A parabolic arch is an

arch An arch is a vertical curved structure that spans an elevated space and may or may not support the weight above it, or in case of a horizontal arch like an arch dam, the hydrostatic pressure against it. Arches may be synonymous with vau ...

in the shape of a

parabola In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One descri ...

.Article about parabolic arch by The Free Dictionary
Parabolic arch , Article about parabolic arch by The Free Dictionary
accessdate: March 2, 2017 In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.

Description

The mathematics

While a parabolic arch may resemble a

catenary arch A catenary arch is a type of architectural arch that follows an inverted catenary curve. The catenary curve has been employed in buildings since ancient times. It forms an underlying principle to the overall system of vaults and buttresses i ...

, a

is a

quadratic function In mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic polynomial. Before 20th century, the distinction was unclear between a polynomia ...

while a

catenary In physics and geometry, a catenary (, ) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field. The catenary curve has a U-like shape, superfici ...

is the

hyperbolic cosine In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the ...

, , a sum of two

exponential function The exponential function is a mathematical function denoted by f(x)=\exp(x) or e^x (where the argument is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, ...

s. One parabola is , and hyperbolic cosine is . The curves are unrelated.

The line of thrust

Unlike a catenary arch, the parabolic

employs the principle that when weight is uniformly applied above, the internal compression (see

line of thrust The line of thrust is the locus of the points, through which forces pass in a retaining wall or an arch. It is the line, along which internal forces flowparabolic curve. Of all arch types, the parabolic arch produces the most thrust at the base. Also, it can span the widest area. It is commonly used in

bridge A bridge is a structure built to span a physical obstacle (such as a body of water, valley, road, or rail) without blocking the way underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually someth ...

design, where long spans are needed.The Design of Prestressed Concrete Bridges/Chapter 17 The Design And Construction Of Arches
/ref>

Compared to catenary arches

When an arch carries a uniformly distributed vertical load, the correct shape is a parabola. When an arch carries only its own weight, the best shape is a

. File:Parabola graphed against a catenary upside down view.png, Parabola (red) graphed against a catenary (blue), view to simulate an arch. File:Parabola graphed against a catenary upside-down, zoomed out.png, Parabola (red) graphed against a catenary (blue), view to simulate an arch. Zoomed out.

Uses

In nature

A hen's egg can be fairly well described as two different

paraboloid In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every plan ...

s connected by part of an

ellipse In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special type of ellipse in ...

.Google Books
https://books.google.co.uk/books?id=CIAAAAAAMAAJ&pg=PA264&lpg=PA264&dq="hen's+egg"+"parabolic+arch"&source=bl&ots=uOzbRBeDwm&sig=ohyUSTlHvU8sNUqTahR_BjU6gp4&hl=en&sa=X&redir_esc=y#v=onepage&q="hen's egg" "parabolic arch"&f=false
accessdate: March 22, 2017

Architectural examples

Interieur van de centrale hal met decoraties - Utrecht - 20349663 - RCE

Self-supporting

es appeared occasionally in ancient architecture, for examples in the main arch of the partially ruined

Sassanian The Sasanian () or Sassanid Empire, officially known as the Empire of Iranians (, ) and also referred to by historians as the Neo-Persian Empire, was the last Iranian empire before the early Muslim conquests of the 7th-8th centuries AD. Named ...

palace Taq Kasra (now in

Iraq Iraq,; ku, عێراق, translit=Êraq officially the Republic of Iraq, '; ku, کۆماری عێراق, translit=Komarî Êraq is a country in Western Asia. It is bordered by Turkey to Iraq–Turkey border, the north, Iran to Iran–Iraq ...

