Editing Isosceles triangle (section)

==Applications==
===In architecture and design===
{{multiple image
|total_width=480
|image1=Pantheon Rome exterior 2015.JPG
|caption1=Obtuse isosceles pediment of the [[Pantheon, Rome]]
|image2=Cathédrale Notre-Dame - Portail du transept sud, dit portail Saint-Etienne, Gables, côté droit - Paris 04 - Médiathèque de l'architecture et du patrimoine - APMH00021092.jpg
|caption2=Acute isosceles gable over the Saint-Etienne portal, [[Notre-Dame de Paris]]
}}
Isosceles triangles commonly appear in [[architecture]] as the shapes of [[gable]]s and [[pediment]]s. In [[ancient Greek architecture]] and its later imitations, the obtuse isosceles triangle was used; in [[Gothic architecture]] this was replaced by the acute isosceles triangle.{{sfnp|Lardner|1840|page=46}}

In the [[Medieval architecture|architecture of the Middle Ages]], another isosceles triangle shape became popular: the Egyptian isosceles triangle. This is an isosceles triangle that is acute, but less so than the equilateral triangle; its height is proportional to 5/8 of its base.{{sfnp|Lavedan|1947}} The Egyptian isosceles triangle was brought back into use in modern architecture by Dutch architect [[Hendrik Petrus Berlage]].{{sfnp|Padovan|2002}}

[[File: DETAIL VIEW OF MODIFIED WARREN TRUSS WITH VERTICALS. - Union Station Viaduct, Spanning Gaspee, Francis, Promenade and Canal Streets, Providence, Providence County, RI HAER RI,4-PROV,179-12.tif|thumb|Detailed view of a modified [[Warren truss]] with verticals]]
[[Warren truss]] structures, such as bridges, are commonly arranged in isosceles triangles, although sometimes vertical beams are also included for additional strength.{{sfnp|Ketchum|1920}}
Surfaces [[tessellation|tessellated]] by obtuse isosceles triangles can be used to form [[deployable structure]]s that have two stable states: an unfolded state in which the surface expands to a cylindrical column, and a folded state in which it folds into a more compact prism shape that can be more easily transported.{{sfnp|Pellegrino|2002}} The same tessellation pattern forms the basis of [[Yoshimura buckling]], a pattern formed when cylindrical surfaces are axially compressed,{{sfnp|Yoshimura|1955}} and of the [[Schwarz lantern]], an example used in mathematics to show that the area of a smooth surface cannot always be accurately approximated by polyhedra converging to the surface.{{sfnp|Schwarz|1890}}

{{multiple image
|total_width=360
|image1=Flag of Guyana.svg
|caption1=[[Flag of Guyana]]
|image2=Flag of Saint Lucia.svg
|caption2=[[Flag of Saint Lucia]]
}}
In [[graphic design]] and the [[decorative arts]], isosceles triangles have been a frequent design element in cultures around the world from at least the [[Early Neolithic]]{{sfnp|Washburn|1984}} to modern times.{{sfnp|Jakway|1922}} They are a common design element in [[flag]]s and [[heraldry]], appearing prominently with a vertical base, for instance, in the [[flag of Guyana]], or with a horizontal base in the [[flag of Saint Lucia]], where they form a stylized image of a mountain island.{{sfnp|Smith|2014}}

They also have been used in designs with religious or mystic significance, for instance in the [[Sri Yantra]] of [[Tantra|Hindu meditational practice]].{{sfnp|Bolton|Nicol|Macleod|1977}}

===In other areas of mathematics===
If a [[cubic equation]] with real coefficients has three roots that are not all [[real number]]s, then when these roots are plotted in the [[complex plane]] as an [[Argand diagram]] they form vertices of an isosceles triangle whose axis of symmetry coincides with the horizontal (real) axis. This is because the complex roots are [[complex conjugate]]s and hence are symmetric about the real axis.{{sfnp|Bardell|2016}}

In [[celestial mechanics]], the [[three-body problem]] has been studied in the special case that the three bodies form an isosceles triangle, because assuming that the bodies are arranged in this way reduces the number of [[degrees of freedom]] of the system without reducing it to the solved [[Lagrangian point]] case when the bodies form an equilateral triangle. The first instances of the three-body problem shown to have unbounded oscillations were in the isosceles three-body problem.{{sfnp|Diacu|Holmes|1999}}