Designed for Justinian by Anthemius of Tralles and Isidore of Miletus — both scholars of geometry and mechanics — Hagia Sophia solves one of the boldest structural moves in architectural history: setting a circular dome on a square plan.

The problem is this: the dome is circular, but the supporting walls enclose a square. The solution is the pendentive — spherical-triangle surfaces rising at the four corners. These triangles take the round base of the dome down to the square and gather the load onto four great piers. The 31.8-metre main dome thus rests not on the walls but on these four points.

The lateral thrust the dome produces is met on the east-west axis by two half-domes and on the north-south axis by massive buttresses — the thrust is poured downward through diminishing tiers of vaulting. At the base of the dome runs a ring of forty windows; these visually erase the mass carrying the dome, so it seems, in the words of the contemporary historian Procopius, to hang "from heaven by a golden chain." Here structural necessity turns into an effect of light. Hagia Sophia thus gives architecture the pendentive dome — establishing, for the next thousand years, the basic grammar of dome architecture from Ottoman mosques to Renaissance churches.