), the largest single-span

vault Vault may refer to: * Jumping, the act of propelling oneself upwards Architecture * Vault (architecture), an arched form above an enclosed space * Bank vault, a reinforced room or compartment where valuables are stored * Burial vault (enclosure ...

of unreinforced

brickwork Brickwork is masonry produced by a bricklayer, using bricks and mortar. Typically, rows of bricks called ''courses'' are laid on top of one another to build up a structure such as a brick wall. Bricks may be differentiated from blocks by si ...

in the world, and the beehive huts of southwestern Ireland. In the modern period, parabolic arches were first used extensively from the 1880s by the Catalan architect

Antoni Gaudí Antoni Gaudí i Cornet (; ; 25 June 1852 – 10 June 1926) was a Catalan architect from Spain known as the greatest exponent of Catalan Modernism. Gaudí's works have a highly individualized, ''sui generis'' style. Most are located in Barcel ...

, deriving them from catenary arched shapes, constructed of brick or stone, and culminating in the catenary based design of the famous

Sagrada Familia Sagrada is a Spanish word meaning "sacred Sacred describes something that is dedicated or set apart for the service or worship of a deity; is considered worthy of spiritual respect or devotion; or inspires awe or reverence among believers. T ...

. Other Catalan architects then used them into the 1920s, and they appeared occasionally in German expressionist architecture of the 1920s-30s. From the 1940s they gained a new popularity in reinforced concrete, including in shell concrete forms often as hyperbolic parabloids, especially by Felix Candela in Mexico and

Oscar Niemeyer Oscar Ribeiro de Almeida Niemeyer Soares Filho (15 December 1907 – 5 December 2012), known as Oscar Niemeyer (), was a Brazilian architect considered to be one of the key figures in the development of modern architecture. Niemeyer was ...

in Brazil, but they could be found around the world, especially for churches, in the 1950s and 60s. Since the 1990s Spanish designer

Santiago Calatrava Santiago Calatrava Valls (born 28 July 1951) is a Spanish architect, structural engineer, sculptor and painter, particularly known for his bridges supported by single leaning pylons, and his railway stations, stadiums, and museums, whose sculp ...

has frequently used parabolas for his signature roof structures and bridges. Structures that are self-supporting arches like the Sheffield Winter Garden are often closer to true catenaries. *

Palau Güell The Palau Güell (, en, Güell Palace) is a mansion designed by the architect Antoni Gaudí for the industrial tycoon Eusebi Güell, and was built between 1886 and 1888. It is situated on the Carrer Nou de la Rambla, in the El Raval neighbor ...

, 1886–88,

Barcelona Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within c ...

, where

Antonio Gaudi Antonio is a masculine given name of Etruscan origin deriving from the root name Antonius. It is a common name among Romance language-speaking populations as well as the Balkans and Lusophone Africa. It has been among the top 400 most popular mal ...

used parabolic arches in stone for the carriageway entrances, and in brick for the structure of the main hall. *

Casa Milà Casa Milà (, ), popularly known as ''La Pedrera'' (, ; "the stone quarry") in reference to its unconventional rough-hewn appearance, is a '' Modernista'' building in Barcelona, Catalonia, Spain. It was the last private residence designed by arc ...

, 1906, where Gaudi used brick parabolic arches support the attic roof, used as a laundry space. * Wrocław Market Hall, 1906-8, Richard Plüddemann and Heinrich Küster, internal structure * Celler modernista, 1921, part of

Sant Cugat Museum The Sant Cugat Museum ( ca, Museu de Sant Cugat, es, Museo de Sant Cugat) was opened on 23 April 2003; its mission was to oversee the conservation and dissemination of the historic, artistic and cultural heritage of Sant Cugat del Vallès in Catal ...

, Catalonia, Spain, Cèsar Martinell i Brunet * Pinell de Brai Cooperative Winery, 1922, Pinell de Brai, Catalonia, Spain, Cèsar Martinell i Brunet * Former main post office, 1919–24, Utrecht, main hall, designed by J. Crouwel Jr. * Priory Chapel at Saint Louis Abbey - July 2013

Priory Chapel at Saint Louis Abbey - July 2013

St. Engelbert,

Cologne Cologne ( ; german: Köln ; ksh, Kölle ) is the largest city of the German western state of North Rhine-Westphalia (NRW) and the fourth-most populous city of Germany with 1.1 million inhabitants in the city proper and 3.6 millio ...

