Approaches to the Use of Geometry in Architecture: A study of the works of Andrea Palladio, Frank Lloyd Wright, and Frank Gehry

摘要

Geometry deals with form, shape, and measurement and is a part of mathematicswhere visual thought is dominant. Both design and construction in architecture deal withvisualization, and architects constantly employ geometry. Today, with the advent ofcomputer software, architects can visualize forms that go beyond our everydayexperience. Some architects claim that the complex forms of their works havecorrelations with non-Euclidean geometry, but the space we experience is stillEuclidean. Given this context, I have explored possible correlations that might existbetween mathematical concepts of geometry and the employment of geometry inarchitectural design from a historic perspective. The main focus will be to describe thetwo phenomena historically, and then investigate any connections that might emergefrom the discussion. While discussing the way geometry has been approached inarchitecture, I have focused on the Renaissance, Modern, and Post-modern phases asthey have a distinct style and expression. Andrea Palladio, Frank Lloyd Wright, and Frank Gehry's works will be case studies for the Renaissance, Modern, and Post-modernphases respectively.One of the important conclusions of this study is that architects use geometry in amore subconscious and intuitive manner while designing. Certain approaches togeometry can be determined by the way an architect deals with form and space. Fromthe discussions of the works of Palladio, Wright, and Gehry, it can be concluded thatfrom a two-dimensional simple approach to form and space in architecture, there hasbeen a development of thinking about complex forms three dimensionally. Similarly, inmathematics, geometry has developed from a two-dimensional and abstract descriptionof our surroundings to something that can capture the complex and specific nature of aphenomena. It is also shown that architects rarely come up with new concepts ofgeometry. Significant developments in geometry have always been in the domain ofmathematics. Hence, most correlations between geometry in architecture and geometryin mathematics develop much later than the introduction of those concepts of geometryin mathematics. It is also found that the use of Euclidean geometry persists inarchitecture and that later concepts like non-Euclidean geometry cannot be used in aninstrumental manner in architecture.