinary topic, from the ages of ancient Mediterranean cultures to the so-called western civilization of the late twentieth century is presented. In this framework, the author first examines the fundamental role of traditional mathematics (e.g. Descriptive and Projective Geometry) in architectural design and fine arts, and in the sequel the discussion extends to the outstanding contribution of modern and computational mathematics (NURBS, Fractals, Boolean matrices, Graph Theory, etc.) to these issues. Besides, the important role of computer-aided design (CAD) is mentioned and emphasized. Indeed, CAD is an exceptional scientific and technological achievement, the scientific background of which is essentially a combination of Informatics, Discrete Mathematics and Descriptive Geometry. In addition, various existing problems that sometimes hinder the application of the science of mathematics to architecture and the fine arts are highlighted and demonstrated. Finally, given that the most appropriate mathematical background for the graduate studies in architectural schools along with the schools of fine arts is a very difficult and rather questionable issue, some suggestions are made in order to encourage and strengthen the relationship among applied mathematics, architecture and fine arts.
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