, 1928−1932, by

Dominikus Böhm Dominikus Böhm (23 October 1880 – 6 August 1955) was a German architect specializing in churches. He built churches in Cologne, the Ruhr area, Swabia, and Hesse. Many of his buildings are examples of Brick Expressionism. Life and career B ...

Church of Saint Francis of Assisi The Church of Saint Francis of Assisi (''Igreja de Sao Francisco de Assis'', commonly known as the ''Igreja da Pampulha'') is a chapel in Pampulha region of Belo Horizonte, in the state of Minas Gerais, southeastern Brazil. It was designed by ...

, 1943, Pampulha,

Belo Horizonte Belo Horizonte (, ; ) is the sixth-largest city in Brazil, with a population around 2.7 million and with a metropolitan area of 6 million people. It is the 13th-largest city in South America and the 18th-largest in the Americas. The metropol ...

, Brazil, Oscar Neimeyer. * Church of La Purísima, 1943,

Monterrey Monterrey ( , ) is the capital and largest city of the northeastern state of Nuevo León, Mexico, and the third largest city in Mexico behind Guadalajara and Mexico City. Located at the foothills of the Sierra Madre Oriental, the city is ancho ...

, Mexico,

Enrique de la Mora Enrique de la Mora y Palomar (16 June 1907 – 9 May 1978) was a Mexican architect who designed prominent university buildings and Roman Catholic churches in which he experimented with hyperbolic-paraboloid roofs. He is generally regarded, alo ...

* Cosmic Rays Pavilion, 1951, Felix Candela with Jorge González Reyna,

UNAM The National Autonomous University of Mexico ( es, Universidad Nacional Autónoma de México, UNAM) is a public research university in Mexico. It is consistently ranked as one of the best universities in Latin America, where it's also the bigge ...

, Mexico City * St Leonard's Church,Interior of St Leonard's church, St... (C) Julian P Guffogg :: Geograph Britain and Ireland
Interior of St Leonard's church, St... (C) Julian P Guffogg :: Geograph Britain and Ireland
accessdate: March 2, 2017Organ, St Leonard's Parish Church (C) Julian P Guffogg :: Geograph Ireland
para
accessdate: March 3, 2017 1953-61, St Leonards on Sea, United Kingdom. * Memorial Cenotaph, 1952, Hiroshima Peace Memorial Park,

Kenzō Tange was a Japanese architect, and winner of the 1987 Pritzker Prize for architecture. He was one of the most significant architects of the 20th century, combining traditional Japanese styles with modernism, and designed major buildings on five co ...

. *

Dorton Arena J. S. Dorton Arena is a 7,610-seat multi-purpose arena located in Raleigh, North Carolina, on the grounds of the North Carolina State Fair. It opened in 1952. Architect Maciej Nowicki of the North Carolina State University Department of Architec ...

1957,

Raleigh Raleigh (; ) is the capital city of the state of North Carolina and the seat of Wake County in the United States. It is the second-most populous city in North Carolina, after Charlotte. Raleigh is the tenth-most populous city in the Southeas ...

* St Mary's Star of the Sea Cathedral, 1958–62, Darwin, Australia, architect Ian Ferrier *

Toast Rack (building) The Toast Rack, or formerly known as the Hollings Building, is a Modernist building in Fallowfield, Manchester, England. The building was completed in 1960 as the Domestic Trades College, became part of Manchester Polytechnic then Manchester Metr ...

(originally Domestic Trades College, Manchester Polytechnic) 1960,

Fallowfield Fallowfield is a suburb of Manchester, England, with a population at the 2011 census of 15,211. Historically in Lancashire, it lies south of Manchester city centre and is bisected east–west by Wilmslow Road and north–south by Wil ...

