Parabolic arch

parabolic archesparabolicparabolic archedparabolic vaultparabolaparabolic concrete archparabolic rib archparabolic shape of the archparabolic steel archparabolic vaults
A parabolic arch is an arch in the shape of a parabola.wikipedia
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Arch

archesround archarched
A parabolic arch is an arch in the shape of a parabola. Unlike a catenary arch, the parabolic arch employs the principle that when weight is uniformly applied above, the internal compression (see line of thrust) resulting from that weight will follow a parabolic curve.
The parabolic arch employs the principle that when weight is uniformly applied to an arch, the internal compression resulting from that weight will follow a parabolic profile.

Catenary

CatenariesInverted catenary archcable structures
While a parabolic arch may resemble a catenary arch, a parabola is a quadratic function while a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions.
The catenary curve has a U-like shape, superficially similar in appearance to a parabolic arch, but it is not a parabola.

16th Street Bridge (Washington, D.C.)

16th Street BridgeSixteenth Street Bridge
The 16th Street Bridge, also known as the Piney Branch Bridge, is an automobile and pedestrian bridge that carries 16th Street NW over Piney Branch and Piney Branch Parkway in Washington, D.C. It was the first parabolic arch bridge in the United States.

Catenary arch

catenarycatenary archesarch
While a parabolic arch may resemble a catenary arch, a parabola is a quadratic function while a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions. Parabolic arches were used by architects Oscar Niemeyer, and Antoni Gaudí, who also used catenary arches. Unlike a catenary arch, the parabolic arch employs the principle that when weight is uniformly applied above, the internal compression (see line of thrust) resulting from that weight will follow a parabolic curve.
It is not a parabolic arch.

Bixby Creek Bridge

The bridge's location on the scenic Central Coast of California, the parabolic shape of the arch, the tall spandrel columns, and the architectural piers contribute to an "intense aesthetic experience."

Oscar Niemeyer

NiemeyerNiemeyer, OscarOscar Niemeyer, o arquiteto no recanto da princesa
Parabolic arches were used by architects Oscar Niemeyer, and Antoni Gaudí, who also used catenary arches.
Auguste Perret, in Casablanca and Robert Maillart in Zurich had experimented with the plastic freedom of concrete, taking advantage of the parabolic arch's geometry to build extremely thin shells.

Casa Milà

La PedreraCasa MiláCasa Mila
The attic, where the laundry rooms were located, was a clear room under a Catalan vault roof supported by 270 parabolic vaults of different heights and spaced by about 80 cm.

Bayonne Bridge

Bayonnebridge
The arch resembles a parabola, but is made up of 40 linear segments.

Cape Creek Bridge

Cape Creek Bridge No. 01113
The bridge resembles a Roman aqueduct, with a single parabolic arch that spans half its length.

St Leonard's Church, St Leonards-on-Sea

St Leonard's ChurchSt Leonarda church
Giles Gilbert Scott's proposal for the rebuilding of war-damaged Coventry Cathedral (1946–47) and his brother's work on the St Mary and St Joseph's Church on the Lansbury Estate in east London (1950–54), both based on a series of parabolic arches, informed their work at St Leonards-on-Sea: the design theme was used both inside and out.

St Paul's Anglican Church, Proserpine

St Paul's Anglican ChurchSt Paul's Anglican Memorial Church
St Paul's Anglican Church, a striking parabolic arched structure of concrete, brick, timber and glass, is located in Proserpine in the Whitsunday Region of northern Queensland.

Paraboloid

hyperbolic paraboloidelliptic paraboloidhyperbolic paraboloids
A hen's egg can be fairly well described as two different paraboloids connected by part of an ellipse

Antoni Gaudí

GaudíAntoni GaudiGaudi
Parabolic arches were used by architects Oscar Niemeyer, and Antoni Gaudí, who also used catenary arches.
Gaudí designed a monumental entrance with a magnificent parabolic arch above iron gates, decorated with the Catalan coat of arms and a helmet with a winged dragon, the work of Joan Oñós.

Tyne Bridge

TynebridgeGeorge V Bridge
The bridge's design uses a parabolic arch.

Cathedral

cathedralscathedral churchproto-cathedral
Such arches are used in bridges, cathedrals, and elsewhere in architecture and engineering.

Parabola

parabolicparabolic curveparabolic arc
A parabolic arch is an arch in the shape of a parabola. While a parabolic arch may resemble a catenary arch, a parabola is a quadratic function while a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions. Unlike a catenary arch, the parabolic arch employs the principle that when weight is uniformly applied above, the internal compression (see line of thrust) resulting from that weight will follow a parabolic curve.

Quadratic function

quadraticquadratic polynomialquadratically
While a parabolic arch may resemble a catenary arch, a parabola is a quadratic function while a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions.

Hyperbolic function

hyperbolic tangenthyperbolichyperbolic cosine
While a parabolic arch may resemble a catenary arch, a parabola is a quadratic function while a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions.

Exponential function

exponentialexponentiallyexp
While a parabolic arch may resemble a catenary arch, a parabola is a quadratic function while a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions.

Line of thrust

thrust line
Unlike a catenary arch, the parabolic arch employs the principle that when weight is uniformly applied above, the internal compression (see line of thrust) resulting from that weight will follow a parabolic curve.

Bridge

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