STAR-BULLETIN / 2001 They're everywhere nowadays, but centuries ago, building a dome was considered a major architectural advance.

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Architectural genius
spans the ages

Look around any Western city and you will see many examples of ancient styles of architecture, notably columns, arches and domes.

Egyptian builders developed the most basic architectural system of post-and-lintel (column and beam) construction and used it exclusively in their monumental building.

The ancient Greeks perfected the post-and-lintel style that reached its culmination in the Parthenon, built between 447-432 B.C. in Athens.

The huge columns and thick beams that characterize the Parthenon are marble from Mount Pentelicus, near Athens. They represent the first use of marble as a building material.

As strong as marble might seem, it is weak under tension and either fractures or deforms plastically over time if the span of the beam is too great. So limits the spacing of the columns.

The Romans found a way to increase the span by using the stone arch, the root of the word "architecture" (arch + tekton = to build, from which we also get "technique" and "technology").

The stones in an arch are carefully shaped such that weight on the arch is transmitted outward and downward. This spreads the stresses throughout the arch and puts all the stone under compression, taking advantage of its superior strength under compression compared with tension.

Roman engineers and architects used the arch to build the aqueducts and the Colosseum but went a step beyond the simple arch with two other innovations.

First was the discovery that the volcanic ash of Mount Vesuvius, when mixed with lime and water, hardened into a waterproof cement. Mixed with gravel it became the composite building material called concrete.

The second innovation was the dome, which is a geometric variation of the arch. It is the hemisphere that results from rotating a semicircular arch.

The combination of these two innovations was used to build the Pantheon ("temple to all gods"), which is now the oldest enclosed structure still standing intact, having been built around 20 B.C.

Behind the columnar entrance of the Pantheon, which is modeled after the Greek Parthenon, is a concrete cylinder 142 feet in diameter covered by a hemispherical dome. It sits on a cylinder that is the same height and diameter as the dome such that a perfect sphere would fit exactly inside the cylinder just touching the floor.

The dome became the most copied architectural model throughout the Western world until the use of steel-reinforced concrete appeared in the 20th century.

As brilliant and innovative as the Roman architects were, they thought it was impossible to place a dome on a square base, so for five centuries domed buildings were constructed on a circular base.

A major advancement in architecture was "rounding the square," that is mounting a dome on a square base. It is mathematically difficult, involving a serious problem in spherical geometry, and the story requires just a bit of historical background.

In A.D. 284 the Roman empire was split into eastern and western sections for administrative efficacy. In 306, Constantine's troops proclaimed him to be Augustus, emperor of the East.

Constantine re-founded the ancient Greek colony of Byzantium in 330 A.D. and made it the capital of the Eastern Roman Empire. Despite its official name of "Nova Roma" (New Rome), it was popularly called "Constantine's City" and so became Constantinople. The Ottomans renamed it Istanbul when they took control of the city in the 15th century.

Emperor Constantine decriminalized Christianity and commissioned a church to be erected over the ruins of an ancient Greek temple of Apollo. The church was called Hagia Sophia, which means "holy wisdom" in Greek, and was completed in A.D. 360.

Rioting crowds burned Constantine's church to the ground in 404. It was rebuilt around 415 but was burned again in 532 during the reign of Justinian (527-565), which many historians believe marks the end of the Roman empire and the beginning of the Byzantine.

Justinian's armies would take control and bring relative peace to most of the territory held by the ancient Roman Empire around the rim of the Mediterranean.

Although sending gold to the Persians to prevent war to the east and spending immense sums in the Gothic wars to the west, Justinian had foresight and enough money to undertake the rebuilding of Hagia Sophia.

Today, the structure dominates the skyline of Istanbul, having survived not only the ravages of time and the Crusades, but several major earthquakes that destroyed most of the other structures in the city.

Hagia Sophia represents both the last great Roman structure and the first great medieval church, looking back to the Pantheon in form but presaging the architecture of the later Middle Ages.

Justinian insisted that the structure must have a dome to represent the eminence of the Roman architecture atop the square base of the ancient Greek temple over which it was constructed.

The designers of Justinian's church were architect Isidore of Miletus and mathematician Anthemius of Tralles, professor of geometry at the University of Constantinople.

Their ingenious geometric solution required both imagination and scientific accuracy. It merged the square and the circle as an architectural metaphor of the transition from the ancient glory of Rome to the medieval eminence of the Byzantine Empire.

The solution used four arches to span columns at the four corners of the square. When connected and filled with masonry, the resulting shapes were segments of spherical triangles, called pendentives, that join the two arches on each of the square corners into a single continuous piece.

The pendentives and the tops of the arches combine to form a strong, circular base for the dome and focus its weight on the four corner columns through the arches.

The Columbia Encyclopedia elegantly describes the structure of Hagia Sophia as "wholly free of suggestion of ponderous load, and its effect is that of a weightless golden shell that seems to possess a miraculous inherent stability."

The pendentive would remain the greatest architectural innovation until the flying buttress was resurrected as an artistic element in the 12th century and combined with the pointed Gothic arch to create the distinctive style of the great Gothic cathedrals such as Westminster Abbey in London and Notre Dame in Paris.

Rounding the square melded science, engineering, mathematics and architecture, setting the stage for today's computer-aided design of structures that the ancient architects could never have imagined.