, Manchester, United Kingdom, city architect,

Leonard Cecil Howitt Leonard Cecil Howitt (1896 – 1964) – often referred to as L. C. Howitt – served in both World Wars and was Manchester City Council's chief architect from 1946 until he retired in 1961. Life Leonard Howitt was born on 27 December 1896 in Isl ...

Theme Building The Theme Building is a structure at Los Angeles International Airport (LAX), considered an architectural example of the Space Age design style. Influenced by "Populuxe" architecture, it is an example of the Mid-century modern design movement ...

, 1961,

Los Angeles International Airport Los Angeles International Airport , commonly referred to as LAX (with each letter pronounced individually), is the primary international airport serving Los Angeles, California and its surrounding metropolitan area. LAX is located in the ...

, Pereira & Luckman Architects, Paul Williams and

Welton Becket Welton David Becket (August 8, 1902 – January 16, 1969) was an American modern architect who designed many buildings in Los Angeles, California. Biography Becket was born in Seattle, Washington and graduated from the University of Washin ...

* Priory Chapel, Saint Louis Abbey, 1962, Creve Coeur, St. Louis, Missouri, United States,

Hellmuth, Obata and Kassabaum HOK, formerly Hellmuth, Obata + Kassabaum and legally HOK Group, Inc., is an American design, architecture, engineering, and urban planning firm, founded in 1955. As of 2018, HOK is the largest U.S.-based architecture-engineering ...

(HOK), with

Pier Luigi Nervi Pier Luigi Nervi (21 June 1891 – 9 January 1979) was an Italian engineer and architect. He studied at the University of Bologna graduating in 1913. Nervi taught as a professor of engineering at Rome University from 1946 to 1961 and is known wor ...

Gateway Arch The Gateway Arch is a monument in St. Louis, Missouri, United States. Clad in stainless steel and built in the form of a weighted catenary arch, it is the world's tallest arch and Missouri's tallest accessible building. Some sources consider ...

, 1960-5,

St Louis St. Louis () is the second-largest city in Missouri, United States. It sits near the confluence of the Mississippi and the Missouri Rivers. In 2020, the city proper had a population of 301,578, while the bi-state metropolitan area, which e ...

, a tall freestanding catenary arch designed by

Eero Saarinen Eero Saarinen (, ; August 20, 1910 – September 1, 1961) was a Finnish-American architect and industrial designer noted for his wide-ranging array of designs for buildings and monuments. Saarinen is best known for designing the General Motors ...

* Allen Lambert Galleria, 1992,

Toronto Toronto ( ; or ) is the capital city of the Canadian province of Ontario. With a recorded population of 2,794,356 in 2021, it is the most populous city in Canada and the fourth most populous city in North America. The city is the anch ...

, Canada,

* L'Umbracle (catenary shade house)Jean McConochie photos at pbase.com
para
accessdate: March 3, 2017 2001, '' Ciutat de les Arts i les Ciències'' (City of Arts and Sciences),

Valencia Valencia ( va, València) is the capital of the autonomous community of Valencia and the third-most populated municipality in Spain, with 791,413 inhabitants. It is also the capital of the province of the same name. The wider urban area al ...

Spain , image_flag = Bandera de España.svg , image_coat = Escudo de España (mazonado).svg , national_motto = '' Plus ultra'' (Latin)(English: "Further Beyond") , national_anthem = (English: "Royal March") , ...

L'Oceanogràfic L'Oceanogràfic (; es, El Oceanográfico , "The Oceanographic") is an oceanarium situated on the dry Turia River bed to the southeast of the city center of Valencia, Spain, where different marine habitats are represented. It was designed by the ...

aquarium, 2003,

, Spain, Felix Candela. * Sheffield Winter Garden (catenary), 2003,

Sheffield Sheffield is a city in South Yorkshire, England, whose name derives from the River Sheaf which runs through it. The city serves as the administrative centre of the City of Sheffield. It is historically part of the West Riding of Yorkshire ...

