Mathematics and Architecture - Ancient Times

Ancient Times

In Greek architecture, the Golden mean, (also known as the Golden rectangle, Golden Section, and Golden Ratio) served as a canon for planning all the architectural designs. Knowledge of the golden mean goes back at least as far as 300BC, when Euclid described the method of geometric construction in Book 6, Proposition 30 of his book the Elements. It corresponds to a proportion of 1: 1.618, considered in Western architectural theory to be very pleasing. This number is also known as Phi. Jay Hambidge believed that the golden mean was the ratio used by Attic Greek architects in the design of the Parthenon and many other ancient Greek buildings, as well as sculptures, paintings, and vases. More recent authors, however, question nineteenth-century assumptions about the Golden Mean in Classical buildings such as the Parthenon, where experiments by George Markowsky failed to find any preference for a Golden rectangle.

In Islamic architecture, a proportion of 1: √2 was often used—the plan would be a square and the elevation would be obtained by projecting from the diagonal of the plan. The dimensions of the various horizontal components of the elevation such as mouldings and cornices too were obtained from the diagonals of the various projections and recesses in plan.

Ancient architecture such as that of the Egyptians and Indians employed planning principles and proportions that rooted the buildings to the cosmos, considering the movements of sun, stars, and other heavenly bodies. Vaastu Shastra, the ancient Indian canons of architecture and town planning employs mathematical drawings called mandalas. Extremely complex calculations are used to arrive at the dimensions of a building and its components. Some of these calculations form part of astrology and astronomy whereas others are based on considerations of aesthetics such as rhythm.

The Cartesian grid planning of cities shows the close association between architecture and geometry. Ancient Greek cities such as Olynthus had such a pattern superimposed on rugged terrain giving rise to dramatic visual qualities, though proving difficult to negotiate heights.