# Elliptical dome

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{{short description|Dome who bottom cross section takes the form of an ellipse}}
[[File:Modena San Domenico cupola ellittica.JPG|right|thumb|300px|An elliptical dome at the [San Domenico, Modena](/source/San_Domenico%2C_Modena), in [Modena](/source/Modena), [Italy](/source/Italy)]]

An '''elliptical dome''', or an ''oval dome'', is a [dome](/source/dome) whose bottom [cross-section](/source/Cross_section_(geometry)) takes the form of an [ellipse](/source/ellipse).<ref name="Behaviour of Masonry Vaults and Domes: Geometrical Considerations ">{{Cite web |last=Arun |first=G |date=2006 |title=Behaviour of Masonry Vaults and Domes: Geometrical Considerations |url=http://www.hms.civil.uminho.pt/sahc/2006/0299.pdf |website=Structural Analysis of Historical Constructions, New Delhi |access-date=2020-12-04 |archive-date=2020-10-23 |archive-url=https://web.archive.org/web/20201023114302/http://www.hms.civil.uminho.pt/sahc/2006/0299.pdf |url-status=dead }}</ref> Technically, an ''[ellipsoidal dome](/source/ellipsoidal_dome)'' has a circular cross-section, so is not quite the same.

While the [cupola](/source/cupola) can take different [geometries](/source/Geometric_shape), when the ceiling's cross-section takes the form of an ellipse, and due to the reflecting properties of an ellipse, any two persons standing at a [focus](/source/Focus_(geometry)) of the floor's ellipse can have one whisper, and the other hears; this is a [whispering gallery](/source/whispering_gallery).

The largest elliptical dome in the world is at the [Sanctuary of Vicoforte](/source/Sanctuary_of_Vicoforte) in [Vicoforte](/source/Vicoforte), [Italy](/source/Italy).<ref name="Visiting the largest elliptical dome in the world, in Vicoforte">{{Cite web |title=Visiting the largest elliptical dome in the world, in Vicoforte |url=https://www.italyrivieralps.com/2016/04/25/read-more/argomenti/video/articolo/visiting-the-largest-elliptical-dome-in-the-world-in-vicoforte.html |access-date=2020-12-04 |website=ItalyRiveirAlps|date=25 April 2016 }}</ref><ref name="Modeling Strategies for the World">{{Cite journal |last=Chiorino |first=Mario Alberto |title=Modeling Strategies for the World's Largest Elliptical Dome at Vicoforte |url=https://www.tandfonline.com/doi/abs/10.1080/15583050802063618?mobileUi=0&journalCode=uarc20 |journal=International Journal of Architectural Heritage|year=2008 |volume=2 |issue=3 |pages=274–303 |doi=10.1080/15583050802063618 |s2cid=109078429 |url-access=subscription }}</ref><ref name="Structural characteristics of the elliptical masonrydome of the sanctuary of Vicoforte">{{Cite web |last=Aoki |first=Takayoshi |title=Structural characteristics of the elliptical masonrydome of the sanctuary of Vicoforte |url=https://www.researchgate.net/publication/247658003}}</ref>

==In architecture==

{{multiple image
   | align     = left 
   | direction = vertical
   | width     = 375
   | footer    = 
   | image1    = A circle, and an ellipse.png
   | alt1      = A blue circle, graphed with a red ellipse
   | caption1  = A blue circle, graphed with a red ellipse. An elliptical dome has an elliptical base, and an ellipsoidal dome has a circular base.
   | image2    = Ellipse jjm.png
   | alt2      = Wispering gallery property of ellipses
   | caption2  = An ellipse, the "reflecting," "whispering gallery" property of the foci {{mvar|F}} and {{mvar|F'}} illustrated: The distance from {{mvar|F}} to {{mvar|F'}} may be great, but a  whisperer at {{mvar|F}} can be heard, as {{mvar|F'}}. <br><br>Both {{mvar|-a}} and {{mvar|a}} are points of the [x-axis](/source/x-axis) and {{mvar|-b}} and {{mvar|b}} are points on the [y-axis](/source/y-axis)
}}

