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It is commonly used in bridge design, where long spans are needed.

The catenary arch has a shape different from the parabolic curve.

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In ancient Persia, the Achaemenid Empire built small barrel vaults (essentially a series of arches built together to form a hall) known as iwan, which became massive, monumental structures during the later Parthian Empire.Throughout the Roman empire, their engineers erected arch structures such as bridges, aqueducts, and gates.The shape of the curve traced by a loose span of chain or rope, the catenary is the structurally ideal shape for a freestanding arch of constant thickness.Types of arches displayed chronologically, roughly in the order in which they were developed: True arches, as opposed to corbel arches, were known by a number of civilizations in the ancient Near East and the Levant, but their use was infrequent and mostly confined to underground structures, such as drains where the problem of lateral thrust is greatly diminished.Corbel arches were found in other parts of ancient Asia, Africa, Europe and the Americas.

In 2010, a robot discovered a long arch-roofed passageway underneath the Pyramid of Quetzalcoatl, which stands in the ancient city of Teotihuacan north of Mexico City, dated to around 200 AD.

The horseshoe arch is based on the semicircular arch, but its lower ends are extended further round the circle until they start to converge.

The first known built horseshoe arches are from Aksum (modern-day Ethiopia and Eritrea) from around the 3rd–4th century, around the same time as the earliest contemporary examples in Roman Syria, suggesting either an Aksumite or Syrian origin for the type.

In ancient China, most architecture was wooden, including the few known arch bridges from literature and one artistic depiction in stone-carved relief.

The first example of an early Gothic arch in Europe is in Sicily in the Greek fortifications of Gela.

Since it is a pure compression form, the arch is useful because many building materials, including stone and unreinforced concrete can resist compression, but are weak when tensile stress is applied to them.