Editing Reuleaux triangle (section)

=== Architecture ===
[[File:Reuleaux triangle shaped window of Onze-Lieve-Vrouwekerk, Bruges.jpg|thumb|Reuleaux triangle shaped window of the [[Church of Our Lady, Bruges]] in Belgium]]
In [[Gothic architecture]], beginning in the late 13th century or early 14th century,<ref name="mcwte">{{citation|url=https://books.google.com/books?id=SY7aHx8KwK0C&pg=PA63|pages=63–64|title=Medieval Church Window Tracery in England|first=Stephen|last=Hart|publisher=Boydell & Brewer Ltd|year=2010|isbn=978-1-84383-533-2}}.</ref> the Reuleaux triangle became one of several curvilinear forms frequently used for windows, window [[tracery]], and other architectural decorations.<ref name="icons" /> For instance, in [[English Gothic architecture]], this shape was associated with the decorated period, both in its geometric style of 1250–1290 and continuing into its curvilinear style of 1290–1350.<ref name="mcwte" /> It also appears in some of the windows of the [[Milan Cathedral]].<ref>{{citation|last1=Marchetti|first1=Elena|last2=Costa|first2=Luisa Rossi|editor1-last=Williams|editor1-first=Kim|editor2-link=Kim Williams (architect)|editor2-last=Ostwald|editor2-first=Michael J.|contribution=What geometries in Milan Cathedral?|doi=10.1007/978-3-319-00137-1_35|pages=509–534|publisher=Birkhäuser|title=Architecture and Mathematics from Antiquity to the Future, Volume I: Antiquity to the 1500s|year=2014|isbn=978-3-319-00136-4 }}</ref> In this context, the shape is sometimes called a ''spherical triangle'',<ref name="mcwte" /><ref>{{citation|title= A glossary of terms used in Grecian, Roman, Italian, and Gothic architecture|volume=1|first=John Henry|last=Parker|edition=5th|year=1850|page=202|url=https://books.google.com/books?id=uXtZAAAAYAAJ&pg=PA202|location=London|publisher=David Rogue}}.</ref><ref>{{citation|title=Practical plane geometry|first=E. S.|last=Burchett|year=1876|at=Caption to Plate LV, Fig. 6|url=https://books.google.com/books?id=oDcDAAAAQAAJ&pg=RA1-PA94|location=London and Glasgow|publisher=William Collins, Sons, and Co.}}.</ref> which should not be confused with [[spherical triangle]] meaning a triangle on the surface of a [[sphere]]. In its use in Gothic church architecture, the three-cornered shape of the Reuleaux triangle may be seen both as a symbol of the [[Trinity]],<ref>{{citation|title=The Symbolism of Churches and Church Ornaments: A Translation of the First Book of the Rationale Divinorum Officiorum|first=Guillaume|last=Durand|edition=3rd|publisher=Gibbings|year=1906|url=https://books.google.com/books?id=vRknpENyAlQC&pg=PR88|page=lxxxviii}}.</ref> and as "an act of opposition to the form of the circle".<ref>{{citation|title=Gothic Architecture|volume=19|series=Pelican history of art|first1=Paul|last1=Frankl|first2=Paul|last2=Crossley|publisher=Yale University Press|year=2000|isbn=978-0-300-08799-4|page=146|url=https://books.google.com/books?id=LBZ6781vvOwC&pg=PA146}}.</ref>

The Reuleaux triangle has also been used in other styles of architecture. For instance, [[Leonardo da Vinci]] sketched this shape as the plan for a fortification.<ref name="moon241">{{harvtxt|Moon|2007|page=241}}.</ref> Modern buildings that have been claimed to use a Reuleaux triangle shaped floorplan include the [[Kresge Auditorium|MIT Kresge Auditorium]], the [[Kölntriangle]], the [[Donauturm]], the [[Torre de Collserola]], and the [[Mercedes-Benz Museum]].<ref name=conti/> However in many cases these are merely rounded triangles, with different geometry than the Reuleaux triangle.