Editing Reuleaux triangle (section)

=== Reuleaux polygons ===
{{main|Reuleaux polygon}}
{{multiple image|total_width=360|image1=Reuleaux polygons.svg|caption1=Reuleaux polygons|image2=Gambia 1 dalasi.JPG|caption2=[[Gambian dalasi]] Reuleaux [[heptagon]] coin}}
The Reuleaux triangle can be generalized to regular or irregular polygons with an odd number of sides, yielding a [[Reuleaux polygon]], a curve of constant width formed from circular arcs of constant radius. The constant width of these shapes allows their use as coins that can be used in coin-operated machines.<ref name="gardner" /> Although coins of this type in general circulation usually have more than three sides, a Reuleaux triangle has been used for a commemorative coin from [[Bermuda]].<ref name=conti>{{citation|last1=Conti|first1=Giuseppe|last2=Paoletti|first2=Raffaella|editor1-last=Magnaghi-Delfino|editor1-first=Paola|editor2-last=Mele|editor2-first=Giampiero|editor3-last=Norando|editor3-first=Tullia|contribution=Reuleaux triangle in architecture and applications|date=October 2019|doi=10.1007/978-3-030-29796-1_7|pages=79–89|publisher=Springer|series=Lecture Notes in Networks and Systems|title=Faces of Geometry: From Agnesi to Mirzakhani|volume=88 |isbn=978-3-030-29795-4 |s2cid=209976466}}</ref>

Similar methods can be used to enclose an arbitrary [[simple polygon]] within a curve of constant width, whose width equals the diameter of the given polygon. The resulting shape consists of circular arcs (at most as many as sides of the polygon), can be constructed algorithmically in [[linear time]], and can be drawn with compass and straightedge.<ref>{{citation
 | last1 = Chandru | first1 = V.
 | last2 = Venkataraman | first2 = R.
 | contribution = Circular hulls and orbiforms of simple polygons
 | contribution-url = http://dl.acm.org/citation.cfm?id=127787.127863
 | isbn = 978-0-89791-376-8
 | location = Philadelphia, PA, USA
 | pages = 433–440
 | publisher = Society for Industrial and Applied Mathematics
 | title = Proceedings of the Second Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '91)
 | year = 1991}}.</ref> Although the Reuleaux polygons all have an odd number of circular-arc sides, it is possible to construct constant-width shapes with an even number of circular-arc sides of varying radii.<ref>{{citation
 | last = Peterson | first = Bruce B.
 | journal = Illinois Journal of Mathematics
 | mr = 0320885
 | pages = 411–420
 | title = Intersection properties of curves of constant width
 | url = http://projecteuclid.org/euclid.ijm/1256051608
 | volume = 17
 | issue = 3
 | year = 1973| doi = 10.1215/ijm/1256051608
 | doi-access = free
 }}.</ref>