In architecture, a triangular segment of a spherical surface that forms the transition between the circular plan of a dome and the polygonal plan of its supporting structure. The problem of placing a round dome on a square base assumed growing importance to Roman builders, but it remained for Byzantine architects to recognize the possibilities of the pendentive and fully develop it (see Hagia Sophia). One of the great architectural inventions of all time, the pendentive became very important in the Renaissance and Baroque periods. As a result of Byzantine influence, pendentives are also frequent in Islamic architecture. The vaulting form in which the curve of the pendentive and dome is continuous is known as a pendentive dome.
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A pendentive is a constructive device permitting the placing of a circular dome over a square room or an elliptical dome over a rectangular room. The pendentives, which are triangular segments of a sphere, taper to points at the bottom and spread at the top to establish the continuous circular or elliptical base needed for the dome. In masonry the pendentives thus receive the weight of the dome, concentrating it at the four corners where it can be received by the piers beneath. Prior to the pendentive's development, the device of corbelling or the use of the squinch in the corners of a room had been employed. The first attempts at pendentives were made by the Romans and full achievement of the form was reached in Hagia Sophia at Constantinople (6th cent.) by the Eastern Roman Byzantine Empire. Pendentives were commonly used in Renaissance and baroque churches, with a drum often inserted between the dome and pendentives.In addition, the pendentive is comprised of the geometric shape of a triangle this further makes a strong base to withstand the dome.