Editing Reuleaux triangle (section)

=== As a counterexample ===
Reuleaux's original motivation for studying the Reuleaux triangle was as a counterexample, showing that three single-point contacts may not be enough to fix a planar object into a single position.<ref>{{harvtxt|Moon|2007}}, [https://books.google.com/books?id=lw7lN8JibZsC&pg=PA239 p.&nbsp;239].</ref> The existence of Reuleaux triangles and other curves of constant width shows that diameter measurements alone cannot verify that an object has a circular cross-section.<ref>{{citation
 | last1 = Granovsky | first1 = V. A.
 | last2 = Siraya | first2 = T. N.
 | editor1-last = Pavese | editor1-first = F.
 | editor2-last = Bär | editor2-first = M.
 | editor3-last = Filtz | editor3-first = J.-R.
 | editor4-last = Forbes | editor4-first = A. B.
 | editor5-last = Pendrill | editor5-first = L.
 | editor6-last = Shirono | editor6-first = K.
 | contribution = Metrological traceability and quality of industrial tests measurements
 | pages = 194–201
 | publisher = World Scientific
 | title = Advanced Mathematical and Computational Tools in Metrology and Testing IX}}. See in particular [https://books.google.com/books?id=2dwn4M7IEWUC&pg=PA200 p.&nbsp;200].</ref>

In connection with the [[inscribed square problem]], {{harvtxt|Eggleston|1958}} observed that the Reuleaux triangle provides an example of a constant-width shape in which no regular polygon with more than four sides can be inscribed, except the regular hexagon, and he described a small modification to this shape that preserves its constant width but also prevents regular hexagons from being inscribed in it. He generalized this result to three dimensions using a cylinder with the same shape as its [[Cross section (geometry)|cross section]].<ref>{{citation
 | last = Eggleston | first = H. G.
 | doi = 10.2307/2308878
 | journal = [[American Mathematical Monthly]]
 | mr = 0097768
 | pages = 76–80
 | title = Figures inscribed in convex sets
 | volume = 65
 | issue = 2
 | year = 1958| jstor = 2308878
 }}.</ref>