Editing Catenary (section)

===Relation to other curves===
When a [[parabola]] is rolled along a straight line, the [[roulette (curve)|roulette]] curve traced by its [[Conic section#Eccentricity, focus and directrix|focus]] is a catenary.<ref name="Yates 13"/> The [[Envelope (mathematics)|envelope]] of the [[Conic section#Eccentricity, focus and directrix|directrix]] of the parabola is also a catenary.<ref>Yates p. 80</ref> The [[involute]] from the vertex, that is the roulette traced by a point starting at the vertex when a line is rolled on a catenary, is the [[tractrix]].<ref name="Yates 13"/>

Another roulette, formed by rolling a line on a catenary, is another line. This implies that [[square wheel]]s can roll perfectly smoothly on a road made of a series of bumps in the shape of an inverted catenary curve. The wheels can be any [[regular polygon]] except a triangle, but the catenary must have parameters corresponding to the shape and dimensions of the wheels.<ref>{{cite journal |last1=Hall |first1=Leon |last2=Wagon |first2=Stan |author2-link=Stan Wagon|year=1992 |title=Roads and Wheels |journal=Mathematics Magazine |volume=65 |issue=5 |pages=283–301 |jstor=2691240 |doi=10.2307/2691240}}
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