, UK,

Pringle Richards Sharratt Pringle Richards Sharratt is an architectural firm that was formed in 1996 by John Pringle, Penny Richards and Ian Sharratt. Based in London, the practice has worked on public buildings, art galleries, museums, libraries, archives, university a ...

Architects and

Buro Happold Buro Happold (previously ''BuroHappold Engineering'') is a British professional services firm that provides engineering consultancy, design, planning, project management, and consulting services for buildings, infrastructure, and the environment ...

*Fjordenhus, 2018, Vejle Fjord, Denmark,

Olafur Eliasson Olafur Eliasson ( is, Ólafur Elíasson; born 5 February 1967) is an Icelandic–Danish artist known for sculptured and large-scale installation art employing elemental materials such as light, water, and air temperature to enhance the viewer's ...

and Sebastian Behmann

Bridges

Bridges have used a variety of arches since ancient times, sometimes in very flat

segmental arch A segmental arch is a type of arch with a circular arc of less than 180 degrees. It is sometimes also called a scheme arch. The segmental arch is one of the strongest arches because it is able to resist thrust. To prevent failure, a segmental ar ...

ed forms but rarely in the form of a parabola. A simple hanging rope bridge describes a catenary, but if they were in the form of a

suspension bridge A suspension bridge is a type of bridge in which the deck is hung below suspension cables on vertical suspenders. The first modern examples of this type of bridge were built in the early 1800s. Simple suspension bridges, which lack vertical ...

s they usually describe a parabola in shape, with the roadway hanging from the inverted arch. Modern suspension bridges were built from the early 19th century, beginning with chains and progressing to more and more elegant steel rope examples, and are still in use today. Parabolic arches that support the roadway from below (or in the form of a through arch) first appeared in the 1870s, and have been used occasionally ever since; examples include: *

Maria Pia Bridge The Maria Pia Bridge (in Portuguese ''Ponte de D. Maria Pia'', commonly known as ''Ponte de Dona Maria Pia'') is a railway bridge built in 1877, and attributed to Gustave Eiffel, situated over the Portuguese northern municipalities of Porto and V ...

Gustave Eiffel Alexandre Gustave Eiffel (born Bonickhausen dit Eiffel; ; ; 15 December 1832 – 27 December 1923) was a French civil engineer. A graduate of École Centrale des Arts et Manufactures, he made his name with various bridges for the French railway ...

and

Théophile Seyrig François Gustave Théophile Seyrig (19 February 1843 to 5 July 1923) was a German engineer, best known for designing bridges. On 6 October 1868, he founded ''Eiffel and Company'' with Gustave Eiffel. Seyrig contributed to the Eiffel and Company ...

Porto Porto or Oporto () is the second-largest city in Portugal, the capital of the Porto District, and one of the Iberian Peninsula's major urban areas. Porto city proper, which is the entire municipality of Porto, is small compared to its metropo ...

Portugal Portugal, officially the Portuguese Republic ( pt, República Portuguesa, links=yes ), is a country whose mainland is located on the Iberian Peninsula of Southwestern Europe, and whose territory also includes the Atlantic archipelagos of th ...

, a railway bridge built in 1877. *

Garabit viaduct The Garabit viaduct (french: viaduc de Garabit) is a railway arch bridge spanning the Truyère, near Ruynes-en-Margeride, Cantal, France, in the mountainous Massif Central region. The bridge was constructed between 1882 and 1884 by Gustave Eiffe ...

, near Ruynes-en-Margeride,

Cantal Cantal (; oc, Cantal or ) is a department in the Auvergne-Rhône-Alpes region of France, with its prefecture in Aurillac. Its other principal towns are Saint-Flour (the episcopal see) and Mauriac; its residents are known as Cantalians (fren ...

France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...

