Entasis

Entasis is the architectural term for applying a convex curve to a surface for aesthetic purposes, or increasing strength. Its best-known use is in certain orders of Classical columns that curve slightly outward as they narrow going upwards.
Etymology
The word we apply to the design principle is used by the Roman architectural historian Vitruvius, and derives from the Greek word έντείνω (enteino), "to stretch or strain tight". Creating the illusion of greater strength or perception of height may have been an objective in the application of entasis.
Examples
Examples of this design principle may be found in cultures throughout the world, from ancient times to contemporary architecture. The first use of entasis is probably in the Later Temple of Aphaia at Aigina, in the 490s BC.
It may be observed among Classical period Greek column designs, for example, in the Doric order temples in Segesta, Selinus, Agrigento, and Paestum.
It was used less frequently in Hellenistic and Roman period architecture. The Roman temples built during these periods were sometimes higher than those of the Greeks, with longer and thinner columns.
Chinese carpenters of the Song Dynasty followed designs in the AD 1103 Yingzao Fashi (Treatise on Architectural Methods or State Building Standards) that specified straight columns or those with an entasis on the upper third of the shaft.
Noted architects, such as the Renaissance master Andrea Palladio, also used entasis in the designs of their buildings.
Entasis was often a feature of Inca walls and doorways to counteract the optical illusion that would make the openings appear narrower in their middles.
Concave curves
The opposite effect, applying concave curves in order to narrow surfaces that otherwise would appear to bulge, is also found in architecture, as in
the sloping or battered walls of some Tibetan and Bhutanese monasteries and fortresses. The lower parts of such walls, approximately one third, have a slight convex or inward curve, while the higher parts retain an even slope, offsetting the outwardly bulging illusion created by a straight sloping wall. An example in Bhutan is the Dobji Dzong. When some collapsed walls of the Punakha Dzong were rebuilt, around 1996, this asymmetry was not used.
In calligraphy
In calligraphy and typography entasis refers to the use of a concave curve to thin — rather than widen — the waist of a stroke or character. In calligraphy this is achieved either through a slight heightening of the pen or brush angle and/or by an increase in the speed of the stroke as it goes into a straight. Visually it is reminiscent of the structure of a bone and a stroke is seen as stronger for it. Entasis in a stroke is intended to counter the illusion a stroke with perfectly straight sides has of bulging slightly.
Origin in Greek columns
No record of the rationale for using entasis in columns by Classical builders has yet been discovered.. As a result, there has been extensive conjecture over its purpose.
An early view, often articulated and still widespread, espoused by Hero of Alexandria, is that entasis corrects the optical illusion of concavity in the columns that the fallible human eye would create if the correction were not made.
Some descriptions of entasis, state simply, that the technique was an enhancement applied to the more primitive conical columns to make them appear more substantial. Other descriptions argue that the technique emphasizes the substantiality of, not the columns, but rather, of some other part or of the building while being viewed as a whole. Yale architectural historian Vincent Scully argues that entasis emphasizes the weight of the roof of a building by making the building columns appear to bulge under the pressure distributed among them. Danish architect Steen Eiler Rasmussen believed that the effect represented strength by imitating the swelling of a strained muscle, a theory that accords well with the etymology of the word, from the Greek meaning "to strain".
It also has been argued that a "stunted cycloid" column that bulges in the middle is stronger structurally than is a column whose diameter changes according to a linear progression, therefore, having a sound engineering purpose. Because their discussion of the application of the principle has never been discovered, it is unknown, however, whether the early Greeks knew this.
Literature
See also
Glossary of architecture
References
Columns and entablature
Optical illusions