Hagia Sophia: The Dome on a Square

A dome is a circle in plan. A room built for people is usually a square, because square rooms are easy to wall and roof with straight timber or stone. Sit a round dome directly on a square and you get a problem: the dome's curved rim only touches the square's walls at four points, leaving four corners with nothing underneath to catch the dome's weight. Builders needed a shape that could gather the circle's load and funnel it down into the square's four corners.

The pendentive is that shape. It is a curved triangular section of masonry, concave like the inside of a sphere, that fills each corner between the square's arches and the dome's circular base. Picture a sphere slightly larger than the dome resting inside the square room, touching all four walls; slice off the top of that sphere flat to seat the dome, then slice down the four sides along the arches, and the four leftover curved triangles are the pendentives. They catch the dome's outward and downward thrust and carry it through the arches into four massive piers.

At Hagia Sophia, built in Constantinople and finished in 537 CE under Justinian, the dome's thrust doesn't stop at the pendentives. It pushes outward into two half domes to the east and west, which pass the load further into still smaller half domes and exedrae, and finally into buttresses and thick walls. Forty windows ring the dome's base, cut into the band above the pendentives rather than through the structural arches themselves, so light pours around the dome's rim without touching the load path. The result looks weightless even though every stone is working.