, designed by

, and built between 1882 and 1884. * Dell Bridge (footbridge),Alamy
para
accessdate: March 4, 2017 1894,

Port Sunlight Port Sunlight is a model village and suburb in the Metropolitan Borough of Wirral, Merseyside. It is located between Lower Bebington and New Ferry, on the Wirral Peninsula. Port Sunlight was built by Lever Brothers to accommodate workers in it ...

, Wirral, England. * Puente Nuevo,Gimeno and Gutierrez. pag.122 1903,

Murcia Murcia (, , ) is a city in south-eastern Spain, the capital and most populous city of the autonomous community of the Region of Murcia, and the seventh largest city in the country. It has a population of 460,349 inhabitants in 2021 (about one ...

, Spain, civil engineer José María Ortiz * Viaduc d'Austerlitz, 1903-4, Paris, engineers Louis Biette and

Fulgence Bienvenüe Fulgence Bienvenüe (; 27 January 1852 – 3 August 1936) was a noted French civil engineer, best known for his role in the construction of the Paris Métro, and has been called "Le Père du Métro" (Father of the Metro). A native of Uzel in Br ...

, architect Jean-Camille Formigé * 16th Street Bridge, 1905-10,

Washington DC ) , image_skyline = , image_caption = Clockwise from top left: the Washington Monument and Lincoln Memorial on the National Mall, United States Capitol, Logan Circle, Jefferson Memorial, White House, Adams Morgan, ...

, the first parabolic arched bridge in the US. *

Victoria Falls Bridge The Victoria Falls Bridge crosses the Zambezi River just below the Victoria Falls and is built over the Second Gorge of the falls. As the river forms the border between Zimbabwe and Zambia, the bridge links the two countries and has border post ...

,The Victoria Falls Bridge
To the Victoria Falls - The Victoria Falls Bridge
accessdate: March 2, 2017Livingstone News
central
accessdate: March 2, 2017Best Bridge Africa Victoria Falls Bridge

accessdate: March 2, 2017 1904-5,

Victoria Falls Victoria Falls ( Lozi: ''Mosi-oa-Tunya'', "The Smoke That Thunders"; Tonga: ''Shungu Namutitima'', "Boiling Water") is a waterfall on the Zambezi River in southern Africa, which provides habitat for several unique species of plants and anim ...

Zimbabwe Zimbabwe (), officially the Republic of Zimbabwe, is a landlocked country located in Southeast Africa, between the Zambezi and Limpopo Rivers, bordered by South Africa to the south, Botswana to the south-west, Zambia to the north, and ...

* Memorial Bridge,Arch Bridges on Waymarking.com
Memorial Bridge - Springfield/West Springfield, MA - Arch Bridges on Waymarking.com
accessdate: March 4, 2017 1920,

Springfield, Massachusetts Springfield is a city in the Commonwealth of Massachusetts, United States, and the seat of Hampden County. Springfield sits on the eastern bank of the Connecticut River near its confluence with three rivers: the western Westfield River, th ...

Tyne Bridge The Tyne Bridge is a through arch bridge over the River Tyne in North East England, linking Newcastle upon Tyne and Gateshead. The bridge was designed by the engineering firm Mott, Hay and Anderson, who later designed the Forth Road Bridge, ...

, 1928,

Newcastle upon Tyne Newcastle upon Tyne ( RP: , ), or simply Newcastle, is a city and metropolitan borough in Tyne and Wear, England. The city is located on the River Tyne's northern bank and forms the largest part of the Tyneside built-up area. Newcastle is ...

, UK. *

Cape Creek Bridge Cape Creek Bridge is an arch bridge that spans Cape Creek in Lane County, Oregon, United States. The bridge carries U.S. Route 101. Opened in 1932, it was designed by noted bridge engineer Conde McCullough and built of reinforced concrete by John ...

