{{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, in Modena, Italy]]
An '''elliptical dome''', or an ''oval dome'', is a dome whose bottom cross-section takes the form of an 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'' has a circular cross-section, so is not quite the same.
While the cupola can take different geometries, 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 of the floor's ellipse can have one whisper, and the other hears; this is a whispering gallery.
The largest elliptical dome in the world is at the Sanctuary of Vicoforte in Vicoforte, 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 and {{mvar|-b}} and {{mvar|b}} are points on the y-axis }}
Elliptical domes have many applications in architecture; and are useful in covering rectangular spaces. The oblate, or horizontal elliptical dome is useful when there is a need to limit height of the space that would result from a spherical dome. As the 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 with a circular base, the triangular elements align so their edges form great circles. Although not geodesic, a new, elliptical design was patented in 1989; it uses hexagons and pentagons to form a dome with a cross section that is elliptical. Due to its mathematical derivation, this design is called "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 in Cairo, Egypt,<ref name="Domes in the Islamic Architecture of Cairo City: A Mathematical Approach" /> * Part of St. Peter's Basilica, in Rome, 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, in Asheville, North Carolina, * The Church of Saint Roch, Žižkov, in Prague, Czech Republic, * The Four Domes Pavilion, in Wroclaw, Poland, * The Indiana Theatre, in Indiana, city of Indianapolis, * The Joe and Rika Mansueto Library, at the University of Chicago, * The Kanteerava Indoor Stadium, in Bangalore, 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, in Washington, DC, * The Mosque–Cathedral of Córdoba, in Andalusia, * The Palau Nacional, in Barcelona, Spain, * The Pisa Cathedral, in Pisa, Italy, * The Rose Hill Mansion, Bluffton, in Bluffton, South Carolina, * The San Filippo Neri, in Turin, region of Piedmont, Italy, * The Sant'Andrea in Via Flaminia, in Rome, Italy, * The Santa Caterina, Casale Monferrato, in Casale Monferrato, Province of Alessandria, region of Piedmont, Italy, * The Seville Cathedral, Spain, * The Skyspace Lech, Tannegg/Oberlech in Vorarlberg, the westernmost federal state of Austria, * The State Savings Bank Building, in City of Sydney, Australia, * The Temple Sinai, in Oakland, California, * The Sanctuary of Vicoforte, in Italy, * BAPS Swaminarayan Akshardham (New Jersey), in Robbinsville, New Jersey.
==See also== {{portal|Architecture}} * Pendentive * Beehive house * Beehive tomb * Catenary arch * Clochán * Ellipsoid * Onion dome * 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