Elliptical domes have many applications in [architecture](/source/architecture); and are useful in covering [rectangular spaces](/source/rectangular_spaces). The [oblate](/source/Spheroid), or horizontal elliptical dome is useful when there is a need to limit height of the space that would result from a [spherical dome](/source/spherical_dome). As the [mathematical](/source/mathematical) description of an elliptical dome is more complex than that of spherical dome, design care is needed.<ref name="Domes in the Islamic Architecture of Cairo City: A Mathematical Approach">{{Cite journal |last=Elkhateeb |first=Ahmed Ali |title=Domes in the Islamic Architecture of Cairo City: A Mathematical Approach |url=https://link.springer.com/content/pdf/10.1007/s00004-011-0103-3.pdf |journal=Nexus Network Journal|year=2012 |volume=14 |pages=151–176 |doi=10.1007/s00004-011-0103-3 |s2cid=119996869 }}</ref>

In a [geodesic dome](/source/geodesic_dome) with a circular base, the triangular elements align so their edges form [great circles](/source/great_circles). Although not geodesic, a new, elliptical design was patented in 1989; it uses [hexagons](/source/hexagons) and [pentagons](/source/pentagons) to form a dome with a cross section that is elliptical. Due to its mathematical derivation, this design is called "[geotangent](/source/geotangent)".<ref name="Polyhedral structures that approximate an ellipsoid">{{Cite web |title=Polyhedral structures that approximate an ellipsoid |url=https://patents.google.com/patent/US4825602A/en}}</ref>

==World examples==

Elliptical domes come up in the design of all of the following:
* A number of [mosques](/source/mosques) in [Cairo, Egypt](/source/Cairo%2C_Egypt),<ref name="Domes in the Islamic Architecture of Cairo City: A Mathematical Approach" />
* Part of [St. Peter's Basilica](/source/St._Peter's_Basilica), in [Rome](/source/Rome), [Italy](/source/Italy)<ref name="The Engineering Behind Saint Peter’s Basilica">{{Cite web |title=The Engineering Behind Saint Peter's Basilica |url=http://engineeringrome.org/the-engineering-behind-saint-peters-basilica/}}</ref>
* The [Basilica of St. Lawrence, Asheville](/source/Basilica_of_St._Lawrence%2C_Asheville), in [Asheville](/source/Asheville%2C_North_Carolina), [North Carolina](/source/North_Carolina),
* The [Church of Saint Roch, Žižkov](/source/Church_of_Saint_Roch%2C_%C5%BDi%C5%BEkov), in [Prague](/source/Prague), [Czech Republic](/source/Czech_Republic),
* The [Four Domes Pavilion](/source/Four_Domes_Pavilion_(Wroclaw)), in [Wroclaw, Poland](/source/Wroclaw%2C_Poland),
* The [Indiana Theatre](/source/Indiana_Theatre_(Indianapolis)), in [Indiana](/source/Indiana), city of [Indianapolis](/source/Indianapolis),
* The [Joe and Rika Mansueto Library](/source/Joe_and_Rika_Mansueto_Library), at the [University of Chicago](/source/University_of_Chicago),
* The [Kanteerava Indoor Stadium](/source/Kanteerava_Indoor_Stadium), in [Bangalore, India](/source/Bangalore%2C_India),<ref name="Oval concrete domes">{{Cite web |last=Kobielak |first=Sylwester |date=November 27, 2016 |title=Oval concrete domes |url=https://coek.info/queue/pdf-oval-concrete-domes-.html}}</ref>
* The [Mayflower Hotel](/source/Mayflower_Hotel), in [Washington, DC](/source/Washington%2C_DC),
* The [Mosque–Cathedral of Córdoba](/source/Mosque%E2%80%93Cathedral_of_C%C3%B3rdoba), in [Andalusia](/source/Andalusia),
* The [Palau Nacional](/source/Palau_Nacional), in [Barcelona](/source/Barcelona), [Spain](/source/Spain),
* The [Pisa Cathedral](/source/Pisa_Cathedral), in [Pisa, Italy](/source/Pisa%2C_Italy),
* The [Rose Hill Mansion, Bluffton](/source/Rose_Hill_Mansion%2C_Bluffton), in [Bluffton, South Carolina](/source/Bluffton%2C_South_Carolina),
* The [San Filippo Neri](/source/San_Filippo_Neri%2C_Turin), in [Turin](/source/Turin), region of [Piedmont](/source/Piedmont), Italy,
* The [Sant'Andrea in Via Flaminia](/source/Sant'Andrea_in_Via_Flaminia), in [Rome, Italy](/source/Rome%2C_Italy),
* The [Santa Caterina, Casale Monferrato](/source/Santa_Caterina%2C_Casale_Monferrato), in [Casale Monferrato](/source/Casale_Monferrato), [Province of Alessandria](/source/Province_of_Alessandria), region of [Piedmont](/source/Piedmont), Italy,
* The [Seville Cathedral](/source/Seville_Cathedral), Spain,
* The [Skyspace Lech](/source/Skyspace_Lech), Tannegg/[Oberlech](/source/Lech_(Vorarlberg)) in [Vorarlberg](/source/Vorarlberg), the westernmost federal state of [Austria](/source/Austria),
* The [State Savings Bank Building](/source/State_Savings_Bank_Building), in [City of Sydney](/source/City_of_Sydney), [Australia](/source/Australia),
* The [Temple Sinai](/source/Temple_Sinai_(Oakland%2C_California)), in [Oakland, California](/source/Oakland%2C_California), 
* The [Sanctuary of Vicoforte](/source/Sanctuary_of_Vicoforte), in Italy,
* BAPS [Swaminarayan Akshardham (New Jersey)](/source/Swaminarayan_Akshardham_(New_Jersey)), in Robbinsville, New Jersey.

