Editing Reuleaux triangle (section)

=== Other objects ===
[[File:V-Pick Psychos.JPG|thumb|Reuleaux triangle shaped [[guitar pick]]s]]
Many [[guitar pick]]s employ the Reuleaux triangle, as its shape combines a sharp point to provide strong articulation, with a wide tip to produce a warm timbre. Because all three points of the shape are usable, it is easier to orient and wears less quickly compared to a pick with a single tip.<ref name="picks">{{citation|last=Hoover|first=Will|date=November 1995|title= Picks!: The Colorful Saga of Vintage Celluloid Guitar Plectrums|pages=32–33|publisher=Backbeat Books|isbn=978-0-87930-377-8}}.</ref>

{{multiple image|total_width=420|image1=Philadelphia fire hydrant.jpg|image2=Tux Hydrant.jpg|footer=Illicit use of a fire hydrant, Philadelphia, 1996, and a newer Philadelphia hydrant with a Reuleaux triangle shaped nut to prevent such use.}}
The Reuleaux triangle has been used as the shape for the cross section of a [[fire hydrant]] valve nut. The constant width of this shape makes it difficult to open the fire hydrant using standard parallel-jawed wrenches; instead, a wrench with a special shape is needed. This property allows the fire hydrants to be opened only by firefighters (who have the special wrench) and not by other people trying to use the hydrant as a source of water for other activities.<ref>{{citation
 | last1 = Martini | first1 = Horst
 | last2 = Montejano | first2 = Luis
 | last3 = Oliveros | first3 = Déborah | author3-link = Déborah Oliveros
 | doi = 10.1007/978-3-030-03868-7
 | isbn = 978-3-030-03866-3
 | mr = 3930585
 | page = 3
 | publisher = Birkhäuser
 | title = Bodies of Constant Width: An Introduction to Convex Geometry with Applications
 | year = 2019| s2cid = 127264210
 }}</ref>

[[File:Smithsonian Submillimeter Array.jpg|thumb|The [[Submillimeter Array]], with seven of its eight antennae arranged on an approximate Reuleaux triangle]]
Following a suggestion of {{harvtxt|Keto|1997}},<ref name="keto">{{citation
 | last = Keto | first = Eric
 | bibcode = 1997ApJ...475..843K
 | doi = 10.1086/303545
 | issue = 2
 | journal = [[The Astrophysical Journal]]
 | pages = 843–852
 | title = The shapes of cross-correlation interferometers
 | volume = 475
 | year = 1997| doi-access = free
 }}.</ref> the antennae of the [[Submillimeter Array]], a radio-wave astronomical observatory on [[Mauna Kea]] in [[Hawaii]], are arranged on four nested Reuleaux triangles.<ref name="blundell">{{citation
 | last = Blundell | first = Raymond
 | contribution = The submillimeter array
 | contribution-url = https://www.cfa.harvard.edu/sma/general/IEEE.pdf
 | doi = 10.1109/mwsym.2007.380132
 | title = Proc. 2007 IEEE/MTT-S International Microwave Symposium
 | pages = 1857–1860
 | year = 2007| isbn = 978-1-4244-0687-6
 | s2cid = 41312640
 }}.</ref><ref name="hml04">{{citation
 | last1 = Ho | first1 = Paul T. P.
 | last2 = Moran | first2 = James M.
 | last3 = Lo | first3 = Kwok Yung
 | bibcode = 2004ApJ...616L...1H
 | doi = 10.1086/423245
 | issue = 1
 | journal = [[The Astrophysical Journal]]
 | pages = L1–L6
 | title = The submillimeter array
 | volume = 616
 | year = 2004| arxiv = astro-ph/0406352| s2cid = 115133614
 }}.</ref> Placing the antennae on a curve of constant width causes the observatory to have the same spatial resolution in all directions, and provides a circular observation beam. As the most asymmetric curve of constant width, the Reuleaux triangle leads to the most uniform coverage of the plane for the [[Fourier transform]] of the signal from the array.<ref name="keto"/><ref name="hml04"/> The antennae may be moved from one Reuleaux triangle to another for different observations, according to the desired angular resolution of each observation.<ref name="blundell"/><ref name="hml04"/> The precise placement of the antennae on these Reuleaux triangles was optimized using a [[neural network]]. In some places the constructed observatory departs from the preferred Reuleaux triangle shape because that shape was not possible within the given site.<ref name="hml04"/>