The role of proportional systems in the forming of Sassanid square domes

One of the common monuments in the Sassanid era was the square dome. Interestingly, corners and parts of the square dome were always geometrically proportionate to each other. Square domes have been mainly studied in terms of their historical background as well as the materials used. The present research, however, aimed to examine the geometric proportions governing the formation of square domes in the Sassanid era. The data were mainly gathered from field studies. First, the intended monuments were individually studied: the sizes were carefully measured and recorded. Then, the data were simulated by Auto CAD and the geometric repetitive proportions of the parts were extracted. The results indicated that the ratio of the corner depth to the radius of the dome circle was 0.3; the ratio of the angle length to the inward length was 0.11 and that of the outward side to the inward side was 1.6.