Domes in the Islamic Architecture of Cairo City: A Mathematical Approach

Abstract

This work analyzes mathematically and graphically the two methods used historically in the transitional zone between the circular base of the dome and the square top of the cube where the dome is supported. The time frame of this work is the distinguished historical buildings of Islamic Cairo built between the ninth and eighteenth centuries. Ten samples were chosen out of a total of thirty. A set of mathematical expressions has been derived to relate the different parts of the squinches/pendentives to the cube with a side of length l. The equations derived were validated twice, first by generating 3D graphical sequences for both squinches and pendentives for the selected domes using CAD software based on the values obtained from the driven equations, and second by executing physical models using a 3D printer for two examples of squinches and pendentives.

Ahmed Ali Elkhateeb graduated in 1990 from the Department of Architecture, Faculty of Engineering of Ain Shams University (Cairo, Egypt). He worked in the same department until summer 2011. He completed his M.Sc. and Ph.D. in the field of architectural acoustics, which is his primary area of interest, in addition to mathematics and its relation with architecture. As of fall 2011, he is a Professor (A) of architecture and building science in the Department of Architecture in Faculty of Environmental Design of King Abdul Aziz University, Jeddah, Kingdom of Saudi Arabia.