Mathematics and architecture

Architecture has always enjoyed a close association with mathematics,not only in the sense of structural calulations and concepts, which in any case is a taken-for-granted, but in the sense of a visual ordering element or being in harmony with the universe. In that sense it is closely allied with geometry.

In Greek architecture, the Golden Mean or the Golden Rectangle served as a canon for planning. The optical illusions of the Parthenon at the Acropolis, Athens, could not have been done without a thorough knowledge of mathematics. Ancient architecture such as that of the Egyptians, Indians, etc., employed certain planning principles and proportions that rooted the buildings to the cosmos- movements of sun, stars, etc.,Renaissance architecture used symmetry as a guiding principle and later High- Renaisssance or Baroque used curved and dramatically twisted shapes. The term Cartesian planning given to the planning of cities in a grid iron fashion shows the close association between architecture and geometry.The beginning of the twentieth century saw the heightened use of Eulidean or Cartesian rectilinear geometry in Modern Architecture- especially in the De Stijl Movement which considered the horizontal and the vertical as the universals and tried to manipulate them. The most recent movement- the Deconstructivist- employs non-Euclidean geometry to achieve its complex objectives resulting in a chaotic order.

As is apparent, architecture has always tried to achieve certain ends apart from mere function- cosmological,aesthetic, philosophical, etc.,- and invariably the means has been the beauty and structure of mathematics.