Mathematical and Geometric proportions Used in Tiles of the Isfahan Mosques in Safavid Era with Respect to Optimization of Construction Materials

Geometrical and mathematical proportions play a fundamental role in art and architecture. Persian architecture has been always closely related to geometry. This is easily visible in decorations and patterns of surfaces. Persian architects made utmost effort to apply construction materials as economically as possible. Studying the tile works in terms of form and geometrical characteristics reveals how tiles have been applied in mosques. In this respect, Esfahan is one of the cities of Iran with an amazing variety in terms of tile works used in its mosques. The spiritual beauty and geometrically skilful representations reach its zenith in Esfahan’s mosques especially at the time it was the capital of an Empire- Safavid era. Applying tiles and materials economically has had a direct relationship with geometric mastery. Most studies in this connection have dealt with symbolic representations and drawing techniques of Persian tile works. This study, however, aimed to examine geometric characteristics of tiles, the quantity of them and the number of workforce needed to apply tiles on the wall surfaces of Isfahan mosques of Safavid era. Through doing library research and geometric analyses, the number of workforce and tiles used was estimated. Then, several tile fretworks were dismantled into its constituents. The area, perimeter and occurrence frequency of each form were examined through applying special soft wares. In addition, the work force needed to make each form was estimated and compared among the different fretworks. The number of tiles applied in terms of their color was determined in each tile inscription. In order to draw the patterns, the techniques used by the distinguished experts (Lorzade, Maher-o-Naghs and Shaarbaf) were followed. In fact, the present study tried to reveal Persian architects’ mastery over geometry. Since the majority of similar studies have been done on famous mosques, it was decided that less famous mosques be examined to, at the same time, make other researchers encourage study less historically distinguished buildings as well. In this connection, two mosques- Khayyatha Mosque and Zolfaghar-e-Neemavard Mosque, both built in Safavid era were studies. The two mosques have various brick and tile patterns. Tile fretworks, composed of formal elements, have their own geometrical characteristics. By studying the constituents of the fretworks, the geometrical and mathematical proportions were obtained. The effect of size and form of tile work on workforce and used materials was recognized. In addition, the most commonly used tile work patterns in Khayyatha mosque and Zolfaghar-e-Neemavard mosque was found. This study may help Persian traditional tile fretworks and tile decorations perpetuate.