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# Geometry in Architecture Research Assignment Paper (Dissertation Sample)

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Geometry in Architecture

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GEOMETRY IN ARCHITECTURE

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Introduction

Architectural geometry is the study of a combination of geometry and architecture. It particularly tries to assess the designs, manufacture, and analyze processes. While designing a building, architects use different shapes which they combine, modify, repeat and repeat combinations (Janson & Janson 1997).

There are two areas that geometry is applied in architecture which include the development of the architectural forms and representing architecture. The importance of geometry is that if provide the system in order to describe the design through the fundamental geometrical forms. Geometry therefore plays a critical role in the development of the architectural structures and forms. Descriptive geometry helps architectures to produce a two-dimensional representation of three-dimensional object through various projection methods. Geometry also gives the communication foundation about the architecture when in the planning stage or drawing. Architectures choose appropriate projection methods which include orthogonal parallel projection, central projection and oblique projection, which only serve as a communication about the design reflection (Hamlin 2010).

Since geometry is the understanding of forms, transformation and creation of forms, the architectures use this as their starting point of understanding. Hence, geometry has been used as a formative idea in architecture as a designing tool. The architectures have been using various forms and spaces that are complex using the geometric elements and form language. Therefore, geometry consists of the point, line, plane basic shapes which include triangle, square, circle through a mathematical aspect (Moore 1968). It is these abstract elements that have given the foundation of a variety of geometries. These elements are utilized in architectural building. The elements have significantly affected or influenced the formation of space and architectural forms to either the conceptual or constructional meaning. Therefore, these geometric elements have added the aesthetic, symbolic, and conceptual aspects of the architectural designs. As a result the architects have widely used these elements in the architectural space organization and in the relative generation of the architectural forms in discipline (Janson & Janson 1997).

The architects use the geometric elements for replying varied requirements which include the philosophic, aesthetic and economic in a variety of steps through design. The conceptual process of building form is only explained through geometric elements as either pure or processed with elements in the principle of organization. In the architectural basic element are enlarged and utilized both in the two dimensional planar elements and in the three dimensional volumetric elements. Therefore the geometric elements and the organization principals enable the architects to utilize geometry more effectively and gives more value to designs by adding richness and developing new designs. Consequently, the geometric elements are utilized as the most important determinants that help the character of the composition of the architectural form and space. Therefore, the generation of form and space by using basic geometric elements enable them to be critical imputes in the architectural designs. The generation of the architectural form and space is based on the geometric rules and abstracting these with the basic geometric elements which make the resulting form more understandable and easy to recognize (Hamlin 2010).

The architects through history have always been on the lookout for the ideas that would give form to their worked and direct their design. The geometrically determined definition of the form and arrangements of part has made it possible for the architects to express their architectural ideas and allow for the development of the sub themes and variations that enable understanding of the strong underlying formal order. The geometric ideas have become the ground rules in the directing complete understanding of the previous architectural designs. Therefore, the basic geometric elements are important in the generation of the architectural form a space (Hamlin 2010).

In the historical perspective, the Greek orders determined the kind of architectures they have which means the masons geometric expertise which determined the Gothic cathedral, the projective geometry which influenced Renaissance man's conception of space architecture. Others, such as the Brunelleschi, Alberti, and Leonardo Da Vinci were the architects that relied on geometry concepts. Christopher Wren who was the architect of the St. Paul cathedral used the elements of geometry. Lobachevski was among the founders of the non-Euclidean geometry was a great architect. Recently, the works of Buckminster Fullerâ€™s domes are architectural structures that are purely based on the geometric and topological theories (Janson & Janson 1997).

Geometry therefore performs double roles for the architects, which include helping in the formal and the technical sense. It means that geometry influences the structural and the visual aspects of the design. Vitruvius understood clearly the role of geometry when he presented the three requirements for an architectural structure which included firmitas that is structure, Utilitas that is function and Venustas that is beauty. Therefore, the building constructed should be able to accommodate certain functions, be able to stand on its own securely and have some aesthetic value or visual stimulation. It implies that any structural system should be consistent with its appearance and should also be able to reflect the function of the building (Hamlin 2010).

Hence, geometry has always been the determinant of proportions of buildings, hence influencing its appearance. The structure of the historical buildings was arrived at through the empirical means and sometimes through the structural system and geometric proportions combines as is the case of the Gothic cathedral whose work has a powerful visual impact. Therefore, from the Renaissance, on to more theoretical works, the builders relied on the residual geometry also referred to as intuition especially in the 17th century. In the 19th century, things started changing, adopting the empirical approach and by the end of the industrial revolution, there was an enormous transformation as man had gained more knowledge on the use of materials and structural theory.

The principles of organization of the architectural form are recognized by architects because it helps them to design and analyze their building. Geometry is the mathematical system that is concerned with the points, lines, solids, and surfaces (Moore 1968). All the mathematical system is usually based on these undefined elements, unproved statements, assumed relations and proven statements. The different sets of the assumption therefore give rise to different geometries (Hamlin 2010). Therefore, this study will look at the effect of the geometric concepts in the generation of the architectural forms and space to be able to establish the set of ground rules that guide the architectural composition. Its aim is to assess the importance of geometry in architectural designs.

Ancient Vitruvius

Marcus Vitruvius Pollio was a Roman military engineer and architect in the period around c.90-c.20 BCE. His work revolved around architecture and he wrote 10 books on architecture which tells a lot about the history of the ancient architecture and the engineering (Trumbull 2007). He was a great admirer of the Greek architecture. In his ten books of architecture, he reveals much more on the concept of architecture which included mathematics and geometry among others. He also looked at the important effect that architecture has both the aesthetic and practical for people. According to him, the architectural work had both the theoretical and practical knowledge based on art. His buildings always showed the important aspects, which include beauty, stability, and usefulness (Janson & Janson 1997). The Vitruvius work of architecture is divided into 10 books which have different themes. Book one looks at the architectural ideal education, principles and divisions of the architecture, principles of town planning, fortifications and where to build a temple (Indra 2004). The second book looks at the origin of buildings and various architectural materials such as bricks, stones, sand and wood, and how to build various types of walls. Book three looks at the mathematical and correct proportions of columns and temples. Book four looks at the Doric, ionic and Corinthian architectural orders, and a variety of temples and alters (Trumbull 2007).

Book five is about roman buildings as basilica which is the best design for theatres that enables it to have the acoustics and the book also contain more about building harbors. The book six talks about the effect of climate on the character and provides information about the best foundation and layouts for private homes. Book seven is about paving, vaults and wall painting which include the best colors and their origin and historical value. Book eight is about water sources and conveyance through aqueducts. Book nine is concerned with the study of astronomy and its importance of architecture and how time could be measured using sundials and water clocks. Lastly, the tenth book Vitruvius is concerned about machines and gadgets, he talks about devices used in measuring distance, machines that use water, weapons such as catapults, siege engines and ballistae among other (Moore 1968).

Vitruvius in addressing the ethos of architecture showed that the quality was dependent on the social relevance of the artistic work but not the form of workmanshi...

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