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The Hagia Sophia church was an important source of authority for its patron, Emperor Justinian.  His success as a ruler could be seen in the cost he spent in constructing it.  The Hagia Sophia was important as a work of architecture, too.  The interior contains columns, domes, and other classical components.  The dome is wide and high, adding space to the building's interior.  The bottom edge of the dome is called the drum.  Here, the drum is cut through with many windows.  These let light pour into the building, but also seem to lift the dome.  Without the drum windows, this building would seem darker and heavier.

How can we put a round dome atop a square building? This problem was solved by the Hagia Sophia's architects using pendentives. Picture a pendentive as a sort of curved triangle. It stands upside down, with the point on the floor in a corner. It rises from there, connecting the two walls of the corner and curving into an arc. At the top, the edge curves around to form part of the circular base of the dome.