pendentive

French pendentif — hanging, suspended — comes from Latin pendere (to hang). In architecture, the pendentive is the concave, triangular surface that spans the angle between two arches at right angles, filling the gap between a square bay and the circular base of a dome above. The pendentive hangs, in a sense, from the dome's rim, bridging the geometrical incompatibility of circle and square.

The problem the pendentive solves is fundamental: a dome is circular; the rooms beneath it are typically square or rectangular. Without a transition element, the dome would need to rest on four points, creating enormous concentrated loads at the corners. The pendentive distributes this load across the arch below it, transforming point loads into distributed loads across curved surfaces.

The Hagia Sophia in Constantinople (532-537 CE), designed by Anthemius of Tralles and Isidorus of Miletus, was the first building to use pendentives at monumental scale. The vast central dome — 31 meters in diameter — floats on four pendentives over a square bay. Emperor Justinian, at the dedication in 537 CE, reportedly said: 'Solomon, I have surpassed thee.'

Brunelleschi's Florence Cathedral dome (1436), Michelangelo's St. Peter's Basilica in Rome (1590), Christopher Wren's St. Paul's Cathedral in London (1710) — all use pendentives. The 6th-century structural solution invented (or perfected) in Constantinople remained the standard way to put a circular dome on a square building for twelve hundred years.