In 10th-century Córdoba, mathematics—and particularly geometry—was applied to architectural design in new ways, constituting a “mathematical turn” of Islamic architecture. In the mosque of Córdoba and in the palaces of Madīnat al-Zahrāʾ, geometry was employed in the design of ground plans, elevations, decorative patterns, and even to measure the human view. While Roman architects like Vitruvius had used mathematics to place each element of a building in its appropriate relation to all other elements of a building, the architects at Córdoba employed geometry to create a spatial web in which all parts are equal to each other and part of a single, unified space. The architects of Córdoba thus pointed the way to new possibilities of designing architecture, possibilities which were to be tested further by architects of Gothic and Renaissance architecture, though to different ends.
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