==See also==
{{portal|Architecture}}
* [Pendentive](/source/Pendentive)
* [Beehive house](/source/Beehive_house)
* [Beehive tomb](/source/Beehive_tomb)
* [Catenary arch](/source/Catenary_arch)
* [Clochán](/source/Cloch%C3%A1n)
* [Ellipsoid](/source/Ellipsoid)
* [Onion dome](/source/Onion_dome)
* [Parabolic arch](/source/Parabolic_arch)

==References==
{{Reflist}}

==External links and references==

===Creating elliptical domes===
* [https://geo-dome.co.uk/article.asp?uname=elliptcal_domes Elliptical domes site]
* [https://help.solidworks.com/2020/English/SolidWorks/sldworks/c_example_elliptical_dome.htm Creating an elliptical dome]
* [https://help.solidworks.com/2018/english/SolidWorks/sldworks/HIDD_DVE_FEAT_DOME.htm Another reference, on creating ellitpical domes]

===Calculations===
* [https://www.monolithic.org/static/calcs/advanced.html Site for calculating figures related to elliptical domes]
* [https://www.monolithic.org/calculators/advanced-dome-calculator Another site for calculations]
* [https://www.monolithic.org/calculators/dome-calculator Dome calculator]

===More general references===
* [https://asmedigitalcollection.asme.org/pressurevesseltech/article-abstract/130/1/011210/475723/Buckling-of-Externally-Pressurized-Prolate?redirectedFrom=fulltext Buckling of Externally Pressurized Prolate Ellipsoidal Domes]
* [http://www.hms.civil.uminho.pt/sahc/2006/0299.pdf An article addressing many topics, including elliptical domes] {{Webarchive|url=https://web.archive.org/web/20201023114302/http://www.hms.civil.uminho.pt/sahc/2006/0299.pdf |date=2020-10-23 }}
* [https://link.springer.com/content/pdf/10.1007/s00004-011-0103-3.pdf Use of elliptical domes, notably in Islamic architecture]

Category:Domes
Category:Architectural elements
Category:Ellipses

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Adapted from the Wikipedia article [Elliptical dome](https://en.wikipedia.org/wiki/Elliptical_dome) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Elliptical_dome?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.