elliptical dome

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| 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'}}.

Both {{mvar|-a}} and {{mvar|a}} are points of the x-axis and {{mvar|-b}} and {{mvar|b}} are points on the y-axis

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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.{{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 }}

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".{{Cite web |title=Polyhedral structures that approximate an ellipsoid |url=https://patents.google.com/patent/US4825602A/en}}

Elliptical domes come up in the design of all of the following:

• A number of mosques in Cairo, Egypt,
• Part of St. Peter's Basilica, in Rome, Italy{{Cite web |title=The Engineering Behind Saint Peter's Basilica |url=http://engineeringrome.org/the-engineering-behind-saint-peters-basilica/}}
• 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,{{Cite web |last=Kobielak |first=Sylwester |date=November 27, 2016 |title=Oval concrete domes |url=https://coek.info/queue/pdf-oval-concrete-domes-.html}}
• 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.

{{portal|Architecture}}

• Pendentive
• Beehive house
• Beehive tomb
• Catenary arch
• Clochán
• Ellipsoid
• Onion dome
• Parabolic arch

{{Reflist}}

• [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]

• [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]

• [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