Let's now walk through the three diagrams. The first is a sort of bird's eye view, from the top, of the problem created for medieval architects who wanted to build a dome. They wanted a dome, and they wanted the round dome to "cover" a square surface below. Thus, they had the problem of "squaring the circle." If they made the diameter of the dome or cupola of the same measurement as one side of the square, it would leave the four corner sections of the square below "uncovered" by the dome. If, however, they wanted to make the diameter of the dome equivalent to the diagonal of the square, the dome would hover over an area beyond that of the square.

They sought a model which would make the dome perfectly "cover" the square. Diagram 2 gives an example of how they tried to do it. The Byzantine builders decided to cut off the dome just above the arches made by a the vertical cutting, thus making the dome cover the square below without jutting out beyond the square. But then, they had arches in the wall. They "solved" the problem by making a second story, as it were, by putting a perfect dome atop of the sliced off dome below, thus creating a sort of ice cream cone double-scoop, with the dome on the top.

By looking at diagram 3, then, we see what a pendentive is. When the sliced out dome is put under a perfect dome, there is the rounded dome surface on top and then a series of four triangular shaped, curved portions of the lower dome below. These lower curved sections abut the stones of the arch, which stones are called voussoirs. A voussoir is a "tapered or wedge-shaped block or stone that composes an arch." So, the arch in diagram 3 above consists of a lower arch, with voussoirs and pendentives, and an upper dome. The pendentives are thus the triangular, but concave, portions of the lower arch.

Conclusion

To show that my interest pendentives is not simply of academic interest, you should know that the dome of the Hagia Sophia, the most famous church in Christendom until the Muslim Conquest of Constantinople, was constructed in an innovative way using pendentives. As one article says, "The dome is supported by pendentives which had never been used before the building of this structure. The pendentive enables the round dome to transition gracefully into the square shape of the piers below." Prior to the use of pendentives, Roman architects used the device of "corbelling" (where a piece of stone just out from a a wall to carry any weight above it) or the use of the "squinch" (corner arch) in the corners of a room.

Now, with these terms defined, let's return to our verbal surfing.

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