, 1931,

Lane County, Oregon Lane County is one of the 36 counties in the U.S. state of Oregon. As of the 2020 census, the population was 382,971, making it the fourth-most populous county in Oregon. The county seat is Eugene. It is named in honor of Joseph Lane, Ore ...

, United States, engineer

Conde McCullough Conde Balcom McCullough (May 30, 1887 – May 6, 1946) was an American civil engineer who is primarily known for designing many of Oregon's coastal bridges on U.S. Route 101. The native of South Dakota worked for the Oregon Department of Tr ...

Bayonne Bridge Bayonne Bridge is an arch bridge spanning the Kill Van Kull and connecting Bayonne, New Jersey with Staten Island in New York City. It carries New York State Route 440 (NY 440) and New Jersey Route 440. It is the sixth-longes ...

,The New York Times
parab
accessdate: March 3, 2017 1931,

Bayonne, New Jersey Bayonne ( ) is a city in Hudson County, New Jersey, United States. Located in the Gateway Region, Bayonne is situated on a peninsula located between Newark Bay to the west, the Kill Van Kull to the south, and New York Bay to the east. As ...

Othmar Ammann Othmar Hermann Ammann (March 26, 1879 – September 22, 1965) was a Swiss-American civil engineer whose bridge designs include the George Washington Bridge, Verrazzano-Narrows Bridge, and Bayonne Bridge. He also directed the planning and constru ...

and

architect An architect is a person who plans, designs and oversees the construction of buildings. To practice architecture means to provide services in connection with the design of buildings and the space within the site surrounding the buildings that h ...

Cass Gilbert Cass Gilbert (November 24, 1859 – May 17, 1934) was an American architect. An early proponent of skyscrapers, his works include the Woolworth Building, the United States Supreme Court building, the state capitols of Minnesota, Arkansas and ...

Bixby Creek Bridge Bixby Creek Bridge, also known as Bixby Canyon Bridge, on the Big Sur coast of California, is one of the most photographed bridges in California due to its aesthetic design, "graceful architecture and magnificent setting". It is a reinforced con ...

,Bixby Creek Bridge on Highway One from the Pat Hathaway Photo Collection
Bixby Creek Bridge on Highway One from the Pat Hathaway Photo Collection
accessdate: March 6, 2017 1931-2,

Big Sur Big Sur () is a rugged and mountainous section of the Central Coast of California between Carmel and San Simeon, where the Santa Lucia Mountains rise abruptly from the Pacific Ocean. It is frequently praised for its dramatic scenery. Big Sur ...

, California, highway engineer C. H. Purcell and engineer F. W. Panhorst * Balclutha Road Bridge,Heritage New Zealand
www.heritage.org.nz/the-list/details/5180
accessdate: March 3, 2017 1933-35, Balclutha,

South Otago South Otago lies in the south east of the South Island of New Zealand. As the name suggests, it forms the southernmost part of the geographical region of Otago. The exact definition of the area designated as South Otago is imprecise, as the area is ...

, New Zealand *

Juscelino Kubitschek Bridge Juscelino Kubitschek Bridge ( pt, Ponte Juscelino Kubitschek), commonly called Ponte JK ( en, JK Bridge), is a steel and concrete arch bridge across Lake Paranoá in Brasília, Brazil. It connects the eastern shore of the lake – where Lago Sul ...

, 2002, Brasilia, Brazil,

Alexandre Chan Alexandre Chan (born ) is a Brazilian architect best known for designing the President Juscelino Kubitschek Bridge in Brasília, Brazil with structural engineer Mario Vila Verde, and the Ponte do Saber, Bridge of Knowledge in Rio de Janeiro. He has ...

and structural engineer Mário Vila Verde

References

External links

On why suspension bridges are parabolic

Many parabolic arches

On a variety of curves, parabolas, catenaries, hyperbolas, and ellipses

YouTube video

Another Youtube video

Bibliography

* {{clear Parabolas Arches and vaults Architectural history Catholic architecture